Metrics for sintan (problem 3.4.5)

analyze498.0ms (2.6%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.9%	50.1%	0%	0%	0%	0
0%	0%	49.9%	50.1%	0%	0%	0%	1
0%	0%	49.9%	50.1%	0%	0%	0%	2
0%	0%	49.9%	50.1%	0%	0%	0%	3
0%	0%	49.9%	50.1%	0%	0%	0%	4
0%	0%	49.9%	50.1%	0%	0%	0%	5
0%	0%	49.9%	50.1%	0%	0%	0%	6
0%	0%	49.9%	50.1%	0%	0%	0%	7
0%	0%	49.9%	50.1%	0%	0%	0%	8
0%	0%	49.9%	50.1%	0%	0%	0%	9
0%	0%	49.9%	50.1%	0%	0%	0%	10
0%	0%	49.9%	50.1%	0%	0%	0%	11
0%	0%	49.9%	50.1%	0%	0%	0%	12

Compiler

Compiled 17 to 11 computations (35.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 304.0ms

...c/correct-round.rkt:119:19: 117.0ms (38.4% of total)

ival-sub: 61.0ms (20% of total)

ival-<=: 40.0ms (13.1% of total)

ival-sin: 35.0ms (11.5% of total)

ival-tan: 26.0ms (8.5% of total)

ival-div: 20.0ms (6.6% of total)

ival-and: 5.0ms (1.6% of total)

backward-pass: 1.0ms (0.3% of total)

sample9.6s (49.3%)

Results

6.2s	4178×	2	valid
1.7s	1280×	3	valid
769.0ms	2728×	1	valid
10.0ms	70×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 8.2s

ival-tan: 4.6s (55.8% of total)

ival-sin: 2.4s (28.9% of total)

ival-sub: 378.0ms (4.6% of total)

backward-pass: 330.0ms (4% of total)

...c/correct-round.rkt:119:19: 328.0ms (4% of total)

ival-div: 115.0ms (1.4% of total)

ival-<=: 92.0ms (1.1% of total)

ival-and: 11.0ms (0.1% of total)

Bogosity

preprocess122.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

1280×	`sum5-define`
800×	`sum4-define`
676×	`fnmadd-define`
610×	`fnmadd-define`
594×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	32
1	37	30
2	90	27
3	273	27
4	724	27
5	1555	27
6	2749	27
7	2787	27
8	3156	27
9	3172	27
0	6	9
1	13	9
2	23	9
3	42	9
4	81	9
5	190	9
6	513	9
7	1101	9
8	2365	9
9	2557	9
10	2576	9
11	2584	9
0	2584	9

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))

Outputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Call 2

Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps))))
(neg (/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps)))))

Outputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps))))
(/ (- eps (sin eps)) (- eps (tan eps)))
(neg (/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps)))))
(/ (- eps (sin eps)) (- (tan eps) eps))

Symmetry

(abs eps)

explain713.0ms (3.7%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
186	-	3	(3.35768854780381e-105)	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`
73	-	0	-	`(-.f64 eps (sin.f64 eps))`
73	-	0	-	`(-.f64 eps (tan.f64 eps))`
0	-	0	-	`(sin.f64 eps)`
0	-	0	-	`eps`
0	-	0	-	`(tan.f64 eps)`

Results

530.0ms	304×	2	valid
76.0ms	64×	3	valid
69.0ms	140×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 58 to 20 computations (65.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 591.0ms

ival-tan: 366.0ms (61.9% of total)

ival-sin: 181.0ms (30.6% of total)

backward-pass: 19.0ms (3.2% of total)

ival-sub: 17.0ms (2.9% of total)

ival-div: 8.0ms (1.4% of total)

const: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 10 to 6 computations (40% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	1.0%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(-.f64 eps (tan.f64 eps))
✓	cost-diff	(sin.f64 eps)
✓	cost-diff	(-.f64 eps (sin.f64 eps))
✓	cost-diff	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Rules

676×	`fnmadd-define`
450×	`fmsub-define`
440×	`fnmsub-define`
394×	`fmm-def`
368×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
1	13	22
2	23	22
3	42	22
4	81	22
5	190	22
6	513	22
7	1101	22
8	2365	22
9	2557	22
10	2576	22
11	2584	22
0	2584	22

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(- eps (sin eps))
eps
(sin eps)
(- eps (tan eps))
(tan eps)

Outputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(- eps (sin eps))
(-.f64 eps (sin.f64 eps))
eps
(sin eps)
(sin.f64 eps)
(- eps (tan eps))
(-.f64 eps (tan.f64 eps))
(tan eps)
(tan.f64 eps)

localize328.0ms (1.7%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	74.9%	(-.f64 eps (tan.f64 eps))
✓	accuracy	74.9%	(-.f64 eps (sin.f64 eps))
✓	accuracy	28.4%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

216.0ms	152×	2	valid
77.0ms	32×	3	valid
23.0ms	70×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 24 to 7 computations (70.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 249.0ms

ival-tan: 147.0ms (59.1% of total)

ival-sin: 70.0ms (28.1% of total)

ival-sub: 20.0ms (8% of total)

backward-pass: 9.0ms (3.6% of total)

ival-div: 4.0ms (1.6% of total)

const: 0.0ms (0% of total)

series7.0ms (0%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/ (- eps (sin eps)) (- eps (tan eps)))>
#<alt (- eps (sin eps))>
#<alt (sin eps)>
#<alt (- eps (tan eps))>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))>
#<alt (* 1/6 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (* -1/3 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	-inf	(- eps (sin eps))
1.0ms	eps	@	inf	(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms	eps	@	-inf	(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms	eps	@	0	(/ (- eps (sin eps)) (- eps (tan eps)))
0.0ms	eps	@	inf	(- eps (tan eps))

rewrite353.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3748×	`-lowering-.f32`
3748×	`-lowering-.f64`
3480×	`/-lowering-/.f32`
3480×	`/-lowering-/.f64`
1496×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
1	46	19
2	422	19
3	6351	19
0	8332	19

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 373

Calls

Call 1

Inputs
(/ (- eps (sin eps)) (- eps (tan eps)))
(- eps (sin eps))
(sin eps)
(- eps (tan eps))

Outputs
(+.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps))) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (sin.f64 eps) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))))
(+.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps))) (fma.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))))) (/.f64 (sin.f64 eps) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))))
(+.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps))) (fma.f64 (-.f64 #s(literal 0 binary64) (+.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps))))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (sin.f64 eps))))
(+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (sin.f64 eps))) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 eps eps)) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 eps eps)))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (+.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 eps (tan.f64 eps))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) eps) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (tan.f64 eps)))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (tan.f64 eps)) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) eps))
(+.f64 (.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 1 binary64)) (.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) #s(literal 1 binary64)))
(+.f64 (.f64 (.f64 eps eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 eps eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 (+.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 eps (tan.f64 eps)) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 eps (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (.f64 (tan.f64 eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(+.f64 (.f64 (tan.f64 eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (.f64 eps (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 eps (tan.f64 eps)) (-.f64 eps (sin.f64 eps)))) #s(literal -1 binary64)))
(-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))) (-.f64 eps (tan.f64 eps))) (/.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 (/.f64 (.f64 eps eps) (+.f64 eps (sin.f64 eps))) (-.f64 eps (tan.f64 eps))) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal 2 binary64))))) (+.f64 eps (sin.f64 eps))) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 (tan.f64 eps) eps)) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))))
(-.f64 (/.f64 (.f64 eps eps) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 eps #s(literal 2 binary64))))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))))
(-.f64 (/.f64 (.f64 eps (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) (/.f64 (.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))))
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(.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (-.f64 eps (tan.f64 eps)))
(.f64 (/.f64 (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (pow.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) #s(literal 3 binary64)))) (+.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (-.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (.f64 eps eps)))))
(.f64 (/.f64 (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (pow.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))
(.f64 (/.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (+.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (+.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) eps))))

simplify240.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

4708×	`-lowering-.f32`
4708×	`-lowering-.f64`
1320×	`+-lowering-+.f64`
1320×	`+-lowering-+.f32`
1274×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	547
1	457	472
2	1539	434
3	6918	432
0	8079	432

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
1
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* -1/3 (pow eps 3))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
1
#s(literal 1 binary64)
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(+.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)) (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) eps) (/.f64 #s(literal -1 binary64) eps))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
(+.f64 (.f64 (sin.f64 eps) (+.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (.f64 (sin.f64 eps) (/.f64 (.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 eps eps))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) eps) (/.f64 #s(literal -1 binary64) eps)))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sin.f64 eps) (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (.f64 (+.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) eps)) #s(literal -1 binary64)))) eps))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))))) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (.f64 eps (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) eps) (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))))) eps))
(* 1/6 (pow eps 3))
(.f64 (.f64 eps (*.f64 eps eps)) #s(literal 1/6 binary64))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(.f64 eps (.f64 eps (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 (*.f64 eps eps) #s(literal -1/120 binary64))))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (*.f64 eps eps) #s(literal 1/5040 binary64))))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 eps eps) #s(literal -1/362880 binary64))))))))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 eps eps) #s(literal -1/5040 binary64))))))))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(* -1/3 (pow eps 3))
(.f64 eps (.f64 (*.f64 eps eps) #s(literal -1/3 binary64)))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/3 binary64) (.f64 (*.f64 eps eps) #s(literal -2/15 binary64)))))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal -1/3 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -2/15 binary64) (.f64 eps (*.f64 eps #s(literal -17/315 binary64)))))))))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/3 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -2/15 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -17/315 binary64) (.f64 (*.f64 eps eps) #s(literal -62/2835 binary64))))))))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))

eval46.0ms (0.2%)

Compiler: Compiled 12278 to 1228 computations (90% saved)

prune93.0ms (0.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	413	8	421
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	413	9	422

Accuracy

100.0%

Counts

422 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	1.6%	(/.f64 (fma.f64 (/.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (pow.f64 (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))))) (-.f64 eps (tan.f64 eps)))
✓	1.0%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
	1.3%	(/.f64 (.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 eps eps) #s(literal -1/362880 binary64)))))))))) (-.f64 eps (tan.f64 eps)))
▶	1.0%	(/.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))) (-.f64 eps (tan.f64 eps)))
	1.3%	(-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))
▶	99.9%	(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
▶	99.8%	(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
	99.6%	(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
▶	99.3%	#s(literal -1/2 binary64)

Compiler

Compiled 334 to 178 computations (46.7% saved)

simplify183.0ms (0.9%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 eps (.f64 eps eps))
✓	cost-diff	0	(/.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (pow.f64 (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))) #s(literal 2 binary64))))
✓	cost-diff	26496	(fma.f64 (/.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (pow.f64 (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))))
✓	cost-diff	26496	(/.f64 (fma.f64 (/.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (pow.f64 (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))))) (-.f64 eps (tan.f64 eps)))
✓	cost-diff	0	(/.f64 (sin.f64 eps) eps)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))
✓	cost-diff	0	(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
✓	cost-diff	0	(/.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))) (-.f64 eps (tan.f64 eps)))
✓	cost-diff	0	(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
✓	cost-diff	0	(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
✓	cost-diff	0	(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
✓	cost-diff	0	(+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
✓	cost-diff	0	(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))

Rules

3074×	`-lowering-.f32`
3074×	`-lowering-.f64`
2168×	`fma-lowering-fma.f32`
2168×	`fma-lowering-fma.f64`
1708×	`fnmadd-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	377
1	135	351
2	418	348
3	1370	321
4	5946	321
0	8038	321

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* (* eps eps) (+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)
(* (* eps eps) (+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000))))))
(* eps eps)
eps
(+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000)))))
9/40
(* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000))))
(* eps (+ -27/2800 (* (* eps eps) 27/112000)))
(+ -27/2800 (* (* eps eps) 27/112000))
-27/2800
(* (* eps eps) 27/112000)
27/112000
-1/2
-1/2
(+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)
(* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))
eps
(* eps (+ 9/40 (* (* eps eps) -27/2800)))
(+ 9/40 (* (* eps eps) -27/2800))
9/40
(* (* eps eps) -27/2800)
(* eps eps)
-27/2800
-1/2
(/ (* eps (- 1 (/ (sin eps) eps))) (- eps (tan eps)))
(* eps (- 1 (/ (sin eps) eps)))
eps
(- 1 (/ (sin eps) eps))
1
(/ (sin eps) eps)
(sin eps)
(- eps (tan eps))
(tan eps)
(/ (+ (* (/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))) (- (* eps eps) (* (sin eps) (+ eps (sin eps))))) (neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps))))))) (- eps (tan eps)))
(+ (* (/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))) (- (* eps eps) (* (sin eps) (+ eps (sin eps))))) (neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps)))))))
(/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2)))
(* eps (* eps eps))
eps
(* eps eps)
(- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))
(* (* eps eps) (* eps eps))
(pow (* (sin eps) (+ eps (sin eps))) 2)
(* (sin eps) (+ eps (sin eps)))
(sin eps)
(+ eps (sin eps))
2
(- (* eps eps) (* (sin eps) (+ eps (sin eps))))
(neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps))))))
(/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps)))))
(pow (sin eps) 3)
3
(+ (* eps eps) (* (sin eps) (+ eps (sin eps))))
(- eps (tan eps))
(tan eps)

Outputs
(+ (* (* eps eps) (+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
(* (* eps eps) (+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
(* eps eps)
(*.f64 eps eps)
eps
(+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000)))))
(+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))
9/40
#s(literal 9/40 binary64)
(* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000))))
(.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))
(* eps (+ -27/2800 (* (* eps eps) 27/112000)))
(.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))
(+ -27/2800 (* (* eps eps) 27/112000))
(+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))
-27/2800
#s(literal -27/2800 binary64)
(* (* eps eps) 27/112000)
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
27/112000
#s(literal 27/112000 binary64)
-1/2
#s(literal -1/2 binary64)
-1/2
#s(literal -1/2 binary64)
(+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
(* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
eps
(* eps (+ 9/40 (* (* eps eps) -27/2800)))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(+ 9/40 (* (* eps eps) -27/2800))
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
9/40
#s(literal 9/40 binary64)
(* (* eps eps) -27/2800)
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* eps eps)
(*.f64 eps eps)
-27/2800
#s(literal -27/2800 binary64)
-1/2
#s(literal -1/2 binary64)
(/ (* eps (- 1 (/ (sin eps) eps))) (- eps (tan eps)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(* eps (- 1 (/ (sin eps) eps)))
(*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
eps
(- 1 (/ (sin eps) eps))
(-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))
1
#s(literal 1 binary64)
(/ (sin eps) eps)
(/.f64 (sin.f64 eps) eps)
(sin eps)
(sin.f64 eps)
(- eps (tan eps))
(-.f64 eps (tan.f64 eps))
(tan eps)
(tan.f64 eps)
(/ (+ (* (/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))) (- (* eps eps) (* (sin eps) (+ eps (sin eps))))) (neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps))))))) (- eps (tan eps)))
(/.f64 (-.f64 (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))) (-.f64 eps (tan.f64 eps)))
(+ (* (/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))) (- (* eps eps) (* (sin eps) (+ eps (sin eps))))) (neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps)))))))
(-.f64 (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))))
(/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2)))
(/.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (pow.f64 (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))) #s(literal 2 binary64))))
(* eps (* eps eps))
(.f64 eps (.f64 eps eps))
eps
(* eps eps)
(*.f64 eps eps)
(- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))
(-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (pow.f64 (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))) #s(literal 2 binary64)))
(* (* eps eps) (* eps eps))
(.f64 eps (.f64 eps (*.f64 eps eps)))
(pow (* (sin eps) (+ eps (sin eps))) 2)
(pow.f64 (*.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))) #s(literal 2 binary64))
(* (sin eps) (+ eps (sin eps)))
(*.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))
(sin eps)
(sin.f64 eps)
(+ eps (sin eps))
(+.f64 eps (sin.f64 eps))
2
#s(literal 2 binary64)
(- (* eps eps) (* (sin eps) (+ eps (sin eps))))
(-.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))
(neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps))))))
(/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (-.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal 0 binary64) (+.f64 eps (sin.f64 eps)))) (.f64 eps eps)))
(/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps)))))
(/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))
(pow (sin eps) 3)
(pow.f64 (sin.f64 eps) #s(literal 3 binary64))
3
#s(literal 3 binary64)
(+ (* eps eps) (* (sin eps) (+ eps (sin eps))))
(+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))
(- eps (tan eps))
(-.f64 eps (tan.f64 eps))
(tan eps)
(tan.f64 eps)

localize1.1s (5.7%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 (sin.f64 eps) #s(literal 3 binary64))
✓	accuracy	100.0%	(/.f64 (fma.f64 (/.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (pow.f64 (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))))) (-.f64 eps (tan.f64 eps)))
✓	accuracy	99.8%	(fma.f64 (/.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (pow.f64 (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))))
✓	accuracy	99.8%	(-.f64 eps (tan.f64 eps))
✓	accuracy	100.0%	(/.f64 (sin.f64 eps) eps)
✓	accuracy	100.0%	(/.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))) (-.f64 eps (tan.f64 eps)))
✓	accuracy	99.8%	(-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))
✓	accuracy	99.8%	(-.f64 eps (tan.f64 eps))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
✓	accuracy	100.0%	(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
✓	accuracy	100.0%	(.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))

Results

984.0ms	253×	5	exit
1.0ms	1×	1	valid
1.0ms	2×	0	valid

Compiler

Compiled 439 to 43 computations (90.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 733.0ms

ival-tan: 168.0ms (22.9% of total)

ival-sin: 161.0ms (22% of total)

backward-pass: 155.0ms (21.2% of total)

ival-mult: 70.0ms (9.6% of total)

ival-pow: 42.0ms (5.7% of total)

ival-div: 31.0ms (4.2% of total)

...c/correct-round.rkt:119:19: 27.0ms (3.7% of total)

ival-add: 26.0ms (3.5% of total)

compiled-spec: 25.0ms (3.4% of total)

ival-sub: 21.0ms (2.9% of total)

ival-neg: 5.0ms (0.7% of total)

const: 2.0ms (0.3% of total)

series31.0ms (0.2%)

Counts

21 → 252

Calls

Call 1

Inputs
#<alt (+ (* (* eps eps) (+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)>
#<alt (* (* eps eps) (+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000))))))>
#<alt (* eps eps)>
#<alt (+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000)))))>
#<alt (+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)>
#<alt (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))>
#<alt (* eps (+ 9/40 (* (* eps eps) -27/2800)))>
#<alt (+ 9/40 (* (* eps eps) -27/2800))>
#<alt (/ (* eps (- 1 (/ (sin eps) eps))) (- eps (tan eps)))>
#<alt (* eps (- 1 (/ (sin eps) eps)))>
#<alt (- 1 (/ (sin eps) eps))>
#<alt (/ (sin eps) eps)>
#<alt (/ (+ (* (/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))) (- (* eps eps) (* (sin eps) (+ eps (sin eps))))) (neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps))))))) (- eps (tan eps)))>
#<alt (+ (* (/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))) (- (* eps eps) (* (sin eps) (+ eps (sin eps))))) (neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps)))))))>
#<alt (/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2)))>
#<alt (* eps (* eps eps))>
#<alt (+ -27/2800 (* (* eps eps) 27/112000))>
#<alt (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000))))>
#<alt (* (* eps eps) -27/2800)>
#<alt (- eps (tan eps))>
#<alt (pow (sin eps) 3)>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))>
#<alt (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt 9/40>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))>
#<alt (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))>
#<alt (* 27/112000 (pow eps 4))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 4))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* 9/40 eps)>
#<alt (* eps (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* eps (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* eps (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* -27/2800 (pow eps 3))>
#<alt (* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))>
#<alt 9/40>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))>
#<alt (* 1/6 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (sin eps) eps)))>
#<alt (+ 1 (* -1 (/ (sin eps) eps)))>
#<alt (+ 1 (* -1 (/ (sin eps) eps)))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (sin eps) eps)))>
#<alt (+ 1 (* -1 (/ (sin eps) eps)))>
#<alt (+ 1 (* -1 (/ (sin eps) eps)))>
#<alt 1>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (* -1 (/ (+ (* -1 (pow (sin eps) 2)) (pow (sin eps) 2)) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (+ (* -1 (/ (+ (* -1 (pow (sin eps) 2)) (pow (sin eps) 2)) (pow eps 2))) (* -1 (/ (pow (sin eps) 3) (pow eps 3)))))) (+ (* -2 (/ (pow (sin eps) 3) (pow eps 3))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (+ (* -1 (pow (sin eps) 2)) (pow (sin eps) 2))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (cos eps))))) (* (pow eps 3) (cos eps)))) (/ (pow (sin eps) 3) (pow eps 3)))))))>
#<alt 1>
#<alt (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* eps (cos eps))))) eps)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* -1 (/ (- (+ (* -1 (/ (pow (sin eps) 3) eps)) (+ (* 2 (/ (pow (sin eps) 3) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (cos eps)))) (+ (* -1 (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* eps (pow (cos eps) 2)))) (/ (pow (sin eps) 3) eps))) eps))) eps)))>
#<alt (* 1/6 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (- (+ 1 (* -1 (/ (+ (* -1 (pow (sin eps) 2)) (pow (sin eps) 2)) (pow eps 2)))) (/ (sin eps) eps)))>
#<alt (* eps (- (+ 1 (* -1 (/ (pow (sin eps) 3) (pow eps 3)))) (+ (* -2 (/ (pow (sin eps) 3) (pow eps 3))) (+ (* -1 (/ (pow (sin eps) 2) (pow eps 2))) (+ (/ (sin eps) eps) (+ (/ (pow (sin eps) 2) (pow eps 2)) (/ (pow (sin eps) 3) (pow eps 3))))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ (* -1 (sin eps)) (+ (* -1 (/ (pow (sin eps) 3) (pow eps 2))) (* 2 (/ (pow (sin eps) 3) (pow eps 2))))) (/ (pow (sin eps) 3) (pow eps 2))) eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ (* -1 (sin eps)) (+ (* -1 (/ (+ (* -2 (pow (sin eps) 4)) (* 2 (pow (sin eps) 4))) (pow eps 3))) (+ (* -1 (/ (pow (sin eps) 3) (pow eps 2))) (* 2 (/ (pow (sin eps) 3) (pow eps 2)))))) (/ (pow (sin eps) 3) (pow eps 2))) eps)) 1)))>
#<alt (/ -1/3 eps)>
#<alt (/ (- (* -2/9 (pow eps 2)) 1/3) eps)>
#<alt (/ (- (* (pow eps 2) (- (* -157/1620 (pow eps 2)) 2/9)) 1/3) eps)>
#<alt (/ (- (* (pow eps 2) (- (* (pow eps 2) (- (* -2573/68040 (pow eps 2)) 157/1620)) 2/9)) 1/3) eps)>
#<alt (/ 1 eps)>
#<alt (/ (+ 1 (/ (pow (sin eps) 2) (pow eps 2))) eps)>
#<alt (/ (- (+ 1 (* 2 (/ (pow (sin eps) 3) (pow eps 3)))) (* -1 (/ (pow (sin eps) 2) (pow eps 2)))) eps)>
#<alt (/ (- (+ 1 (* 2 (/ (pow (sin eps) 4) (pow eps 4)))) (+ (* -2 (/ (pow (sin eps) 3) (pow eps 3))) (* -1 (/ (pow (sin eps) 2) (pow eps 2))))) eps)>
#<alt (/ 1 eps)>
#<alt (* -1 (/ (- (* -1 (/ (pow (sin eps) 2) (pow eps 2))) 1) eps))>
#<alt (* -1 (/ (- (* -2 (/ (pow (sin eps) 3) (pow eps 3))) (+ 1 (/ (pow (sin eps) 2) (pow eps 2)))) eps))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 2 (/ (pow (sin eps) 4) eps)) (* -2 (pow (sin eps) 3))) (pow eps 3))) (+ 1 (/ (pow (sin eps) 2) (pow eps 2)))) eps))>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt -27/2800>
#<alt (- (* 27/112000 (pow eps 2)) 27/2800)>
#<alt (- (* 27/112000 (pow eps 2)) 27/2800)>
#<alt (- (* 27/112000 (pow eps 2)) 27/2800)>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* 27/112000 (pow eps 4))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 4))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -1/3 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (pow eps 3)>
#<alt (* (pow eps 3) (+ 1 (* -1/2 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1 (* (pow eps 2) (- (* 13/120 (pow eps 2)) 1/2))))>
#<alt (* (pow eps 3) (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 13/120 (* -41/3024 (pow eps 2)))) 1/2))))>
#<alt (pow (sin eps) 3)>
#<alt (pow (sin eps) 3)>
#<alt (pow (sin eps) 3)>
#<alt (pow (sin eps) 3)>
#<alt (pow (sin eps) 3)>
#<alt (pow (sin eps) 3)>
#<alt (pow (sin eps) 3)>
#<alt (pow (sin eps) 3)>

Calls

63 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	0	(+ (* (* eps eps) (+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)
2.0ms	eps	@	-inf	(+ (* (/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))) (- (* eps eps) (* (sin eps) (+ eps (sin eps))))) (neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps)))))))
2.0ms	eps	@	-inf	(/ (+ (* (/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))) (- (* eps eps) (* (sin eps) (+ eps (sin eps))))) (neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps))))))) (- eps (tan eps)))
2.0ms	eps	@	inf	(/ (+ (* (/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))) (- (* eps eps) (* (sin eps) (+ eps (sin eps))))) (neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps))))))) (- eps (tan eps)))
1.0ms	eps	@	0	(/ (+ (* (/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))) (- (* eps eps) (* (sin eps) (+ eps (sin eps))))) (neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps))))))) (- eps (tan eps)))

rewrite322.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3100×	`-lowering-.f32`
3100×	`-lowering-.f64`
2510×	`fma-lowering-fma.f32`
2510×	`fma-lowering-fma.f64`
2018×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	247
1	320	203
2	3005	200
0	8356	200

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 427

Calls

Call 1

Inputs
(+ (* (* eps eps) (+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)
(* (* eps eps) (+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000))))))
(* eps eps)
(+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000)))))
(+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)
(* eps (* eps (+ 9/40 (* (* eps eps) -27/2800))))
(* eps (+ 9/40 (* (* eps eps) -27/2800)))
(+ 9/40 (* (* eps eps) -27/2800))
(/ (* eps (- 1 (/ (sin eps) eps))) (- eps (tan eps)))
(* eps (- 1 (/ (sin eps) eps)))
(- 1 (/ (sin eps) eps))
(/ (sin eps) eps)
(/ (+ (* (/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))) (- (* eps eps) (* (sin eps) (+ eps (sin eps))))) (neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps))))))) (- eps (tan eps)))
(+ (* (/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2))) (- (* eps eps) (* (sin eps) (+ eps (sin eps))))) (neg (/ (pow (sin eps) 3) (+ (* eps eps) (* (sin eps) (+ eps (sin eps)))))))
(/ (* eps (* eps eps)) (- (* (* eps eps) (* eps eps)) (pow (* (sin eps) (+ eps (sin eps))) 2)))
(* eps (* eps eps))
(+ -27/2800 (* (* eps eps) 27/112000))
(* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000))))
(* (* eps eps) -27/2800)
(- eps (tan eps))
(pow (sin eps) 3)

Outputs
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) #s(literal -1/2 binary64)))
(+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 9/40 binary64))) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal 1/2 binary64))))
(fma.f64 eps (.f64 eps #s(literal 9/40 binary64)) (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))) #s(literal -1/2 binary64)))
(fma.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) #s(literal 9/40 binary64) (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))) #s(literal -1/2 binary64))
(fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))) #s(literal -1/2 binary64)))
(fma.f64 (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps #s(literal 9/40 binary64)) eps (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))) eps #s(literal -1/2 binary64))
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(fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) (.f64 eps (.f64 eps (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))
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(fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) (.f64 (.f64 eps (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))) eps))
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(fma.f64 (.f64 eps eps) #s(literal -27/2800 binary64) (.f64 eps (.f64 eps (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))
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(.f64 (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) eps)
(.f64 eps (.f64 eps #s(literal -27/2800 binary64)))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
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(-.f64 (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (+.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))))))
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(pow.f64 (/.f64 (+.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) #s(literal -1 binary64))
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(exp.f64 (.f64 (.f64 (log.f64 (sin.f64 eps)) #s(literal 3/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 (sin.f64 eps)) #s(literal 3/2 binary64)) (.f64 (log.f64 (sin.f64 eps)) #s(literal 3/2 binary64))))
(pow.f64 (sin.f64 eps) #s(literal 3 binary64))
(pow.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) #s(literal 3/2 binary64))
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(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 (sin.f64 eps)))
(.f64 (sin.f64 eps) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))))
(.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) eps)))) (sin.f64 eps))
(*.f64 (pow.f64 (sin.f64 eps) #s(literal 3/2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 3/2 binary64)))

simplify265.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

2742×	`-lowering-.f32`
2742×	`-lowering-.f64`
2618×	`+-lowering-+.f64`
2618×	`+-lowering-+.f32`
1400×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	340	2635
1	1114	2254
2	4033	2191
0	9429	2191

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
9/40
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))
(+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))
(* 27/112000 (pow eps 4))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 4))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* 9/40 eps)
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(* -27/2800 (pow eps 3))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 3) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 3))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 27/2800 (* 9/40 (/ 1 (pow eps 2))))))
9/40
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
1
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* 1/6 (pow eps 2))
(* (pow eps 2) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
1
(+ 1 (* -1 (/ (sin eps) eps)))
(+ 1 (* -1 (/ (sin eps) eps)))
(+ 1 (* -1 (/ (sin eps) eps)))
1
(+ 1 (* -1 (/ (sin eps) eps)))
(+ 1 (* -1 (/ (sin eps) eps)))
(+ 1 (* -1 (/ (sin eps) eps)))
1
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))
(/ (sin eps) eps)
(/ (sin eps) eps)
(/ (sin eps) eps)
(/ (sin eps) eps)
(/ (sin eps) eps)
(/ (sin eps) eps)
(/ (sin eps) eps)
(/ (sin eps) eps)
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (* -1 (/ (+ (* -1 (pow (sin eps) 2)) (pow (sin eps) 2)) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (+ (* -1 (/ (+ (* -1 (pow (sin eps) 2)) (pow (sin eps) 2)) (pow eps 2))) (* -1 (/ (pow (sin eps) 3) (pow eps 3)))))) (+ (* -2 (/ (pow (sin eps) 3) (pow eps 3))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (+ (* -1 (pow (sin eps) 2)) (pow (sin eps) 2))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (cos eps))))) (* (pow eps 3) (cos eps)))) (/ (pow (sin eps) 3) (pow eps 3)))))))
1
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* eps (cos eps))))) eps)))
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* -1 (/ (- (+ (* -1 (/ (pow (sin eps) 3) eps)) (+ (* 2 (/ (pow (sin eps) 3) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (cos eps)))) (+ (* -1 (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* eps (pow (cos eps) 2)))) (/ (pow (sin eps) 3) eps))) eps))) eps)))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (- (+ 1 (* -1 (/ (+ (* -1 (pow (sin eps) 2)) (pow (sin eps) 2)) (pow eps 2)))) (/ (sin eps) eps)))
(* eps (- (+ 1 (* -1 (/ (pow (sin eps) 3) (pow eps 3)))) (+ (* -2 (/ (pow (sin eps) 3) (pow eps 3))) (+ (* -1 (/ (pow (sin eps) 2) (pow eps 2))) (+ (/ (sin eps) eps) (+ (/ (pow (sin eps) 2) (pow eps 2)) (/ (pow (sin eps) 3) (pow eps 3))))))))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ (* -1 (sin eps)) (+ (* -1 (/ (pow (sin eps) 3) (pow eps 2))) (* 2 (/ (pow (sin eps) 3) (pow eps 2))))) (/ (pow (sin eps) 3) (pow eps 2))) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ (* -1 (sin eps)) (+ (* -1 (/ (+ (* -2 (pow (sin eps) 4)) (* 2 (pow (sin eps) 4))) (pow eps 3))) (+ (* -1 (/ (pow (sin eps) 3) (pow eps 2))) (* 2 (/ (pow (sin eps) 3) (pow eps 2)))))) (/ (pow (sin eps) 3) (pow eps 2))) eps)) 1)))
(/ -1/3 eps)
(/ (- (* -2/9 (pow eps 2)) 1/3) eps)
(/ (- (* (pow eps 2) (- (* -157/1620 (pow eps 2)) 2/9)) 1/3) eps)
(/ (- (* (pow eps 2) (- (* (pow eps 2) (- (* -2573/68040 (pow eps 2)) 157/1620)) 2/9)) 1/3) eps)
(/ 1 eps)
(/ (+ 1 (/ (pow (sin eps) 2) (pow eps 2))) eps)
(/ (- (+ 1 (* 2 (/ (pow (sin eps) 3) (pow eps 3)))) (* -1 (/ (pow (sin eps) 2) (pow eps 2)))) eps)
(/ (- (+ 1 (* 2 (/ (pow (sin eps) 4) (pow eps 4)))) (+ (* -2 (/ (pow (sin eps) 3) (pow eps 3))) (* -1 (/ (pow (sin eps) 2) (pow eps 2))))) eps)
(/ 1 eps)
(* -1 (/ (- (* -1 (/ (pow (sin eps) 2) (pow eps 2))) 1) eps))
(* -1 (/ (- (* -2 (/ (pow (sin eps) 3) (pow eps 3))) (+ 1 (/ (pow (sin eps) 2) (pow eps 2)))) eps))
(* -1 (/ (- (* -1 (/ (- (* 2 (/ (pow (sin eps) 4) eps)) (* -2 (pow (sin eps) 3))) (pow eps 3))) (+ 1 (/ (pow (sin eps) 2) (pow eps 2)))) eps))
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
-27/2800
(- (* 27/112000 (pow eps 2)) 27/2800)
(- (* 27/112000 (pow eps 2)) 27/2800)
(- (* 27/112000 (pow eps 2)) 27/2800)
(* 27/112000 (pow eps 2))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 2))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))
(* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))
(* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))
(* 27/112000 (pow eps 4))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 4))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -1/3 (pow eps 3))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(pow eps 3)
(* (pow eps 3) (+ 1 (* -1/2 (pow eps 2))))
(* (pow eps 3) (+ 1 (* (pow eps 2) (- (* 13/120 (pow eps 2)) 1/2))))
(* (pow eps 3) (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 13/120 (* -41/3024 (pow eps 2)))) 1/2))))
(pow (sin eps) 3)
(pow (sin eps) 3)
(pow (sin eps) 3)
(pow (sin eps) 3)
(pow (sin eps) 3)
(pow (sin eps) 3)
(pow (sin eps) 3)
(pow (sin eps) 3)

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 #s(literal 27/112000 binary64) (-.f64 (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 6 binary64)))))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 #s(literal 27/112000 binary64) (-.f64 (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)) (/.f64 #s(literal 1/2 binary64) (pow.f64 eps #s(literal 6 binary64)))))))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
(* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
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(.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -2/15 binary64) (.f64 (*.f64 eps eps) #s(literal -17/315 binary64)))))))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -2/15 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -17/315 binary64) (.f64 (*.f64 eps eps) #s(literal -62/2835 binary64)))))))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 (+.f64 #s(literal -1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 (+.f64 #s(literal -1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 (+.f64 #s(literal -1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))) (-.f64 #s(literal 0 binary64) eps))
(pow eps 3)
(.f64 eps (.f64 eps eps))
(* (pow eps 3) (+ 1 (* -1/2 (pow eps 2))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(* (pow eps 3) (+ 1 (* (pow eps 2) (- (* 13/120 (pow eps 2)) 1/2))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 13/120 binary64))))))
(* (pow eps 3) (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 13/120 (* -41/3024 (pow eps 2)))) 1/2))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 13/120 binary64) (.f64 (*.f64 eps eps) #s(literal -41/3024 binary64)))))))))
(pow (sin eps) 3)
(pow.f64 (sin.f64 eps) #s(literal 3 binary64))
(pow (sin eps) 3)
(pow.f64 (sin.f64 eps) #s(literal 3 binary64))
(pow (sin eps) 3)
(pow.f64 (sin.f64 eps) #s(literal 3 binary64))
(pow (sin eps) 3)
(pow.f64 (sin.f64 eps) #s(literal 3 binary64))
(pow (sin eps) 3)
(pow.f64 (sin.f64 eps) #s(literal 3 binary64))
(pow (sin eps) 3)
(pow.f64 (sin.f64 eps) #s(literal 3 binary64))
(pow (sin eps) 3)
(pow.f64 (sin.f64 eps) #s(literal 3 binary64))
(pow (sin eps) 3)
(pow.f64 (sin.f64 eps) #s(literal 3 binary64))

eval111.0ms (0.6%)

Compiler: Compiled 30851 to 2131 computations (93.1% saved)

prune90.0ms (0.5%)

Pruning

12 alts after pruning (7 fresh and 5 done)

	Pruned	Kept	Total
New	836	6	842
Fresh	2	1	3
Picked	1	4	5
Done	0	1	1
Total	839	12	851

Accuracy

100.0%

Counts

851 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	1.5%	(/.f64 (fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 eps) #s(literal 3 binary64))) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (pow.f64 (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))) (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (*.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))))) (-.f64 eps (tan.f64 eps)))
✓	1.6%	(/.f64 (fma.f64 (/.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (pow.f64 (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))))) (-.f64 eps (tan.f64 eps)))
✓	1.0%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
▶	99.9%	(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))) (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))))))
▶	1.3%	(/.f64 (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 eps (*.f64 eps #s(literal -1/362880 binary64)))))))))) (-.f64 eps (tan.f64 eps)))
	1.3%	(-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))
✓	99.9%	(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
▶	99.9%	(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) #s(literal -1/2 binary64)))
▶	99.6%	(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	99.8%	(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
▶	1.0%	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)) (-.f64 eps (tan.f64 eps))) eps)
✓	99.3%	#s(literal -1/2 binary64)

Compiler

Compiled 526 to 238 computations (54.8% saved)

simplify219.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (sin.f64 eps) eps)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)) (-.f64 eps (tan.f64 eps)))
✓	cost-diff	0	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)) (-.f64 eps (tan.f64 eps))) eps)
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 eps (.f64 eps #s(literal -1/362880 binary64)))))))))
✓	cost-diff	0	(.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 eps (*.f64 eps #s(literal -1/362880 binary64))))))))))
✓	cost-diff	0	(/.f64 (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 eps (*.f64 eps #s(literal -1/362880 binary64)))))))))) (-.f64 eps (tan.f64 eps)))
✓	cost-diff	0	(+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(.f64 (.f64 eps eps) #s(literal 9/40 binary64))
✓	cost-diff	256	(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) #s(literal -1/2 binary64)))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(.f64 (.f64 eps eps) #s(literal 9/40 binary64))
✓	cost-diff	0	(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))
✓	cost-diff	0	(.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))))
✓	cost-diff	0	(-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))))))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))) (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))))))

Rules

3000×	`-lowering-.f32`
3000×	`-lowering-.f64`
2694×	`+-lowering-+.f64`
2694×	`+-lowering-+.f32`
1464×	`fnmsub-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	394
1	159	353
2	676	351
3	2841	351
4	6811	351
0	8190	351

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (- 1/4 (* (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))) (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))) (- -1/2 (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))))
(- 1/4 (* (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))) (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))))
1/4
(* (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))) (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))
(* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))
(* eps eps)
eps
(+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))
9/40
(* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))
(+ -27/2800 (* (* eps eps) 27/112000))
-27/2800
(* (* eps eps) 27/112000)
27/112000
(- -1/2 (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))
-1/2
(+ (* (* eps eps) 9/40) -1/2)
(* (* eps eps) 9/40)
(* eps eps)
eps
9/40
-1/2
(+ (* (* eps eps) 9/40) (+ (* (* (* eps eps) (* eps eps)) (+ -27/2800 (* (* eps eps) 27/112000))) -1/2))
(* (* eps eps) 9/40)
(* eps eps)
eps
9/40
(+ (* (* (* eps eps) (* eps eps)) (+ -27/2800 (* (* eps eps) 27/112000))) -1/2)
(* (* (* eps eps) (* eps eps)) (+ -27/2800 (* (* eps eps) 27/112000)))
(* (* eps eps) (* eps eps))
(+ -27/2800 (* (* eps eps) 27/112000))
-27/2800
(* (* eps eps) 27/112000)
27/112000
-1/2
(/ (* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))))))) (- eps (tan eps)))
(* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880)))))))))
eps
(* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))))))
(* eps eps)
(+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880)))))))
1/6
(* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))))
(+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880)))))
-1/120
(* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))
(+ 1/5040 (* eps (* eps -1/362880)))
1/5040
(* eps (* eps -1/362880))
(* eps -1/362880)
-1/362880
(- eps (tan eps))
(tan eps)
(* (/ (- 1 (/ (sin eps) eps)) (- eps (tan eps))) eps)
(/ (- 1 (/ (sin eps) eps)) (- eps (tan eps)))
(- 1 (/ (sin eps) eps))
1
(/ (sin eps) eps)
(sin eps)
eps
(- eps (tan eps))
(tan eps)

Outputs
(/ (- 1/4 (* (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))) (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))) (- -1/2 (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))) (.f64 (-.f64 #s(literal -9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))) (.f64 eps (.f64 eps eps)))))) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal -9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))))))
(- 1/4 (* (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))) (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))))
(+.f64 #s(literal 1/4 binary64) (.f64 eps (.f64 (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))) (.f64 (-.f64 #s(literal -9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))) (.f64 eps (*.f64 eps eps))))))
1/4
#s(literal 1/4 binary64)
(* (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))) (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))
(.f64 (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) (.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))))))
(* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
(* eps eps)
(*.f64 eps eps)
eps
(+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))
9/40
#s(literal 9/40 binary64)
(* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))
(.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))
(+ -27/2800 (* (* eps eps) 27/112000))
(+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))
-27/2800
#s(literal -27/2800 binary64)
(* (* eps eps) 27/112000)
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
27/112000
#s(literal 27/112000 binary64)
(- -1/2 (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (-.f64 #s(literal -9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
-1/2
#s(literal -1/2 binary64)
(+ (* (* eps eps) 9/40) -1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 9/40 binary64)))
(* (* eps eps) 9/40)
(.f64 (.f64 eps eps) #s(literal 9/40 binary64))
(* eps eps)
(*.f64 eps eps)
eps
9/40
#s(literal 9/40 binary64)
-1/2
#s(literal -1/2 binary64)
(+ (* (* eps eps) 9/40) (+ (* (* (* eps eps) (* eps eps)) (+ -27/2800 (* (* eps eps) 27/112000))) -1/2))
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
(* (* eps eps) 9/40)
(.f64 (.f64 eps eps) #s(literal 9/40 binary64))
(* eps eps)
(*.f64 eps eps)
eps
9/40
#s(literal 9/40 binary64)
(+ (* (* (* eps eps) (* eps eps)) (+ -27/2800 (* (* eps eps) 27/112000))) -1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps (.f64 eps eps)))))
(* (* (* eps eps) (* eps eps)) (+ -27/2800 (* (* eps eps) 27/112000)))
(.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps (.f64 eps eps))))
(* (* eps eps) (* eps eps))
(.f64 eps (.f64 eps (*.f64 eps eps)))
(+ -27/2800 (* (* eps eps) 27/112000))
(+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))
-27/2800
#s(literal -27/2800 binary64)
(* (* eps eps) 27/112000)
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
27/112000
#s(literal 27/112000 binary64)
-1/2
#s(literal -1/2 binary64)
(/ (* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))))))) (- eps (tan eps)))
(.f64 (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))))) (/.f64 (.f64 eps (*.f64 eps eps)) (-.f64 eps (tan.f64 eps))))
(* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880)))))))))
(.f64 (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))))) (.f64 eps (*.f64 eps eps)))
eps
(* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))))))
(* eps eps)
(*.f64 eps eps)
(+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880)))))))
(+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))))))
1/6
#s(literal 1/6 binary64)
(* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))))
(+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880)))))
(+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))))
-1/120
#s(literal -1/120 binary64)
(* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))
(+ 1/5040 (* eps (* eps -1/362880)))
(+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))
1/5040
#s(literal 1/5040 binary64)
(* eps (* eps -1/362880))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(* eps -1/362880)
(*.f64 eps #s(literal -1/362880 binary64))
-1/362880
#s(literal -1/362880 binary64)
(- eps (tan eps))
(-.f64 eps (tan.f64 eps))
(tan eps)
(tan.f64 eps)
(* (/ (- 1 (/ (sin eps) eps)) (- eps (tan eps))) eps)
(/.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))) (-.f64 eps (tan.f64 eps)))
(/ (- 1 (/ (sin eps) eps)) (- eps (tan eps)))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)) (-.f64 eps (tan.f64 eps)))
(- 1 (/ (sin eps) eps))
(-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))
1
#s(literal 1 binary64)
(/ (sin eps) eps)
(/.f64 (sin.f64 eps) eps)
(sin eps)
(sin.f64 eps)
eps
(- eps (tan eps))
(-.f64 eps (tan.f64 eps))
(tan eps)
(tan.f64 eps)

localize826.0ms (4.3%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)) (-.f64 eps (tan.f64 eps))) eps)
✓	accuracy	74.9%	(-.f64 eps (tan.f64 eps))
✓	accuracy	58.0%	(-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))
✓	accuracy	28.7%	(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)) (-.f64 eps (tan.f64 eps)))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 eps (.f64 eps #s(literal -1/362880 binary64)))))))))
✓	accuracy	99.4%	(*.f64 eps #s(literal -1/362880 binary64))
✓	accuracy	74.9%	(-.f64 eps (tan.f64 eps))
✓	accuracy	28.4%	(/.f64 (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 eps (*.f64 eps #s(literal -1/362880 binary64)))))))))) (-.f64 eps (tan.f64 eps)))
✓	accuracy	99.9%	(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))
✓	accuracy	99.9%	(.f64 (.f64 eps eps) (*.f64 eps eps))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) #s(literal 9/40 binary64))
✓	accuracy	100.0%	(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	99.8%	(.f64 (.f64 eps eps) #s(literal 9/40 binary64))
✓	accuracy	99.9%	(.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))

Results

491.0ms	152×	2	valid
138.0ms	32×	3	valid
92.0ms	69×	1	valid
1.0ms	3×	0	valid

Compiler

Compiled 528 to 45 computations (91.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 549.0ms

ival-tan: 200.0ms (36.4% of total)

ival-sin: 95.0ms (17.3% of total)

ival-add: 59.0ms (10.7% of total)

ival-mult: 57.0ms (10.4% of total)

backward-pass: 47.0ms (8.6% of total)

...c/correct-round.rkt:119:19: 45.0ms (8.2% of total)

ival-sub: 29.0ms (5.3% of total)

ival-div: 15.0ms (2.7% of total)

const: 1.0ms (0.2% of total)

series15.0ms (0.1%)

Counts

22 → 264

Calls

Call 1

Inputs
#<alt (/ (- 1/4 (* (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))) (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))) (- -1/2 (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))))>
#<alt (- 1/4 (* (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))) (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))))>
#<alt (* (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))) (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))>
#<alt (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))>
#<alt (+ (* (* eps eps) 9/40) -1/2)>
#<alt (* (* eps eps) 9/40)>
#<alt (* eps eps)>
#<alt (+ (* (* eps eps) 9/40) (+ (* (* (* eps eps) (* eps eps)) (+ -27/2800 (* (* eps eps) 27/112000))) -1/2))>
#<alt (+ (* (* (* eps eps) (* eps eps)) (+ -27/2800 (* (* eps eps) 27/112000))) -1/2)>
#<alt (/ (* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))))))) (- eps (tan eps)))>
#<alt (* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880)))))))))>
#<alt (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))))))>
#<alt (* (/ (- 1 (/ (sin eps) eps)) (- eps (tan eps))) eps)>
#<alt (/ (- 1 (/ (sin eps) eps)) (- eps (tan eps)))>
#<alt (- 1 (/ (sin eps) eps))>
#<alt (/ (sin eps) eps)>
#<alt (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))>
#<alt (* (* eps eps) 27/112000)>
#<alt (* (* eps eps) (* eps eps))>
#<alt (* (* (* eps eps) (* eps eps)) (+ -27/2800 (* (* eps eps) 27/112000)))>
#<alt (- eps (tan eps))>
#<alt (* eps -1/362880)>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt 1/4>
#<alt (+ 1/4 (* -81/1600 (pow eps 4)))>
#<alt (+ 1/4 (* (pow eps 4) (- (* 243/56000 (pow eps 2)) 81/1600)))>
#<alt (+ 1/4 (* (pow eps 4) (- (* (pow eps 2) (+ 243/56000 (* -3159/15680000 (pow eps 2)))) 81/1600)))>
#<alt (* -729/12544000000 (pow eps 12))>
#<alt (* (pow eps 12) (- (* 729/156800000 (/ 1 (pow eps 2))) 729/12544000000))>
#<alt (* (pow eps 12) (- (* 729/156800000 (/ 1 (pow eps 2))) (+ 729/12544000000 (/ 3159/15680000 (pow eps 4)))))>
#<alt (* (pow eps 12) (- (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6)))) (+ 729/12544000000 (/ 3159/15680000 (pow eps 4)))))>
#<alt (* -729/12544000000 (pow eps 12))>
#<alt (* (pow eps 12) (- (* 729/156800000 (/ 1 (pow eps 2))) 729/12544000000))>
#<alt (* (pow eps 12) (- (* 729/156800000 (/ 1 (pow eps 2))) (+ 729/12544000000 (/ 3159/15680000 (pow eps 4)))))>
#<alt (* (pow eps 12) (- (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6)))) (+ 729/12544000000 (/ 3159/15680000 (pow eps 4)))))>
#<alt (* 81/1600 (pow eps 4))>
#<alt (* (pow eps 4) (+ 81/1600 (* -243/56000 (pow eps 2))))>
#<alt (* (pow eps 4) (+ 81/1600 (* (pow eps 2) (- (* 3159/15680000 (pow eps 2)) 243/56000))))>
#<alt (* (pow eps 4) (+ 81/1600 (* (pow eps 2) (- (* (pow eps 2) (+ 3159/15680000 (* -729/156800000 (pow eps 2)))) 243/56000))))>
#<alt (* 729/12544000000 (pow eps 12))>
#<alt (* (pow eps 12) (- 729/12544000000 (* 729/156800000 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (* 729/156800000 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6))))))>
#<alt (* 729/12544000000 (pow eps 12))>
#<alt (* (pow eps 12) (- 729/12544000000 (* 729/156800000 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (* 729/156800000 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6))))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))>
#<alt (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt -1/2>
#<alt (- (* -27/2800 (pow eps 4)) 1/2)>
#<alt (- (* (pow eps 4) (- (* 27/112000 (pow eps 2)) 27/2800)) 1/2)>
#<alt (- (* (pow eps 4) (- (* 27/112000 (pow eps 2)) 27/2800)) 1/2)>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (+ 27/112000 (* -1 (/ (+ 27/2800 (* 1/2 (/ 1 (pow eps 4)))) (pow eps 2)))))>
#<alt (* (pow eps 6) (+ 27/112000 (* -1 (/ (+ 27/2800 (* 1/2 (/ 1 (pow eps 4)))) (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (+ 27/112000 (* -1 (/ (+ 27/2800 (* 1/2 (/ 1 (pow eps 4)))) (pow eps 2)))))>
#<alt (* (pow eps 6) (+ 27/112000 (* -1 (/ (+ 27/2800 (* 1/2 (/ 1 (pow eps 4)))) (pow eps 2)))))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt (* -1/362880 (pow eps 8))>
#<alt (* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))>
#<alt (* (pow eps 8) (- (/ 1/5040 (pow eps 2)) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))>
#<alt (* (pow eps 8) (- (+ (/ 1/5040 (pow eps 2)) (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* (pow eps 3) (cos eps)))) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))>
#<alt (* -1/362880 (pow eps 8))>
#<alt (* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))>
#<alt (* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))>
#<alt (* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- (+ 1/5040 (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))>
#<alt (* 1/6 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt (* -1/362880 (pow eps 9))>
#<alt (* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))>
#<alt (* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* (pow eps 9) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* -1/362880 (pow eps 9))>
#<alt (* -1 (* (pow eps 9) (- 1/362880 (* 1/5040 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 9) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (* 1/5040 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 9) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))))))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt (* -1/362880 (pow eps 8))>
#<alt (* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))>
#<alt (* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* (pow eps 8) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* -1/362880 (pow eps 8))>
#<alt (* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))>
#<alt (* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* (pow eps 8) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))>
#<alt (/ -1/2 eps)>
#<alt (/ (- (* 9/40 (pow eps 2)) 1/2) eps)>
#<alt (/ (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2) eps)>
#<alt (/ (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2) eps)>
#<alt (/ 1 eps)>
#<alt (/ (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps))))) eps)>
#<alt (/ (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps))))) eps)>
#<alt (/ (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps)))))) eps)>
#<alt (/ 1 eps)>
#<alt (* -1 (/ (- (/ (sin eps) eps) (+ 1 (/ (sin eps) (* eps (cos eps))))) eps))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* -1 (- (sin eps) (/ (sin eps) (cos eps)))) (* -1 (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps))))) eps)) 1) eps))>
#<alt (* -1 (/ (- (* -1 (/ (+ (* -1 (- (sin eps) (/ (sin eps) (cos eps)))) (* -1 (/ (+ (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps)) (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) eps))) eps)) 1) eps))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (sin eps) eps)))>
#<alt (+ 1 (* -1 (/ (sin eps) eps)))>
#<alt (+ 1 (* -1 (/ (sin eps) eps)))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (sin eps) eps)))>
#<alt (+ 1 (* -1 (/ (sin eps) eps)))>
#<alt (+ 1 (* -1 (/ (sin eps) eps)))>
#<alt 1>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt (/ (sin eps) eps)>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* 27/112000 (pow eps 4))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 4))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (pow eps 4)>
#<alt (pow eps 4)>
#<alt (pow eps 4)>
#<alt (pow eps 4)>
#<alt (pow eps 4)>
#<alt (pow eps 4)>
#<alt (pow eps 4)>
#<alt (pow eps 4)>
#<alt (pow eps 4)>
#<alt (pow eps 4)>
#<alt (pow eps 4)>
#<alt (pow eps 4)>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* (pow eps 4) (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* (pow eps 4) (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* -1/3 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>

Calls

66 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	-inf	(/ (- 1 (/ (sin eps) eps)) (- eps (tan eps)))
1.0ms	eps	@	inf	(/ (* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))))))) (- eps (tan eps)))
0.0ms	eps	@	-inf	(/ (* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))))))) (- eps (tan eps)))
0.0ms	eps	@	inf	(/ (- 1/4 (* (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))) (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))) (- -1/2 (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))))
0.0ms	eps	@	inf	(+ (* (* (* eps eps) (* eps eps)) (+ -27/2800 (* (* eps eps) 27/112000))) -1/2)

rewrite811.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4998×	`-lowering-.f32`
4998×	`-lowering-.f64`
2548×	`fma-lowering-fma.f32`
2548×	`fma-lowering-fma.f64`
2356×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	269
1	339	207
2	3316	207
0	9579	207

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 776

Calls

Call 1

Inputs
(/ (- 1/4 (* (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))) (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))) (- -1/2 (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))))
(- 1/4 (* (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))) (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))))
(* (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))) (* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))
(* (* eps eps) (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))
(+ (* (* eps eps) 9/40) -1/2)
(* (* eps eps) 9/40)
(* eps eps)
(+ (* (* eps eps) 9/40) (+ (* (* (* eps eps) (* eps eps)) (+ -27/2800 (* (* eps eps) 27/112000))) -1/2))
(+ (* (* (* eps eps) (* eps eps)) (+ -27/2800 (* (* eps eps) 27/112000))) -1/2)
(/ (* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))))))) (- eps (tan eps)))
(* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880)))))))))
(* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* eps (* eps -1/362880))))))))
(* (/ (- 1 (/ (sin eps) eps)) (- eps (tan eps))) eps)
(/ (- 1 (/ (sin eps) eps)) (- eps (tan eps)))
(- 1 (/ (sin eps) eps))
(/ (sin eps) eps)
(* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))
(* (* eps eps) 27/112000)
(* (* eps eps) (* eps eps))
(* (* (* eps eps) (* eps eps)) (+ -27/2800 (* (* eps eps) 27/112000)))
(- eps (tan eps))
(* eps -1/362880)

Outputs
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))))
(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps (.f64 eps eps))))))
(+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 9/40 binary64))) (.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps (.f64 eps eps)))))
(+.f64 (.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps (.f64 eps eps)))) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 9/40 binary64))))
(+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps eps) #s(literal 9/40 binary64)))
(+.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))))) (neg.f64 (/.f64 (.f64 (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))))) (-.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))))) (/.f64 (.f64 (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))))) (-.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))))))))
(-.f64 (/.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 81/1600 binary64)) (-.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)) (.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps (.f64 eps eps)))))) (/.f64 (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps (.f64 eps eps))))) (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps (.f64 eps eps)))))) (-.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)) (.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps (*.f64 eps eps)))))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))))) (neg.f64 (/.f64 (.f64 (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))))) (-.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))))))))
(fma.f64 eps (.f64 eps #s(literal 9/40 binary64)) (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps (*.f64 eps eps))))))
(fma.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal -1/2 binary64))
(fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 9/40 binary64))))
(fma.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 9/40 binary64))))
(fma.f64 eps (.f64 (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) (.f64 eps eps)) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 9/40 binary64))))
(fma.f64 (.f64 eps eps) #s(literal 9/40 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps (*.f64 eps eps))))))
(fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 9/40 binary64))))
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(.f64 eps (.f64 eps #s(literal 27/112000 binary64)))
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(.f64 #s(literal 27/112000 binary64) (.f64 eps eps))
(.f64 (.f64 eps #s(literal 27/112000 binary64)) eps)
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 eps)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 4 binary64)))
(exp.f64 (+.f64 (.f64 #s(literal 2 binary64) (log.f64 eps)) (.f64 #s(literal 2 binary64) (log.f64 eps))))
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(pow.f64 (.f64 eps (.f64 eps (*.f64 eps eps))) #s(literal 1 binary64))
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(.f64 (.f64 eps eps) (*.f64 eps eps))
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(fma.f64 (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)) (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -27/2800 binary64))))
(fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal -27/2800 binary64) (.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (*.f64 eps eps))))))
(fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)) (.f64 eps (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -27/2800 binary64))))
(fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -27/2800 binary64)) (.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (*.f64 eps eps))))))
(fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -27/2800 binary64))))
(fma.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) (.f64 eps eps) (.f64 eps (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -27/2800 binary64))))
(fma.f64 (.f64 eps (.f64 eps #s(literal -27/2800 binary64))) (.f64 eps eps) (.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (*.f64 eps eps))))))
(fma.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal 27/112000 binary64) (.f64 eps (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -27/2800 binary64))))
(fma.f64 (.f64 #s(literal -27/2800 binary64) eps) (.f64 eps (.f64 eps eps)) (.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (*.f64 eps eps))))))
(fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)) eps) (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -27/2800 binary64))))
(fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)) (.f64 eps (.f64 eps eps))) eps (.f64 eps (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -27/2800 binary64))))
(fma.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) eps) (.f64 eps #s(literal 27/112000 binary64)) (.f64 eps (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -27/2800 binary64))))
(fma.f64 (.f64 #s(literal -27/2800 binary64) (.f64 eps (.f64 eps eps))) eps (.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (*.f64 eps eps))))))
(/.f64 (+.f64 (.f64 #s(literal -19683/21952000000 binary64) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))))) (.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 19683/1404928000000000 binary64))) (.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))))) (+.f64 (.f64 (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) #s(literal -27/2800 binary64))) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) #s(literal -27/2800 binary64)))) (-.f64 (.f64 (.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) (.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))))) (.f64 (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) #s(literal -27/2800 binary64))) (.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (*.f64 eps eps)))))))))
(/.f64 (-.f64 (.f64 (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) #s(literal -27/2800 binary64))) (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) #s(literal -27/2800 binary64)))) (.f64 (.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) (.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))))) (-.f64 (.f64 eps (.f64 (.f64 eps (.f64 eps eps)) #s(literal -27/2800 binary64))) (.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))))))
(/.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 #s(literal -19683/21952000000 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 19683/1404928000000000 binary64))))) (+.f64 #s(literal 729/7840000 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)) (-.f64 (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))))
(/.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (-.f64 #s(literal 729/7840000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 729/12544000000 binary64)))) (+.f64 #s(literal -27/2800 binary64) (.f64 #s(literal -27/112000 binary64) (.f64 eps eps))))
(/.f64 (.f64 (+.f64 #s(literal -19683/21952000000 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 19683/1404928000000000 binary64)))) (.f64 eps (.f64 eps (.f64 eps eps)))) (+.f64 #s(literal 729/7840000 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)) (-.f64 (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 729/7840000 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 729/12544000000 binary64))) (.f64 eps (.f64 eps (.f64 eps eps)))) (+.f64 #s(literal -27/2800 binary64) (.f64 #s(literal -27/112000 binary64) (.f64 eps eps))))
(.f64 eps (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))
(.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))
(.f64 eps (.f64 (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) (.f64 eps eps)))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))
(.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps (.f64 eps eps))))
(.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) (.f64 eps eps))
(.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))
(.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))
(.f64 (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) (.f64 eps (.f64 eps eps)))
(.f64 (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) eps) eps)
(.f64 (.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 eps (.f64 eps eps))) eps)
(+.f64 eps (-.f64 #s(literal 0 binary64) (tan.f64 eps)))
(+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 eps)) eps)
(-.f64 eps (tan.f64 eps))
(-.f64 (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (+.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))))))
(-.f64 (/.f64 (*.f64 eps eps) (+.f64 eps (tan.f64 eps))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (+.f64 eps (tan.f64 eps))))
(fma.f64 #s(literal -1 binary64) (tan.f64 eps) eps)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 eps (tan.f64 eps)) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (+.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (+.f64 (.f64 eps eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (-.f64 #s(literal 0 binary64) (tan.f64 eps))))))
(/.f64 (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (+.f64 eps (tan.f64 eps)))
(/.f64 (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (-.f64 eps (-.f64 #s(literal 0 binary64) (tan.f64 eps))))
(/.f64 (neg.f64 (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (neg.f64 (+.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))))))
(/.f64 (neg.f64 (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (neg.f64 (+.f64 eps (tan.f64 eps))))
(pow.f64 (/.f64 (+.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 eps (tan.f64 eps)) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) #s(literal -1 binary64))
(.f64 (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (*.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))))))
(.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))))
(*.f64 eps #s(literal -1/362880 binary64))
(*.f64 #s(literal -1/362880 binary64) eps)

simplify352.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

5258×	`-lowering-.f32`
5258×	`-lowering-.f64`
2992×	`+-lowering-+.f64`
2992×	`+-lowering-+.f32`
1740×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	338	2847
1	1053	2494
2	3306	2427
0	8385	2427

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
1/4
(+ 1/4 (* -81/1600 (pow eps 4)))
(+ 1/4 (* (pow eps 4) (- (* 243/56000 (pow eps 2)) 81/1600)))
(+ 1/4 (* (pow eps 4) (- (* (pow eps 2) (+ 243/56000 (* -3159/15680000 (pow eps 2)))) 81/1600)))
(* -729/12544000000 (pow eps 12))
(* (pow eps 12) (- (* 729/156800000 (/ 1 (pow eps 2))) 729/12544000000))
(* (pow eps 12) (- (* 729/156800000 (/ 1 (pow eps 2))) (+ 729/12544000000 (/ 3159/15680000 (pow eps 4)))))
(* (pow eps 12) (- (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6)))) (+ 729/12544000000 (/ 3159/15680000 (pow eps 4)))))
(* -729/12544000000 (pow eps 12))
(* (pow eps 12) (- (* 729/156800000 (/ 1 (pow eps 2))) 729/12544000000))
(* (pow eps 12) (- (* 729/156800000 (/ 1 (pow eps 2))) (+ 729/12544000000 (/ 3159/15680000 (pow eps 4)))))
(* (pow eps 12) (- (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6)))) (+ 729/12544000000 (/ 3159/15680000 (pow eps 4)))))
(* 81/1600 (pow eps 4))
(* (pow eps 4) (+ 81/1600 (* -243/56000 (pow eps 2))))
(* (pow eps 4) (+ 81/1600 (* (pow eps 2) (- (* 3159/15680000 (pow eps 2)) 243/56000))))
(* (pow eps 4) (+ 81/1600 (* (pow eps 2) (- (* (pow eps 2) (+ 3159/15680000 (* -729/156800000 (pow eps 2)))) 243/56000))))
(* 729/12544000000 (pow eps 12))
(* (pow eps 12) (- 729/12544000000 (* 729/156800000 (/ 1 (pow eps 2)))))
(* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (* 729/156800000 (/ 1 (pow eps 2)))))
(* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6))))))
(* 729/12544000000 (pow eps 12))
(* (pow eps 12) (- 729/12544000000 (* 729/156800000 (/ 1 (pow eps 2)))))
(* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (* 729/156800000 (/ 1 (pow eps 2)))))
(* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6))))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
-1/2
(- (* -27/2800 (pow eps 4)) 1/2)
(- (* (pow eps 4) (- (* 27/112000 (pow eps 2)) 27/2800)) 1/2)
(- (* (pow eps 4) (- (* 27/112000 (pow eps 2)) 27/2800)) 1/2)
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (+ 27/112000 (* -1 (/ (+ 27/2800 (* 1/2 (/ 1 (pow eps 4)))) (pow eps 2)))))
(* (pow eps 6) (+ 27/112000 (* -1 (/ (+ 27/2800 (* 1/2 (/ 1 (pow eps 4)))) (pow eps 2)))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (+ 27/112000 (* -1 (/ (+ 27/2800 (* 1/2 (/ 1 (pow eps 4)))) (pow eps 2)))))
(* (pow eps 6) (+ 27/112000 (* -1 (/ (+ 27/2800 (* 1/2 (/ 1 (pow eps 4)))) (pow eps 2)))))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(* -1/362880 (pow eps 8))
(* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))
(* (pow eps 8) (- (/ 1/5040 (pow eps 2)) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))
(* (pow eps 8) (- (+ (/ 1/5040 (pow eps 2)) (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* (pow eps 3) (cos eps)))) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))
(* -1/362880 (pow eps 8))
(* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))
(* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))
(* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- (+ 1/5040 (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(* -1/362880 (pow eps 9))
(* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* (pow eps 9) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* -1/362880 (pow eps 9))
(* -1 (* (pow eps 9) (- 1/362880 (* 1/5040 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 9) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (* 1/5040 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 9) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))))))
(* 1/6 (pow eps 2))
(* (pow eps 2) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(* -1/362880 (pow eps 8))
(* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* (pow eps 8) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* -1/362880 (pow eps 8))
(* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* (pow eps 8) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
1
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(/ -1/2 eps)
(/ (- (* 9/40 (pow eps 2)) 1/2) eps)
(/ (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2) eps)
(/ (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2) eps)
(/ 1 eps)
(/ (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps))))) eps)
(/ (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps))))) eps)
(/ (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps)))))) eps)
(/ 1 eps)
(* -1 (/ (- (/ (sin eps) eps) (+ 1 (/ (sin eps) (* eps (cos eps))))) eps))
(* -1 (/ (- (* -1 (/ (+ (* -1 (- (sin eps) (/ (sin eps) (cos eps)))) (* -1 (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps))))) eps)) 1) eps))
(* -1 (/ (- (* -1 (/ (+ (* -1 (- (sin eps) (/ (sin eps) (cos eps)))) (* -1 (/ (+ (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps)) (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) eps))) eps)) 1) eps))
(* 1/6 (pow eps 2))
(* (pow eps 2) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
1
(+ 1 (* -1 (/ (sin eps) eps)))
(+ 1 (* -1 (/ (sin eps) eps)))
(+ 1 (* -1 (/ (sin eps) eps)))
1
(+ 1 (* -1 (/ (sin eps) eps)))
(+ 1 (* -1 (/ (sin eps) eps)))
(+ 1 (* -1 (/ (sin eps) eps)))
1
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6)))
(/ (sin eps) eps)
(/ (sin eps) eps)
(/ (sin eps) eps)
(/ (sin eps) eps)
(/ (sin eps) eps)
(/ (sin eps) eps)
(/ (sin eps) eps)
(/ (sin eps) eps)
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))
(* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))
(* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))
(* 27/112000 (pow eps 4))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 4))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(pow eps 4)
(pow eps 4)
(pow eps 4)
(pow eps 4)
(pow eps 4)
(pow eps 4)
(pow eps 4)
(pow eps 4)
(pow eps 4)
(pow eps 4)
(pow eps 4)
(pow eps 4)
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 27/112000 (pow eps 2)) 27/2800))
(* (pow eps 4) (- (* 27/112000 (pow eps 2)) 27/2800))
(* (pow eps 4) (- (* 27/112000 (pow eps 2)) 27/2800))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* -1/3 (pow eps 3))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))) (+.f64 (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 6 binary64))))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))) (+.f64 (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 6 binary64))))))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -81/1600 (pow eps 4)))
(+.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal -81/1600 binary64)))
(+ 1/4 (* (pow eps 4) (- (* 243/56000 (pow eps 2)) 81/1600)))
(+.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -81/1600 binary64) (.f64 (.f64 eps eps) #s(literal 243/56000 binary64)))))
(+ 1/4 (* (pow eps 4) (- (* (pow eps 2) (+ 243/56000 (* -3159/15680000 (pow eps 2)))) 81/1600)))
(+.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -81/1600 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 243/56000 binary64) (.f64 (.f64 eps eps) #s(literal -3159/15680000 binary64)))))))
(* -729/12544000000 (pow eps 12))
(*.f64 #s(literal -729/12544000000 binary64) (pow.f64 eps #s(literal 12 binary64)))
(* (pow eps 12) (- (* 729/156800000 (/ 1 (pow eps 2))) 729/12544000000))
(.f64 (pow.f64 eps #s(literal 12 binary64)) (+.f64 #s(literal -729/12544000000 binary64) (/.f64 #s(literal 729/156800000 binary64) (.f64 eps eps))))
(* (pow eps 12) (- (* 729/156800000 (/ 1 (pow eps 2))) (+ 729/12544000000 (/ 3159/15680000 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 12 binary64)) (+.f64 (/.f64 #s(literal 729/156800000 binary64) (.f64 eps eps)) (-.f64 #s(literal -729/12544000000 binary64) (/.f64 #s(literal 3159/15680000 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps))))))
(* (pow eps 12) (- (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6)))) (+ 729/12544000000 (/ 3159/15680000 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 12 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 729/156800000 binary64) (.f64 eps eps)) (+.f64 (/.f64 #s(literal 243/56000 binary64) (pow.f64 eps #s(literal 6 binary64))) #s(literal -729/12544000000 binary64))) (/.f64 #s(literal 3159/15680000 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* -729/12544000000 (pow eps 12))
(*.f64 #s(literal -729/12544000000 binary64) (pow.f64 eps #s(literal 12 binary64)))
(* (pow eps 12) (- (* 729/156800000 (/ 1 (pow eps 2))) 729/12544000000))
(.f64 (pow.f64 eps #s(literal 12 binary64)) (+.f64 #s(literal -729/12544000000 binary64) (/.f64 #s(literal 729/156800000 binary64) (.f64 eps eps))))
(* (pow eps 12) (- (* 729/156800000 (/ 1 (pow eps 2))) (+ 729/12544000000 (/ 3159/15680000 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 12 binary64)) (+.f64 (/.f64 #s(literal 729/156800000 binary64) (.f64 eps eps)) (-.f64 #s(literal -729/12544000000 binary64) (/.f64 #s(literal 3159/15680000 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps))))))
(* (pow eps 12) (- (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6)))) (+ 729/12544000000 (/ 3159/15680000 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 12 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 729/156800000 binary64) (.f64 eps eps)) (+.f64 (/.f64 #s(literal 243/56000 binary64) (pow.f64 eps #s(literal 6 binary64))) #s(literal -729/12544000000 binary64))) (/.f64 #s(literal 3159/15680000 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* 81/1600 (pow eps 4))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 81/1600 binary64))
(* (pow eps 4) (+ 81/1600 (* -243/56000 (pow eps 2))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 81/1600 binary64) (.f64 eps (.f64 eps #s(literal -243/56000 binary64)))))
(* (pow eps 4) (+ 81/1600 (* (pow eps 2) (- (* 3159/15680000 (pow eps 2)) 243/56000))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 81/1600 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -243/56000 binary64) (.f64 (.f64 eps eps) #s(literal 3159/15680000 binary64))))))
(* (pow eps 4) (+ 81/1600 (* (pow eps 2) (- (* (pow eps 2) (+ 3159/15680000 (* -729/156800000 (pow eps 2)))) 243/56000))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal 81/1600 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -243/56000 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 3159/15680000 binary64) (.f64 (.f64 eps eps) #s(literal -729/156800000 binary64))))))))
(* 729/12544000000 (pow eps 12))
(*.f64 (pow.f64 eps #s(literal 12 binary64)) #s(literal 729/12544000000 binary64))
(* (pow eps 12) (- 729/12544000000 (* 729/156800000 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 12 binary64)) (+.f64 #s(literal 729/12544000000 binary64) (/.f64 #s(literal -729/156800000 binary64) (.f64 eps eps))))
(* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (* 729/156800000 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 12 binary64)) (+.f64 #s(literal 729/12544000000 binary64) (+.f64 (/.f64 #s(literal 3159/15680000 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal -729/156800000 binary64) (*.f64 eps eps)))))
(* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6))))))
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(pow eps 4)
(.f64 (.f64 eps eps) (*.f64 eps eps))
(pow eps 4)
(.f64 (.f64 eps eps) (*.f64 eps eps))
(pow eps 4)
(.f64 (.f64 eps eps) (*.f64 eps eps))
(pow eps 4)
(.f64 (.f64 eps eps) (*.f64 eps eps))
(pow eps 4)
(.f64 (.f64 eps eps) (*.f64 eps eps))
(pow eps 4)
(.f64 (.f64 eps eps) (*.f64 eps eps))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* (pow eps 4) (- (* 27/112000 (pow eps 2)) 27/2800))
(.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 (.f64 eps eps) (.f64 eps eps)))
(* (pow eps 4) (- (* 27/112000 (pow eps 2)) 27/2800))
(.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 (.f64 eps eps) (.f64 eps eps)))
(* (pow eps 4) (- (* 27/112000 (pow eps 2)) 27/2800))
(.f64 (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))) (.f64 (.f64 eps eps) (.f64 eps eps)))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* -1/3 (pow eps 3))
(.f64 eps (.f64 (*.f64 eps eps) #s(literal -1/3 binary64)))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/3 binary64) (.f64 (*.f64 eps eps) #s(literal -2/15 binary64))))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -2/15 binary64) (.f64 (*.f64 eps eps) #s(literal -17/315 binary64)))))))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -2/15 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -17/315 binary64) (.f64 (*.f64 eps eps) #s(literal -62/2835 binary64))))))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))

eval321.0ms (1.7%)

Compiler: Compiled 90553 to 3408 computations (96.2% saved)

prune155.0ms (0.8%)

Pruning

20 alts after pruning (12 fresh and 8 done)

	Pruned	Kept	Total
New	1623	11	1634
Fresh	1	1	2
Picked	1	4	5
Done	1	4	5
Total	1626	20	1646

Accuracy

100.0%

Counts

1646 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	1.0%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
	99.9%	(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 81/1600 binary64))) (+.f64 #s(literal 729/7840000 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)) (-.f64 (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))))) (.f64 (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 9/40 binary64))) (.f64 (+.f64 #s(literal -19683/21952000000 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 19683/1404928000000000 binary64)))) (.f64 eps (.f64 eps (.f64 eps eps)))))) (.f64 (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 9/40 binary64))) (+.f64 #s(literal 729/7840000 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)) (-.f64 (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))))))
	1.2%	(/.f64 (.f64 eps (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) (.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))))))) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))))))))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 eps eps) #s(literal -1/362880 binary64)))))))))))) (-.f64 eps (tan.f64 eps)))
✓	1.3%	(/.f64 (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 eps (*.f64 eps #s(literal -1/362880 binary64)))))))))) (-.f64 eps (tan.f64 eps)))
▶	99.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))))
	1.3%	(-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))
✓	99.9%	(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
✓	99.9%	(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) #s(literal -1/2 binary64)))
▶	99.8%	(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) (+.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) #s(literal -1/2 binary64)))
✓	99.6%	(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	99.8%	(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
	1.0%	(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (sin.f64 eps) eps) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 (sin.f64 eps) eps) (+.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))))) (-.f64 eps (tan.f64 eps))) eps)
	1.0%	(.f64 (/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (*.f64 (-.f64 eps (tan.f64 eps)) (/.f64 (sin.f64 eps) eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) eps)
✓	1.0%	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)) (-.f64 eps (tan.f64 eps))) eps)
	99.6%	(.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))) eps) eps)
▶	99.4%	(.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps))) eps) eps)
▶	1.3%	(.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))))))))
▶	99.1%	(*.f64 (/.f64 #s(literal -1/2 binary64) eps) eps)
	45.2%	(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
✓	99.3%	#s(literal -1/2 binary64)

Compiler

Compiled 861 to 411 computations (52.3% saved)

simplify178.0ms (0.9%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(tan.f64 eps)
✓	cost-diff	0	(-.f64 eps (tan.f64 eps))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps)))
✓	cost-diff	128	(.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))))))))
✓	cost-diff	0	(+.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(.f64 (.f64 eps eps) #s(literal 9/40 binary64))
✓	cost-diff	256	(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) (+.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) #s(literal -1/2 binary64)))
✓	cost-diff	0	(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
✓	cost-diff	0	(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps))) eps)
✓	cost-diff	256	(.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps))) eps) eps)
✓	cost-diff	0	(/.f64 #s(literal -1/2 binary64) eps)
✓	cost-diff	256	(*.f64 (/.f64 #s(literal -1/2 binary64) eps) eps)
✓	cost-diff	0	(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
✓	cost-diff	0	(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64)))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))))

Rules

2588×	`+-lowering-+.f64`
2588×	`+-lowering-+.f32`
1898×	`-lowering-.f32`
1898×	`-lowering-.f64`
1466×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	352
1	144	304
2	501	300
3	1567	295
4	4237	295
5	7927	295
0	8057	295

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (/ 1 (+ (* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)))
1
(/ 1 (+ (* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2))
(+ (* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)
(* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))
eps
(* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))
(+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))
9/40
(* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))
(* eps eps)
(+ -27/2800 (* (* eps eps) 27/112000))
-27/2800
(* (* eps eps) 27/112000)
27/112000
-1/2
(* (/ -1/2 eps) eps)
(/ -1/2 eps)
-1/2
eps
(* (/ (+ -1/2 (* 9/40 (* eps eps))) eps) eps)
(/ (+ -1/2 (* 9/40 (* eps eps))) eps)
(+ -1/2 (* 9/40 (* eps eps)))
-1/2
(* 9/40 (* eps eps))
9/40
(* eps eps)
eps
(+ (* (* eps eps) 9/40) (+ (* (* eps eps) (* (* eps eps) -27/2800)) -1/2))
(* (* eps eps) 9/40)
(* eps eps)
eps
9/40
(+ (* (* eps eps) (* (* eps eps) -27/2800)) -1/2)
(* (* eps eps) (* (* eps eps) -27/2800))
(* (* eps eps) -27/2800)
-27/2800
-1/2
(* (/ 1 (- eps (tan eps))) (* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))))))))
(/ 1 (- eps (tan eps)))
1
(- eps (tan eps))
eps
(tan eps)
(* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880)))))))))
(* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))))))
(* eps eps)
(+ 1/6 (* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880)))))))
1/6
(* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))))
(+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880)))))
-1/120
(* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))
(* eps (+ 1/5040 (* (* eps eps) -1/362880)))
(+ 1/5040 (* (* eps eps) -1/362880))
1/5040
(* (* eps eps) -1/362880)
-1/362880

Outputs
(/ 1 (/ 1 (+ (* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)))
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
1
#s(literal 1 binary64)
(/ 1 (+ (* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2))
(/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64)))
(+ (* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
(* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
eps
(* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))))
(+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))
(+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))
9/40
#s(literal 9/40 binary64)
(* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))
(.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))
(* eps eps)
(*.f64 eps eps)
(+ -27/2800 (* (* eps eps) 27/112000))
(+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))
-27/2800
#s(literal -27/2800 binary64)
(* (* eps eps) 27/112000)
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
27/112000
#s(literal 27/112000 binary64)
-1/2
#s(literal -1/2 binary64)
(* (/ -1/2 eps) eps)
#s(literal -1/2 binary64)
(/ -1/2 eps)
(/.f64 #s(literal -1/2 binary64) eps)
-1/2
#s(literal -1/2 binary64)
eps
(* (/ (+ -1/2 (* 9/40 (* eps eps))) eps) eps)
(+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 9/40 binary64))))
(/ (+ -1/2 (* 9/40 (* eps eps))) eps)
(/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 9/40 binary64)))) eps)
(+ -1/2 (* 9/40 (* eps eps)))
(+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 9/40 binary64))))
-1/2
#s(literal -1/2 binary64)
(* 9/40 (* eps eps))
(.f64 eps (.f64 eps #s(literal 9/40 binary64)))
9/40
#s(literal 9/40 binary64)
(* eps eps)
(*.f64 eps eps)
eps
(+ (* (* eps eps) 9/40) (+ (* (* eps eps) (* (* eps eps) -27/2800)) -1/2))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
(* (* eps eps) 9/40)
(.f64 eps (.f64 eps #s(literal 9/40 binary64)))
(* eps eps)
(*.f64 eps eps)
eps
9/40
#s(literal 9/40 binary64)
(+ (* (* eps eps) (* (* eps eps) -27/2800)) -1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -27/2800 binary64) (.f64 eps (.f64 eps (.f64 eps eps)))))
(* (* eps eps) (* (* eps eps) -27/2800))
(.f64 #s(literal -27/2800 binary64) (.f64 eps (.f64 eps (.f64 eps eps))))
(* (* eps eps) -27/2800)
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
-27/2800
#s(literal -27/2800 binary64)
-1/2
#s(literal -1/2 binary64)
(* (/ 1 (- eps (tan eps))) (* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))))))))
(/.f64 (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 eps eps) #s(literal -1/362880 binary64))))))))) (-.f64 eps (tan.f64 eps)))
(/ 1 (- eps (tan eps)))
(/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps)))
1
#s(literal 1 binary64)
(- eps (tan eps))
(-.f64 eps (tan.f64 eps))
eps
(tan eps)
(tan.f64 eps)
(* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880)))))))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 eps eps) #s(literal -1/362880 binary64)))))))))
(* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))))))
(* eps eps)
(*.f64 eps eps)
(+ 1/6 (* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880)))))))
(+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))))
1/6
#s(literal 1/6 binary64)
(* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))))
(+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880)))))
(+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))
-1/120
#s(literal -1/120 binary64)
(* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))
(* eps (+ 1/5040 (* (* eps eps) -1/362880)))
(.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 eps eps) #s(literal -1/362880 binary64))))
(+ 1/5040 (* (* eps eps) -1/362880))
(+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))
1/5040
#s(literal 1/5040 binary64)
(* (* eps eps) -1/362880)
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
-1/362880
#s(literal -1/362880 binary64)

localize653.0ms (3.4%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))))))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
✓	accuracy	74.9%	(-.f64 eps (tan.f64 eps))
✓	accuracy	27.4%	(.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))))))))
✓	accuracy	100.0%	(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) (+.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) #s(literal -1/2 binary64)))
✓	accuracy	99.9%	(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) #s(literal 9/40 binary64))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps))) eps)
✓	accuracy	99.8%	(.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps))) eps) eps)
✓	accuracy	99.8%	(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
✓	accuracy	100.0%	(/.f64 #s(literal -1/2 binary64) eps)
✓	accuracy	99.8%	(*.f64 (/.f64 #s(literal -1/2 binary64) eps) eps)
✓	accuracy	99.9%	(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
✓	accuracy	99.7%	(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))

Results

362.0ms	143×	2	valid
112.0ms	41×	3	valid
85.0ms	69×	1	valid
1.0ms	3×	0	valid

Compiler

Compiled 426 to 45 computations (89.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 403.0ms

ival-tan: 178.0ms (44.2% of total)

...c/correct-round.rkt:119:19: 69.0ms (17.1% of total)

ival-mult: 64.0ms (15.9% of total)

backward-pass: 43.0ms (10.7% of total)

ival-add: 22.0ms (5.5% of total)

ival-div: 21.0ms (5.2% of total)

ival-sub: 4.0ms (1% of total)

const: 1.0ms (0.2% of total)

series12.0ms (0.1%)

Counts

25 → 300

Calls

Call 1

Inputs
#<alt (/ 1 (/ 1 (+ (* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)))>
#<alt (/ 1 (+ (* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2))>
#<alt (+ (* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)>
#<alt (* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))>
#<alt (* (/ -1/2 eps) eps)>
#<alt (/ -1/2 eps)>
#<alt (* (/ (+ -1/2 (* 9/40 (* eps eps))) eps) eps)>
#<alt (/ (+ -1/2 (* 9/40 (* eps eps))) eps)>
#<alt (+ -1/2 (* 9/40 (* eps eps)))>
#<alt (* 9/40 (* eps eps))>
#<alt (+ (* (* eps eps) 9/40) (+ (* (* eps eps) (* (* eps eps) -27/2800)) -1/2))>
#<alt (* (* eps eps) 9/40)>
#<alt (* eps eps)>
#<alt (+ (* (* eps eps) (* (* eps eps) -27/2800)) -1/2)>
#<alt (* (/ 1 (- eps (tan eps))) (* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))))))))>
#<alt (/ 1 (- eps (tan eps)))>
#<alt (- eps (tan eps))>
#<alt (tan eps)>
#<alt (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))>
#<alt (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))>
#<alt (* (* eps eps) 27/112000)>
#<alt (* (* eps eps) -27/2800)>
#<alt (* (* eps eps) (* (* eps eps) -27/2800))>
#<alt (* (* eps eps) -1/362880)>
#<alt (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))))))>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt -2>
#<alt (- (* -9/10 (pow eps 2)) 2)>
#<alt (- (* (pow eps 2) (- (* -513/1400 (pow eps 2)) 9/10)) 2)>
#<alt (- (* (pow eps 2) (- (* (pow eps 2) (- (* -297/2000 (pow eps 2)) 513/1400)) 9/10)) 2)>
#<alt (/ 112000/27 (pow eps 6))>
#<alt (/ (+ 112000/27 (* 4480000/27 (/ 1 (pow eps 2)))) (pow eps 6))>
#<alt (/ (+ 112000/27 (+ (* 4480000/27 (/ 1 (pow eps 2))) (/ 224000000/81 (pow eps 4)))) (pow eps 6))>
#<alt (/ (- (+ 112000/27 (+ (* 4480000/27 (/ 1 (pow eps 2))) (/ 224000000/81 (pow eps 4)))) (* 25984000000/729 (/ 1 (pow eps 6)))) (pow eps 6))>
#<alt (/ 112000/27 (pow eps 6))>
#<alt (/ (+ 112000/27 (* 4480000/27 (/ 1 (pow eps 2)))) (pow eps 6))>
#<alt (/ (+ 112000/27 (+ (* 4480000/27 (/ 1 (pow eps 2))) (/ 224000000/81 (pow eps 4)))) (pow eps 6))>
#<alt (/ (- (+ 112000/27 (+ (* 4480000/27 (/ 1 (pow eps 2))) (/ 224000000/81 (pow eps 4)))) (* 25984000000/729 (/ 1 (pow eps 6)))) (pow eps 6))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))>
#<alt (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt -1/2>
#<alt -1/2>
#<alt -1/2>
#<alt -1/2>
#<alt -1/2>
#<alt -1/2>
#<alt -1/2>
#<alt -1/2>
#<alt -1/2>
#<alt -1/2>
#<alt -1/2>
#<alt -1/2>
#<alt (/ -1/2 eps)>
#<alt (/ -1/2 eps)>
#<alt (/ -1/2 eps)>
#<alt (/ -1/2 eps)>
#<alt (/ -1/2 eps)>
#<alt (/ -1/2 eps)>
#<alt (/ -1/2 eps)>
#<alt (/ -1/2 eps)>
#<alt (/ -1/2 eps)>
#<alt (/ -1/2 eps)>
#<alt (/ -1/2 eps)>
#<alt (/ -1/2 eps)>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (/ -1/2 eps)>
#<alt (/ (- (* 9/40 (pow eps 2)) 1/2) eps)>
#<alt (/ (- (* 9/40 (pow eps 2)) 1/2) eps)>
#<alt (/ (- (* 9/40 (pow eps 2)) 1/2) eps)>
#<alt (* 9/40 eps)>
#<alt (* eps (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* eps (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* eps (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 eps)>
#<alt (* -1 (* eps (- (* 1/2 (/ 1 (pow eps 2))) 9/40)))>
#<alt (* -1 (* eps (- (* 1/2 (/ 1 (pow eps 2))) 9/40)))>
#<alt (* -1 (* eps (- (* 1/2 (/ 1 (pow eps 2))) 9/40)))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* 9/40 (pow eps 2))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt -1/2>
#<alt (- (* -27/2800 (pow eps 4)) 1/2)>
#<alt (- (* -27/2800 (pow eps 4)) 1/2)>
#<alt (- (* -27/2800 (pow eps 4)) 1/2)>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -1 (* (pow eps 4) (+ 27/2800 (* 1/2 (/ 1 (pow eps 4))))))>
#<alt (* -1 (* (pow eps 4) (+ 27/2800 (* 1/2 (/ 1 (pow eps 4))))))>
#<alt (* -1 (* (pow eps 4) (+ 27/2800 (* 1/2 (/ 1 (pow eps 4))))))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -1 (* (pow eps 4) (+ 27/2800 (* 1/2 (/ 1 (pow eps 4))))))>
#<alt (* -1 (* (pow eps 4) (+ 27/2800 (* 1/2 (/ 1 (pow eps 4))))))>
#<alt (* -1 (* (pow eps 4) (+ 27/2800 (* 1/2 (/ 1 (pow eps 4))))))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt (* -1/362880 (pow eps 8))>
#<alt (* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))>
#<alt (* (pow eps 8) (- (/ 1/5040 (pow eps 2)) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))>
#<alt (* (pow eps 8) (- (+ (/ 1/5040 (pow eps 2)) (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* (pow eps 3) (cos eps)))) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))>
#<alt (* -1/362880 (pow eps 8))>
#<alt (* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))>
#<alt (* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))>
#<alt (* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- (+ 1/5040 (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))>
#<alt (/ -3 (pow eps 3))>
#<alt (/ (- (* 6/5 (pow eps 2)) 3) (pow eps 3))>
#<alt (/ (- (* (pow eps 2) (+ 6/5 (* 1/175 (pow eps 2)))) 3) (pow eps 3))>
#<alt (/ (- (* (pow eps 2) (+ 6/5 (* (pow eps 2) (+ 1/175 (* 2/7875 (pow eps 2)))))) 3) (pow eps 3))>
#<alt (/ 1 eps)>
#<alt (/ (+ 1 (/ (sin eps) (* eps (cos eps)))) eps)>
#<alt (/ (- (+ 1 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2)))) (* -1 (/ (sin eps) (* eps (cos eps))))) eps)>
#<alt (/ (- (+ 1 (/ (pow (sin eps) 3) (* (pow eps 3) (pow (cos eps) 3)))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2)))))) eps)>
#<alt (/ 1 eps)>
#<alt (* -1 (/ (- (* -1 (/ (sin eps) (* eps (cos eps)))) 1) eps))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow (sin eps) 2) (* eps (pow (cos eps) 2))) (* -1 (/ (sin eps) (cos eps)))) eps)) 1) eps))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow (sin eps) 3) (* eps (pow (cos eps) 3)))) (/ (pow (sin eps) 2) (pow (cos eps) 2))) eps)) (* -1 (/ (sin eps) (cos eps)))) eps)) 1) eps))>
#<alt (* -1/3 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt eps>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))>
#<alt (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* 27/112000 (pow eps 4))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 4))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 eps)>
#<alt (* eps (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* eps (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))>
#<alt (* eps (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))>
#<alt (* 27/112000 (pow eps 5))>
#<alt (* (pow eps 5) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 5) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 5))>
#<alt (* -1 (* (pow eps 5) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))>
#<alt (* -1 (* (pow eps 5) (- (* 27/2800 (/ 1 (pow eps 2))) (+ 27/112000 (/ 9/40 (pow eps 4))))))>
#<alt (* -1 (* (pow eps 5) (- (* 27/2800 (/ 1 (pow eps 2))) (+ 27/112000 (/ 9/40 (pow eps 4))))))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* -1/362880 (pow eps 2))>
#<alt (* -1/362880 (pow eps 2))>
#<alt (* -1/362880 (pow eps 2))>
#<alt (* -1/362880 (pow eps 2))>
#<alt (* -1/362880 (pow eps 2))>
#<alt (* -1/362880 (pow eps 2))>
#<alt (* -1/362880 (pow eps 2))>
#<alt (* -1/362880 (pow eps 2))>
#<alt (* -1/362880 (pow eps 2))>
#<alt (* -1/362880 (pow eps 2))>
#<alt (* -1/362880 (pow eps 2))>
#<alt (* -1/362880 (pow eps 2))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt (* -1/362880 (pow eps 8))>
#<alt (* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))>
#<alt (* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* (pow eps 8) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* -1/362880 (pow eps 8))>
#<alt (* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))>
#<alt (* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* (pow eps 8) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>

Calls

75 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	0	(* (/ 1 (- eps (tan eps))) (* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))))))))
0.0ms	eps	@	inf	(/ 1 (- eps (tan eps)))
0.0ms	eps	@	-inf	(/ 1 (- eps (tan eps)))
0.0ms	eps	@	inf	(/ (+ -1/2 (* 9/40 (* eps eps))) eps)
0.0ms	eps	@	0	(/ -1/2 eps)

rewrite393.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

3198×	`-lowering-.f32`
3198×	`-lowering-.f64`
2788×	`/-lowering-/.f32`
2788×	`/-lowering-/.f64`
2230×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	223
1	315	192
2	2635	186
0	8103	186

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 639

Calls

Call 1

Inputs
(/ 1 (/ 1 (+ (* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)))
(/ 1 (+ (* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2))
(+ (* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)
(* eps (* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000))))))
(* (/ -1/2 eps) eps)
(/ -1/2 eps)
(* (/ (+ -1/2 (* 9/40 (* eps eps))) eps) eps)
(/ (+ -1/2 (* 9/40 (* eps eps))) eps)
(+ -1/2 (* 9/40 (* eps eps)))
(* 9/40 (* eps eps))
(+ (* (* eps eps) 9/40) (+ (* (* eps eps) (* (* eps eps) -27/2800)) -1/2))
(* (* eps eps) 9/40)
(* eps eps)
(+ (* (* eps eps) (* (* eps eps) -27/2800)) -1/2)
(* (/ 1 (- eps (tan eps))) (* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))))))))
(/ 1 (- eps (tan eps)))
(- eps (tan eps))
(tan eps)
(* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))
(* eps (+ 9/40 (* (* eps eps) (+ -27/2800 (* (* eps eps) 27/112000)))))
(* (* eps eps) 27/112000)
(* (* eps eps) -27/2800)
(* (* eps eps) (* (* eps eps) -27/2800))
(* (* eps eps) -1/362880)
(* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))))))

Outputs
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))))))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
(+.f64 (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal 1 binary64)) #s(literal -1/2 binary64))
(exp.f64 (log.f64 (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal -1/2 binary64))))
(exp.f64 (.f64 (log.f64 (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) (.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))) (/.f64 (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal -1/2 binary64))
(fma.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))) #s(literal -1/2 binary64))
(fma.f64 (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))) eps #s(literal -1/2 binary64))
(fma.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal 1 binary64) #s(literal -1/2 binary64))
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(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))))))
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(.f64 (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))))) eps)

simplify380.0ms (2%)

Algorithm

1×	egg-herbie

Rules

4254×	`-lowering-.f32`
4254×	`-lowering-.f64`
2726×	`+-lowering-+.f64`
2726×	`+-lowering-+.f32`
2560×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	300	2602
1	932	2268
2	2835	2203
0	8551	2203

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 300

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
-2
(- (* -9/10 (pow eps 2)) 2)
(- (* (pow eps 2) (- (* -513/1400 (pow eps 2)) 9/10)) 2)
(- (* (pow eps 2) (- (* (pow eps 2) (- (* -297/2000 (pow eps 2)) 513/1400)) 9/10)) 2)
(/ 112000/27 (pow eps 6))
(/ (+ 112000/27 (* 4480000/27 (/ 1 (pow eps 2)))) (pow eps 6))
(/ (+ 112000/27 (+ (* 4480000/27 (/ 1 (pow eps 2))) (/ 224000000/81 (pow eps 4)))) (pow eps 6))
(/ (- (+ 112000/27 (+ (* 4480000/27 (/ 1 (pow eps 2))) (/ 224000000/81 (pow eps 4)))) (* 25984000000/729 (/ 1 (pow eps 6)))) (pow eps 6))
(/ 112000/27 (pow eps 6))
(/ (+ 112000/27 (* 4480000/27 (/ 1 (pow eps 2)))) (pow eps 6))
(/ (+ 112000/27 (+ (* 4480000/27 (/ 1 (pow eps 2))) (/ 224000000/81 (pow eps 4)))) (pow eps 6))
(/ (- (+ 112000/27 (+ (* 4480000/27 (/ 1 (pow eps 2))) (/ 224000000/81 (pow eps 4)))) (* 25984000000/729 (/ 1 (pow eps 6)))) (pow eps 6))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
-1/2
(/ -1/2 eps)
(/ -1/2 eps)
(/ -1/2 eps)
(/ -1/2 eps)
(/ -1/2 eps)
(/ -1/2 eps)
(/ -1/2 eps)
(/ -1/2 eps)
(/ -1/2 eps)
(/ -1/2 eps)
(/ -1/2 eps)
(/ -1/2 eps)
-1/2
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(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(/ -1/2 eps)
(/ (- (* 9/40 (pow eps 2)) 1/2) eps)
(/ (- (* 9/40 (pow eps 2)) 1/2) eps)
(/ (- (* 9/40 (pow eps 2)) 1/2) eps)
(* 9/40 eps)
(* eps (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* eps (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* eps (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 eps)
(* -1 (* eps (- (* 1/2 (/ 1 (pow eps 2))) 9/40)))
(* -1 (* eps (- (* 1/2 (/ 1 (pow eps 2))) 9/40)))
(* -1 (* eps (- (* 1/2 (/ 1 (pow eps 2))) 9/40)))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
-1/2
(- (* -27/2800 (pow eps 4)) 1/2)
(- (* -27/2800 (pow eps 4)) 1/2)
(- (* -27/2800 (pow eps 4)) 1/2)
(* -27/2800 (pow eps 4))
(* -1 (* (pow eps 4) (+ 27/2800 (* 1/2 (/ 1 (pow eps 4))))))
(* -1 (* (pow eps 4) (+ 27/2800 (* 1/2 (/ 1 (pow eps 4))))))
(* -1 (* (pow eps 4) (+ 27/2800 (* 1/2 (/ 1 (pow eps 4))))))
(* -27/2800 (pow eps 4))
(* -1 (* (pow eps 4) (+ 27/2800 (* 1/2 (/ 1 (pow eps 4))))))
(* -1 (* (pow eps 4) (+ 27/2800 (* 1/2 (/ 1 (pow eps 4))))))
(* -1 (* (pow eps 4) (+ 27/2800 (* 1/2 (/ 1 (pow eps 4))))))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(* -1/362880 (pow eps 8))
(* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))
(* (pow eps 8) (- (/ 1/5040 (pow eps 2)) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))
(* (pow eps 8) (- (+ (/ 1/5040 (pow eps 2)) (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* (pow eps 3) (cos eps)))) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))
(* -1/362880 (pow eps 8))
(* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))
(* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))
(* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- (+ 1/5040 (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))
(/ -3 (pow eps 3))
(/ (- (* 6/5 (pow eps 2)) 3) (pow eps 3))
(/ (- (* (pow eps 2) (+ 6/5 (* 1/175 (pow eps 2)))) 3) (pow eps 3))
(/ (- (* (pow eps 2) (+ 6/5 (* (pow eps 2) (+ 1/175 (* 2/7875 (pow eps 2)))))) 3) (pow eps 3))
(/ 1 eps)
(/ (+ 1 (/ (sin eps) (* eps (cos eps)))) eps)
(/ (- (+ 1 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2)))) (* -1 (/ (sin eps) (* eps (cos eps))))) eps)
(/ (- (+ 1 (/ (pow (sin eps) 3) (* (pow eps 3) (pow (cos eps) 3)))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2)))))) eps)
(/ 1 eps)
(* -1 (/ (- (* -1 (/ (sin eps) (* eps (cos eps)))) 1) eps))
(* -1 (/ (- (* -1 (/ (- (/ (pow (sin eps) 2) (* eps (pow (cos eps) 2))) (* -1 (/ (sin eps) (cos eps)))) eps)) 1) eps))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow (sin eps) 3) (* eps (pow (cos eps) 3)))) (/ (pow (sin eps) 2) (pow (cos eps) 2))) eps)) (* -1 (/ (sin eps) (cos eps)))) eps)) 1) eps))
(* -1/3 (pow eps 3))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))
(* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))
(* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))
(* 27/112000 (pow eps 4))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 4))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* 9/40 eps)
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(* eps (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(* eps (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(* 27/112000 (pow eps 5))
(* (pow eps 5) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 5) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 5))
(* -1 (* (pow eps 5) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(* -1 (* (pow eps 5) (- (* 27/2800 (/ 1 (pow eps 2))) (+ 27/112000 (/ 9/40 (pow eps 4))))))
(* -1 (* (pow eps 5) (- (* 27/2800 (/ 1 (pow eps 2))) (+ 27/112000 (/ 9/40 (pow eps 4))))))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* 27/112000 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 2))
(* -27/2800 (pow eps 4))
(* -27/2800 (pow eps 4))
(* -27/2800 (pow eps 4))
(* -27/2800 (pow eps 4))
(* -27/2800 (pow eps 4))
(* -27/2800 (pow eps 4))
(* -27/2800 (pow eps 4))
(* -27/2800 (pow eps 4))
(* -27/2800 (pow eps 4))
(* -27/2800 (pow eps 4))
(* -27/2800 (pow eps 4))
(* -27/2800 (pow eps 4))
(* -1/362880 (pow eps 2))
(* -1/362880 (pow eps 2))
(* -1/362880 (pow eps 2))
(* -1/362880 (pow eps 2))
(* -1/362880 (pow eps 2))
(* -1/362880 (pow eps 2))
(* -1/362880 (pow eps 2))
(* -1/362880 (pow eps 2))
(* -1/362880 (pow eps 2))
(* -1/362880 (pow eps 2))
(* -1/362880 (pow eps 2))
(* -1/362880 (pow eps 2))
(* 1/6 (pow eps 2))
(* (pow eps 2) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(* -1/362880 (pow eps 8))
(* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* (pow eps 8) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* -1/362880 (pow eps 8))
(* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* (pow eps 8) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 6 binary64))))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 6 binary64))))))
-2
#s(literal -2 binary64)
(- (* -9/10 (pow eps 2)) 2)
(+.f64 (.f64 (.f64 eps eps) #s(literal -9/10 binary64)) #s(literal -2 binary64))
(- (* (pow eps 2) (- (* -513/1400 (pow eps 2)) 9/10)) 2)
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -9/10 binary64) (.f64 (.f64 eps eps) #s(literal -513/1400 binary64)))) #s(literal -2 binary64))
(- (* (pow eps 2) (- (* (pow eps 2) (- (* -297/2000 (pow eps 2)) 513/1400)) 9/10)) 2)
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -9/10 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -513/1400 binary64) (.f64 (.f64 eps eps) #s(literal -297/2000 binary64))))))) #s(literal -2 binary64))
(/ 112000/27 (pow eps 6))
(/.f64 #s(literal 112000/27 binary64) (pow.f64 eps #s(literal 6 binary64)))
(/ (+ 112000/27 (* 4480000/27 (/ 1 (pow eps 2)))) (pow eps 6))
(/.f64 (+.f64 #s(literal 112000/27 binary64) (/.f64 #s(literal 4480000/27 binary64) (*.f64 eps eps))) (pow.f64 eps #s(literal 6 binary64)))
(/ (+ 112000/27 (+ (* 4480000/27 (/ 1 (pow eps 2))) (/ 224000000/81 (pow eps 4)))) (pow eps 6))
(/.f64 (+.f64 (/.f64 #s(literal 4480000/27 binary64) (.f64 eps eps)) (+.f64 #s(literal 112000/27 binary64) (/.f64 #s(literal 224000000/81 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))) (pow.f64 eps #s(literal 6 binary64)))
(/ (- (+ 112000/27 (+ (* 4480000/27 (/ 1 (pow eps 2))) (/ 224000000/81 (pow eps 4)))) (* 25984000000/729 (/ 1 (pow eps 6)))) (pow eps 6))
(+.f64 (/.f64 (+.f64 (/.f64 #s(literal 4480000/27 binary64) (.f64 eps eps)) (+.f64 #s(literal 112000/27 binary64) (/.f64 #s(literal 224000000/81 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))) (pow.f64 eps #s(literal 6 binary64))) (/.f64 #s(literal -25984000000/729 binary64) (pow.f64 eps #s(literal 12 binary64))))
(/ 112000/27 (pow eps 6))
(/.f64 #s(literal 112000/27 binary64) (pow.f64 eps #s(literal 6 binary64)))
(/ (+ 112000/27 (* 4480000/27 (/ 1 (pow eps 2)))) (pow eps 6))
(/.f64 (+.f64 #s(literal 112000/27 binary64) (/.f64 #s(literal 4480000/27 binary64) (*.f64 eps eps))) (pow.f64 eps #s(literal 6 binary64)))
(/ (+ 112000/27 (+ (* 4480000/27 (/ 1 (pow eps 2))) (/ 224000000/81 (pow eps 4)))) (pow eps 6))
(/.f64 (+.f64 (/.f64 #s(literal 4480000/27 binary64) (.f64 eps eps)) (+.f64 #s(literal 112000/27 binary64) (/.f64 #s(literal 224000000/81 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))) (pow.f64 eps #s(literal 6 binary64)))
(/ (- (+ 112000/27 (+ (* 4480000/27 (/ 1 (pow eps 2))) (/ 224000000/81 (pow eps 4)))) (* 25984000000/729 (/ 1 (pow eps 6)))) (pow eps 6))
(+.f64 (/.f64 (+.f64 (/.f64 #s(literal 4480000/27 binary64) (.f64 eps eps)) (+.f64 #s(literal 112000/27 binary64) (/.f64 #s(literal 224000000/81 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))) (pow.f64 eps #s(literal 6 binary64))) (/.f64 #s(literal -25984000000/729 binary64) (pow.f64 eps #s(literal 12 binary64))))
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 6 binary64))))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 6 binary64))))))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))
(* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
(* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
-1/2
#s(literal -1/2 binary64)
-1/2
#s(literal -1/2 binary64)
-1/2
#s(literal -1/2 binary64)
-1/2
#s(literal -1/2 binary64)
-1/2
#s(literal -1/2 binary64)
-1/2
#s(literal -1/2 binary64)
-1/2
#s(literal -1/2 binary64)
-1/2
#s(literal -1/2 binary64)
-1/2
#s(literal -1/2 binary64)
-1/2
#s(literal -1/2 binary64)
-1/2
#s(literal -1/2 binary64)
-1/2
#s(literal -1/2 binary64)
(/ -1/2 eps)
(/.f64 #s(literal -1/2 binary64) eps)
(/ -1/2 eps)
(/.f64 #s(literal -1/2 binary64) eps)
(/ -1/2 eps)
(/.f64 #s(literal -1/2 binary64) eps)
(/ -1/2 eps)
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(* -1 (/ (- (* -1 (/ (- (/ (pow (sin eps) 2) (* eps (pow (cos eps) 2))) (* -1 (/ (sin eps) (cos eps)))) eps)) 1) eps))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) eps)) eps)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow (sin eps) 3) (* eps (pow (cos eps) 3)))) (/ (pow (sin eps) 2) (pow (cos eps) 2))) eps)) (* -1 (/ (sin eps) (cos eps)))) eps)) 1) eps))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (*.f64 eps (pow.f64 (cos.f64 eps) #s(literal 3 binary64)))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) eps)) eps)) eps)
(* -1/3 (pow eps 3))
(.f64 (.f64 eps eps) (*.f64 eps #s(literal -1/3 binary64)))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/3 binary64) (.f64 eps (*.f64 eps #s(literal -2/15 binary64)))))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -2/15 binary64) (.f64 eps (*.f64 eps #s(literal -17/315 binary64)))))))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -2/15 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -17/315 binary64) (.f64 (*.f64 eps eps) #s(literal -62/2835 binary64))))))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (.f64 eps (cos.f64 eps)))))
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 1/3 binary64))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (*.f64 eps eps) #s(literal 2/15 binary64))) eps) eps)))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 2/15 binary64) (.f64 (*.f64 eps eps) #s(literal 17/315 binary64)))))))))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))
(.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))
(* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))
(.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))
(* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))
(.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))
(* 27/112000 (pow eps 4))
(.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 eps eps)))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 eps eps)))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 eps eps)))
(* 27/112000 (pow eps 4))
(.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 eps eps)))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 eps eps)))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 eps eps)))
(* 9/40 eps)
(*.f64 #s(literal 9/40 binary64) eps)
(* eps (+ 9/40 (* -27/2800 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
(* eps (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))))
(* eps (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)))))))
(* 27/112000 (pow eps 5))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 5 binary64)))
(* (pow eps 5) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 5 binary64)))
(* (pow eps 5) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))) (pow.f64 eps #s(literal 5 binary64)))
(* (pow eps 5) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))) (pow.f64 eps #s(literal 5 binary64)))
(* 27/112000 (pow eps 5))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 5 binary64)))
(* -1 (* (pow eps 5) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (pow.f64 eps #s(literal 5 binary64)))
(* -1 (* (pow eps 5) (- (* 27/2800 (/ 1 (pow eps 2))) (+ 27/112000 (/ 9/40 (pow eps 4))))))
(.f64 (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))) (pow.f64 eps #s(literal 5 binary64)))
(* -1 (* (pow eps 5) (- (* 27/2800 (/ 1 (pow eps 2))) (+ 27/112000 (/ 9/40 (pow eps 4))))))
(.f64 (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))) (pow.f64 eps #s(literal 5 binary64)))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(* -1/362880 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(* -1/362880 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(* -1/362880 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(* -1/362880 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(* -1/362880 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(* -1/362880 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(* -1/362880 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(* -1/362880 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(* -1/362880 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(* -1/362880 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(* -1/362880 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(* -1/362880 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(* 1/6 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/6 binary64)))
(* (pow eps 2) (+ 1/6 (* -1/120 (pow eps 2))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) #s(literal -1/120 binary64))))
(* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) #s(literal 1/5040 binary64))))))
(* (pow eps 2) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))))))
(* -1/362880 (pow eps 8))
(*.f64 #s(literal -1/362880 binary64) (pow.f64 eps #s(literal 8 binary64)))
(* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(.f64 (pow.f64 eps #s(literal 8 binary64)) (+.f64 #s(literal -1/362880 binary64) (/.f64 #s(literal 1/5040 binary64) (.f64 eps eps))))
(* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 8 binary64)) (+.f64 #s(literal -1/362880 binary64) (+.f64 (/.f64 #s(literal 1/5040 binary64) (.f64 eps eps)) (/.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps))))))
(* (pow eps 8) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 8 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/5040 binary64) (.f64 eps eps)) (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 6 binary64))) #s(literal -1/362880 binary64))) (/.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* -1/362880 (pow eps 8))
(*.f64 #s(literal -1/362880 binary64) (pow.f64 eps #s(literal 8 binary64)))
(* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(.f64 (pow.f64 eps #s(literal 8 binary64)) (+.f64 #s(literal -1/362880 binary64) (/.f64 #s(literal 1/5040 binary64) (.f64 eps eps))))
(* (pow eps 8) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 8 binary64)) (+.f64 #s(literal -1/362880 binary64) (+.f64 (/.f64 #s(literal 1/5040 binary64) (.f64 eps eps)) (/.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps))))))
(* (pow eps 8) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 8 binary64)) (+.f64 (+.f64 (/.f64 #s(literal 1/5040 binary64) (.f64 eps eps)) (+.f64 (/.f64 #s(literal 1/6 binary64) (pow.f64 eps #s(literal 6 binary64))) #s(literal -1/362880 binary64))) (/.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))

eval154.0ms (0.8%)

Compiler: Compiled 35595 to 2728 computations (92.3% saved)

prune168.0ms (0.9%)

Pruning

21 alts after pruning (8 fresh and 13 done)

	Pruned	Kept	Total
New	1080	3	1083
Fresh	2	5	7
Picked	0	5	5
Done	0	8	8
Total	1082	21	1103

Accuracy

100.0%

Counts

1103 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	1.0%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
	1.2%	(/.f64 (.f64 eps (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) (.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))))))) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))))))))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 eps eps) #s(literal -1/362880 binary64)))))))))))) (-.f64 eps (tan.f64 eps)))
✓	1.3%	(/.f64 (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 eps (*.f64 eps #s(literal -1/362880 binary64)))))))))) (-.f64 eps (tan.f64 eps)))
✓	99.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))))
	1.3%	(-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))
✓	99.9%	(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
✓	99.9%	(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) #s(literal -1/2 binary64)))
✓	99.8%	(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) (+.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) #s(literal -1/2 binary64)))
✓	99.6%	(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	99.8%	(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
	1.0%	(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (sin.f64 eps) eps) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 (sin.f64 eps) eps) (+.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))))) (-.f64 eps (tan.f64 eps))) eps)
	1.0%	(.f64 (/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (*.f64 (-.f64 eps (tan.f64 eps)) (/.f64 (sin.f64 eps) eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) eps)
✓	1.0%	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)) (-.f64 eps (tan.f64 eps))) eps)
	99.6%	(.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))) eps) eps)
✓	99.4%	(.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps))) eps) eps)
	1.2%	(.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (.f64 eps (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) (.f64 (.f64 (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))) (.f64 eps (.f64 eps (.f64 eps eps)))))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))) (.f64 eps (.f64 eps (.f64 eps eps))))))))
✓	1.3%	(.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))))))))
✓	99.1%	(*.f64 (/.f64 #s(literal -1/2 binary64) eps) eps)
	26.7%	(.f64 (+.f64 (.f64 (+.f64 #s(literal 6/5 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/175 binary64) (.f64 (.f64 eps eps) #s(literal 2/7875 binary64))))) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal -3 binary64) (.f64 eps (.f64 eps eps)))) (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 eps eps) #s(literal -1/362880 binary64)))))))))))
	45.2%	(.f64 (.f64 eps (-.f64 #s(literal 9/40 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)))) eps)
✓	99.3%	#s(literal -1/2 binary64)

Compiler

Compiled 1404 to 459 computations (67.3% saved)

regimes126.0ms (0.6%)

Counts

29 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(*.f64 (/.f64 #s(literal -1/2 binary64) eps) eps)
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(.f64 (.f64 eps (-.f64 #s(literal 9/40 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)))) eps)
(.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps))) eps) eps)
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))) eps) eps)
(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) (+.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) #s(literal -1/2 binary64)))
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))))
(.f64 (+.f64 (.f64 (+.f64 #s(literal 6/5 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/175 binary64) (.f64 (.f64 eps eps) #s(literal 2/7875 binary64))))) (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal -3 binary64) (.f64 eps (.f64 eps eps)))) (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 eps eps) #s(literal -1/362880 binary64)))))))))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))) (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))))))
(/.f64 (+.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) #s(literal 81/1600 binary64))) (+.f64 #s(literal 729/7840000 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)) (-.f64 (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))))) (.f64 (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 9/40 binary64))) (.f64 (+.f64 #s(literal -19683/21952000000 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 19683/1404928000000000 binary64)))) (.f64 eps (.f64 eps (.f64 eps eps)))))) (.f64 (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 9/40 binary64))) (+.f64 #s(literal 729/7840000 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)) (-.f64 (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))))))
(/.f64 (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 eps (*.f64 eps #s(literal -1/362880 binary64)))))))))) (-.f64 eps (tan.f64 eps)))
(/.f64 (.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 eps eps) #s(literal -1/362880 binary64)))))))))) (-.f64 eps (tan.f64 eps)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64)))))))))))
(/.f64 (.f64 eps (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) (.f64 (.f64 eps (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))))))) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))))))))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 eps (.f64 eps (.f64 (.f64 eps eps) (+.f64 #s(literal -1/120 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/5040 binary64) (.f64 (*.f64 eps eps) #s(literal -1/362880 binary64)))))))))))) (-.f64 eps (tan.f64 eps)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (.f64 eps (/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 (.f64 eps eps) #s(literal 1/6 binary64))) (.f64 (.f64 (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))) (.f64 eps (.f64 eps (.f64 eps eps)))))) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/6 binary64)) (.f64 (+.f64 #s(literal -1/120 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/5040 binary64) (.f64 (.f64 eps eps) #s(literal -1/362880 binary64))))) (.f64 eps (.f64 eps (.f64 eps eps))))))))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)) (-.f64 eps (tan.f64 eps))) eps)
(/.f64 (*.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))) (-.f64 eps (tan.f64 eps)))
(-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))
(.f64 (/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (*.f64 (-.f64 eps (tan.f64 eps)) (/.f64 (sin.f64 eps) eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) eps)
(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (sin.f64 eps) eps) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 (sin.f64 eps) eps) (+.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))))) (-.f64 eps (tan.f64 eps))) eps)
(/.f64 (fma.f64 (/.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (pow.f64 (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))) (neg.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (+.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))))) (-.f64 eps (tan.f64 eps)))
(/.f64 (fma.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (sin.f64 eps) #s(literal 3 binary64))) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (pow.f64 (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))) (.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (*.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))))) (-.f64 eps (tan.f64 eps)))

Outputs

(+.f64 (*.f64 (*.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (*.f64 eps (*.f64 eps (+.f64 #s(literal -27/2800 binary64) (*.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))

Calls

2 calls:

117.0ms	eps
6.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
99.9%	1	`eps`
99.9%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes4.0ms (0%)

Counts

10 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(*.f64 (/.f64 #s(literal -1/2 binary64) eps) eps)
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(.f64 (.f64 eps (-.f64 #s(literal 9/40 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)))) eps)
(.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps))) eps) eps)
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64)))))) eps) eps)
(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) (+.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))) #s(literal -1/2 binary64)))

Outputs
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))

Calls

1 calls:

3.0ms

eps

Results

Accuracy	Segments	Branch
99.8%	1	`eps`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts

7 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(*.f64 (/.f64 #s(literal -1/2 binary64) eps) eps)
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 (.f64 (.f64 eps eps) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(.f64 (.f64 eps (-.f64 #s(literal 9/40 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)))) eps)
(.f64 (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (*.f64 eps eps))) eps) eps)

Outputs
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))

Calls

1 calls:

3.0ms

eps

Results

Accuracy	Segments	Branch
99.6%	1	`eps`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total -0.1b remaining (-23.1%)

Threshold costs -0.1b (-23.1%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(*.f64 (/.f64 #s(literal -1/2 binary64) eps) eps)

Outputs
#s(literal -1/2 binary64)

Calls

1 calls:

1.0ms

eps

Results

Accuracy	Segments	Branch
99.3%	1	`eps`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify30.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
12×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	34	40

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)

Outputs
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64))))))) #s(literal -1/2 binary64))
(+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64))))))
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 9/40 binary64)))
#s(literal -1/2 binary64)

soundness434.0ms (2.2%)

Rules

4708×	`-lowering-.f32`
4708×	`-lowering-.f64`
1320×	`+-lowering-+.f64`
1320×	`+-lowering-+.f32`
1274×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	547
1	457	472
2	1539	434
3	6918	432
0	8079	432

Stop Event

1×	fuel
1×	iter limit
1×	node limit

Compiler

Compiled 66 to 39 computations (40.9% saved)

preprocess51.0ms (0.3%)

Remove: (abs eps)
Compiler: Compiled 298 to 174 computations (41.6% saved)

analyze498.0ms (2.6%)

sample9.6s (49.3%)

preprocess122.0ms (0.6%)

explain713.0ms (3.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify56.0ms (0.3%)

localize328.0ms (1.7%)

series7.0ms (0%)

rewrite353.0ms (1.8%)

simplify240.0ms (1.2%)

eval46.0ms (0.2%)

prune93.0ms (0.5%)

simplify183.0ms (0.9%)

localize1.1s (5.7%)

series31.0ms (0.2%)

rewrite322.0ms (1.7%)

simplify265.0ms (1.4%)

eval111.0ms (0.6%)

prune90.0ms (0.5%)

simplify219.0ms (1.1%)

localize826.0ms (4.3%)

series15.0ms (0.1%)

rewrite811.0ms (4.2%)

simplify352.0ms (1.8%)

eval321.0ms (1.7%)

prune155.0ms (0.8%)

simplify178.0ms (0.9%)

localize653.0ms (3.4%)

series12.0ms (0.1%)

rewrite393.0ms (2%)

simplify380.0ms (2%)

eval154.0ms (0.8%)

prune168.0ms (0.9%)

regimes126.0ms (0.6%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes2.0ms (0%)

simplify30.0ms (0.2%)

soundness434.0ms (2.2%)

preprocess51.0ms (0.3%)

end0.0ms (0%)

Profiling