Metrics for sintan (problem 3.4.5)

analyze557.0ms (3.2%)

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: 298.0ms

...c/correct-round.rkt:119:19: 125.0ms (41.9% of total)

ival-sub: 46.0ms (15.4% of total)

ival-sin: 41.0ms (13.7% of total)

ival-<=: 33.0ms (11.1% of total)

ival-tan: 31.0ms (10.4% of total)

ival-div: 12.0ms (4% of total)

ival-and: 8.0ms (2.7% of total)

backward-pass: 2.0ms (0.7% of total)

sample9.3s (53.1%)

Results

6.1s	4102×	2	valid
1.5s	1280×	3	valid
1.2s	2787×	1	valid
10.0ms	87×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 8.0s

ival-tan: 4.5s (57% of total)

ival-sin: 2.2s (28.1% of total)

backward-pass: 345.0ms (4.3% of total)

...c/correct-round.rkt:119:19: 316.0ms (4% of total)

ival-sub: 298.0ms (3.7% of total)

ival-div: 136.0ms (1.7% of total)

ival-<=: 73.0ms (0.9% of total)

ival-and: 17.0ms (0.2% of total)

Bogosity

preprocess94.0ms (0.5%)

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)

explain622.0ms (3.5%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
162	-	1	(9.179555982533702e-104)	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`
95	-	0	-	`(-.f64 eps (sin.f64 eps))`
94	-	0	-	`(-.f64 eps (tan.f64 eps))`
0	-	0	-	`(sin.f64 eps)`
0	-	0	-	`eps`
0	-	0	-	`(tan.f64 eps)`

Results

381.0ms	256×	2	valid
104.0ms	68×	3	valid
93.0ms	184×	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: 502.0ms

ival-tan: 237.0ms (47.2% of total)

ival-sin: 139.0ms (27.7% of total)

backward-pass: 67.0ms (13.4% of total)

ival-sub: 51.0ms (10.2% of total)

ival-div: 7.0ms (1.4% of total)

const: 1.0ms (0.2% 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
▶	1.1%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify51.0ms (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)

localize305.0ms (1.7%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	66.6%	(-.f64 eps (tan.f64 eps))
✓	accuracy	66.5%	(-.f64 eps (sin.f64 eps))
✓	accuracy	37.5%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

218.0ms	128×	2	valid
49.0ms	34×	3	valid
26.0ms	92×	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: 222.0ms

ival-tan: 115.0ms (51.8% of total)

ival-sin: 81.0ms (36.5% of total)

backward-pass: 11.0ms (5% of total)

ival-sub: 10.0ms (4.5% of total)

ival-div: 4.0ms (1.8% of total)

const: 0.0ms (0% of total)

series4.0ms (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
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))
0.0ms	eps	@	inf	(- eps (tan eps))

rewrite307.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

2006×	`-lowering-.f32`
2006×	`-lowering-.f64`
1458×	`sum3-define`
1434×	`fnmadd-define`
1382×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
1	23	19
2	97	19
3	528	19
4	4039	19
0	8308	19

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 321

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

simplify279.0ms (1.6%)

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	6919	432
0	8081	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 #s(literal 1 binary64) (+.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 (/.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 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) 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 (.f64 eps 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 eps (.f64 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 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 (* -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 (.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)))))

eval41.0ms (0.2%)

Compiler: Compiled 7408 to 859 computations (88.4% saved)

prune51.0ms (0.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	362	7	369
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	362	8	370

Accuracy

100.0%

Counts

370 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	1.1%	(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (/.f64 #s(literal -1 binary64) (-.f64 eps (sin.f64 eps))))
✓	1.1%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
▶	1.2%	(/.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)))
	1.2%	(-.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 (tan.f64 eps) 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))
▶	99.7%	(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
▶	99.3%	#s(literal -1/2 binary64)

Compiler

Compiled 218 to 136 computations (37.6% saved)

simplify223.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 eps eps)
✓	cost-diff	(.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))))))))
✓	cost-diff	(.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)))))))))
✓	cost-diff	(/.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)))
✓	cost-diff	(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
✓	cost-diff	(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
✓	cost-diff	(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
✓	cost-diff	(+.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	(*.f64 eps eps)
✓	cost-diff	(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
✓	cost-diff	(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
✓	cost-diff	(+.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	(*.f64 eps eps)
✓	cost-diff	(.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	(+.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

4288×	`-lowering-.f32`
4288×	`-lowering-.f64`
1566×	`+-lowering-+.f64`
1566×	`+-lowering-+.f32`
1496×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	272
1	118	238
2	431	238
3	1173	238
4	2859	238
5	5320	238
6	6685	238
0	8617	238

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
(+ (* 9/40 (* eps eps)) -1/2)
(* 9/40 (* eps eps))
9/40
(* eps eps)
eps
-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 (* (* 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)
-1/362880
(- eps (tan eps))
(tan eps)

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

localize1.5s (8.6%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.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))))))))
✓	accuracy	99.6%	(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
✓	accuracy	66.6%	(-.f64 eps (tan.f64 eps))
✓	accuracy	37.5%	(/.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)))
✓	accuracy	100.0%	(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
✓	accuracy	99.7%	(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) #s(literal -27/2800 binary64))
✓	accuracy	99.7%	(.f64 eps (+.f64 #s(literal 9/40 binary64) (.f64 (*.f64 eps eps) #s(literal -27/2800 binary64))))
✓	accuracy	100.0%	(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	99.7%	(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
✓	accuracy	99.7%	(.f64 eps (.f64 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 9/40 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
✓	accuracy	99.4%	(.f64 eps (+.f64 #s(literal -27/2800 binary64) (.f64 (*.f64 eps eps) #s(literal 27/112000 binary64))))

Results

645.0ms	91×	1	valid
614.0ms	123×	2	valid
174.0ms	40×	3	valid
1.0ms	2×	0	valid

Compiler

Compiled 326 to 36 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 824.0ms

ival-mult: 317.0ms (38.5% of total)

...c/correct-round.rkt:119:19: 293.0ms (35.6% of total)

ival-tan: 119.0ms (14.4% of total)

backward-pass: 62.0ms (7.5% of total)

ival-add: 24.0ms (2.9% of total)

ival-div: 4.0ms (0.5% of total)

ival-sub: 4.0ms (0.5% of total)

const: 1.0ms (0.1% of total)

series15.0ms (0.1%)

Counts

19 → 228

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 (+ (* 9/40 (* eps eps)) -1/2)>
#<alt (* 9/40 (* eps eps))>
#<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 (* (* 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 (* eps (+ -27/2800 (* (* eps eps) 27/112000)))>
#<alt (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000))))>
#<alt (* (* eps eps) 27/112000)>
#<alt (* (* eps eps) -27/2800)>
#<alt (- eps (tan eps))>
#<alt (* (* 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 (* 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 (- (* 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 (* (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 (* -1/362880 (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 (* -27/2800 eps)>
#<alt (* eps (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* eps (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* eps (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* 27/112000 (pow eps 3))>
#<alt (* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))>
#<alt (* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))>
#<alt (* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))>
#<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 (* -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 (* -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))>

Calls

57 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	-inf	(+ (* eps (* eps (+ 9/40 (* (* eps eps) -27/2800)))) -1/2)
2.0ms	eps	@	inf	(/ (* eps (* (* eps eps) (+ 1/6 (* (* eps eps) (+ -1/120 (* (* eps eps) (+ 1/5040 (* (* eps eps) -1/362880)))))))) (- eps (tan eps)))
1.0ms	eps	@	0	(+ (* (* eps eps) (+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)
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) (+ 9/40 (* eps (* eps (+ -27/2800 (* (* eps eps) 27/112000)))))) -1/2)

rewrite804.0ms (4.6%)

Algorithm

1×	batch-egg-rewrite

Rules

4418×	`-lowering-.f32`
4418×	`-lowering-.f64`
2560×	`+-lowering-+.f64`
2560×	`+-lowering-+.f32`
2040×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	184
1	131	160
2	520	160
3	1974	160
0	8342	160

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 693

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

simplify559.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

4536×	`-lowering-.f32`
4536×	`-lowering-.f64`
1882×	`sum3-define`
1842×	`+-lowering-+.f64`
1842×	`+-lowering-+.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	2178
1	611	1884
2	1876	1842
3	6731	1842
0	8161	1842

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

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)
(- (* 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))
(* (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)
(* -1/362880 (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)))))
(* -27/2800 eps)
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(* 27/112000 (pow eps 3))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 3))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(* -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))
(* -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)))
(* -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))

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 (.f64 eps 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 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))) #s(literal -1/2 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) (pow.f64 eps #s(literal 4 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) (pow.f64 eps #s(literal 4 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) (pow.f64 eps #s(literal 4 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) (pow.f64 eps #s(literal 4 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 (.f64 eps 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 (.f64 eps 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) (pow.f64 eps #s(literal 4 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) (pow.f64 eps #s(literal 4 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 (/ 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) (pow.f64 eps #s(literal 4 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) (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
9/40
#s(literal 9/40 binary64)
(+ 9/40 (* -27/2800 (pow eps 2)))
(+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))
(+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))
(+.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 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))
(+.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)))))
(* 27/112000 (pow eps 4))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 4 binary64)))
(* (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))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 27/112000 binary64) (+.f64 (/.f64 #s(literal 9/40 binary64) (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 27/112000 binary64) (+.f64 (/.f64 #s(literal 9/40 binary64) (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
(* 27/112000 (pow eps 4))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 4 binary64)))
(* (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))) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 27/112000 binary64) (+.f64 (/.f64 #s(literal 9/40 binary64) (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal 27/112000 binary64) (+.f64 (/.f64 #s(literal 9/40 binary64) (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
-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))
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #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))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
-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 (.f64 eps 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 (* -27/2800 (pow eps 2)))) 1/2)
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) #s(literal -27/2800 binary64)))) #s(literal -1/2 binary64))
(* -27/2800 (pow eps 4))
(*.f64 #s(literal -27/2800 binary64) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (.f64 eps eps))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 4 binary64))))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 4 binary64))))))
(* -27/2800 (pow eps 4))
(*.f64 #s(literal -27/2800 binary64) (pow.f64 eps #s(literal 4 binary64)))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
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(.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (.f64 eps (.f64 eps 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 (.f64 eps 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 (.f64 eps 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 (.f64 eps 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) (pow.f64 eps #s(literal 4 binary64)))
(* (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))) (pow.f64 eps #s(literal 4 binary64)))
(* (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))) (pow.f64 eps #s(literal 4 binary64)))
(* (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))) (pow.f64 eps #s(literal 4 binary64)))
(* 27/112000 (pow eps 4))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 4 binary64)))
(* (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))) (pow.f64 eps #s(literal 4 binary64)))
(* (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))) (pow.f64 eps #s(literal 4 binary64)))
(* (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))) (pow.f64 eps #s(literal 4 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))
(* -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 (.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 eps (.f64 eps (+.f64 #s(literal -17/315 binary64) (.f64 eps (*.f64 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 (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))

eval162.0ms (0.9%)

Compiler: Compiled 29175 to 2328 computations (92% saved)

prune91.0ms (0.5%)

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	1045	2	1047
Fresh	0	2	2
Picked	1	4	5
Done	0	1	1
Total	1046	9	1055

Accuracy

100.0%

Counts

1055 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	1.1%	(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (/.f64 #s(literal -1 binary64) (-.f64 eps (sin.f64 eps))))
✓	1.1%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
▶	1.2%	(/.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 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 eps)) (-.f64 eps (tan.f64 eps)))
▶	1.2%	(-.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 (tan.f64 eps) 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))
✓	99.7%	(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
▶	55.2%	(.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 126 to 81 computations (35.7% saved)

simplify154.0ms (0.9%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(tan.f64 eps)
✓	cost-diff	0	(-.f64 (tan.f64 eps) eps)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps))
✓	cost-diff	256	(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (/.f64 #s(literal -1 binary64) (-.f64 eps (sin.f64 eps))))
✓	cost-diff	0	(+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 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 eps (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 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 eps (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 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 eps))
✓	cost-diff	0	(/.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 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 eps)) (-.f64 eps (tan.f64 eps)))
✓	cost-diff	0	(-.f64 (tan.f64 eps) eps)
✓	cost-diff	0	(sin.f64 eps)
✓	cost-diff	0	(/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps))
✓	cost-diff	6656	(-.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 (tan.f64 eps) eps)))
✓	cost-diff	0	(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
✓	cost-diff	0	(+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
✓	cost-diff	128	(.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
✓	cost-diff	128	(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))

Rules

2692×	`-lowering-.f32`
2692×	`-lowering-.f64`
2334×	`+-lowering-+.f64`
2334×	`+-lowering-+.f32`
1766×	`distribute-lft-in`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	267
1	102	246
2	303	244
3	827	238
4	2499	228
0	8035	228

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize875.0ms (5%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f64 #s(literal -1 binary64) (-.f64 eps (sin.f64 eps)))
✓	accuracy	66.6%	(-.f64 (tan.f64 eps) eps)
✓	accuracy	66.5%	(-.f64 eps (sin.f64 eps))
✓	accuracy	36.3%	(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (/.f64 #s(literal -1 binary64) (-.f64 eps (sin.f64 eps))))
✓	accuracy	99.6%	(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
✓	accuracy	99.5%	(.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 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	66.6%	(-.f64 eps (tan.f64 eps))
✓	accuracy	37.5%	(/.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 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 eps)) (-.f64 eps (tan.f64 eps)))
✓	accuracy	84.0%	(/.f64 eps (-.f64 (tan.f64 eps) eps))
✓	accuracy	84.0%	(/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps))
✓	accuracy	66.6%	(-.f64 (tan.f64 eps) eps)
✓	accuracy	3.1%	(-.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 (tan.f64 eps) eps)))
✓	accuracy	100.0%	(+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
✓	accuracy	99.8%	(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
✓	accuracy	99.8%	(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
✓	accuracy	57.3%	(.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))))

Results

511.0ms	104×	3	valid
181.0ms	86×	2	valid
84.0ms	65×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 302 to 37 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 478.0ms

ival-tan: 192.0ms (40.1% of total)

ival-sin: 96.0ms (20.1% of total)

backward-pass: 59.0ms (12.3% of total)

ival-mult: 40.0ms (8.4% of total)

...c/correct-round.rkt:119:19: 35.0ms (7.3% of total)

ival-div: 29.0ms (6.1% of total)

ival-sub: 17.0ms (3.6% of total)

ival-add: 10.0ms (2.1% of total)

const: 1.0ms (0.2% of total)

series17.0ms (0.1%)

Counts

20 → 240

Calls

Call 1

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

Outputs
#<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 (pow eps 2))>
#<alt (/ (- (* 9/40 (pow eps 2)) 1/2) (pow eps 2))>
#<alt (/ (- (* 9/40 (pow eps 2)) 1/2) (pow eps 2))>
#<alt (/ (- (* 9/40 (pow eps 2)) 1/2) (pow eps 2))>
#<alt 9/40>
#<alt (- 9/40 (* 1/2 (/ 1 (pow eps 2))))>
#<alt (- 9/40 (* 1/2 (/ 1 (pow eps 2))))>
#<alt (- 9/40 (* 1/2 (/ 1 (pow eps 2))))>
#<alt 9/40>
#<alt (- 9/40 (* 1/2 (/ 1 (pow eps 2))))>
#<alt (- 9/40 (* 1/2 (/ 1 (pow eps 2))))>
#<alt (- 9/40 (* 1/2 (/ 1 (pow eps 2))))>
#<alt (/ -1/2 (pow eps 2))>
#<alt (/ -1/2 (pow eps 2))>
#<alt (/ -1/2 (pow eps 2))>
#<alt (/ -1/2 (pow eps 2))>
#<alt (/ -1/2 (pow eps 2))>
#<alt (/ -1/2 (pow eps 2))>
#<alt (/ -1/2 (pow eps 2))>
#<alt (/ -1/2 (pow eps 2))>
#<alt (/ -1/2 (pow eps 2))>
#<alt (/ -1/2 (pow eps 2))>
#<alt (/ -1/2 (pow eps 2))>
#<alt (/ -1/2 (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>
#<alt (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (+ (/ (sin eps) (* eps (cos eps))) (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2)))))) (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (+ (/ (sin eps) (* eps (cos eps))) (+ (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))) (/ (pow (sin eps) 3) (* (pow eps 3) (pow (cos eps) 3))))))) (+ (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps))) (/ (pow (sin eps) 3) (* (pow eps 3) (pow (cos eps) 2)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (+ (* -1 (/ (pow (sin eps) 2) (* eps (pow (cos eps) 2)))) (/ (pow (sin eps) 2) (* eps (cos eps))))) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (+ (* -1 (/ (pow (sin eps) 3) (* eps (pow (cos eps) 2)))) (/ (pow (sin eps) 3) (* eps (pow (cos eps) 3)))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (cos eps)))) eps))) (/ (sin eps) (cos eps))) eps)))>
#<alt (/ 3 (pow eps 2))>
#<alt (/ (+ 3 (* -17/10 (pow eps 2))) (pow eps 2))>
#<alt (/ (+ 3 (* (pow eps 2) (- (* 307/1400 (pow eps 2)) 17/10))) (pow eps 2))>
#<alt (/ (+ 3 (* (pow eps 2) (- (* (pow eps 2) (+ 307/1400 (* -1247/126000 (pow eps 2)))) 17/10))) (pow eps 2))>
#<alt (* -1 (/ (sin eps) eps))>
#<alt (/ (+ (* -1 (sin eps)) (* -1 (/ (pow (sin eps) 2) (* eps (cos eps))))) eps)>
#<alt (/ (- (+ (* -1 (sin eps)) (* -1 (/ (pow (sin eps) 3) (* (pow eps 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps)>
#<alt (/ (- (+ (* -1 (sin eps)) (* -1 (/ (pow (sin eps) 4) (* (pow eps 3) (pow (cos eps) 3))))) (+ (/ (pow (sin eps) 2) (* eps (cos eps))) (/ (pow (sin eps) 3) (* (pow eps 2) (pow (cos eps) 2))))) eps)>
#<alt (* -1 (/ (sin eps) eps))>
#<alt (* -1 (/ (+ (sin eps) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))>
#<alt (* -1 (/ (+ (sin eps) (* -1 (/ (- (* -1 (/ (pow (sin eps) 3) (* eps (pow (cos eps) 2)))) (/ (pow (sin eps) 2) (cos eps))) eps))) eps))>
#<alt (* -1 (/ (+ (sin eps) (* -1 (/ (- (* -1 (/ (- (/ (pow (sin eps) 4) (* eps (pow (cos eps) 3))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 2)))) eps)) (/ (pow (sin eps) 2) (cos eps))) eps))) eps))>
#<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) (+ 1/3 (* 2/15 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))>
#<alt (* (pow eps 3) (+ 1/3 (* (pow eps 2) (+ 2/15 (* (pow eps 2) (+ 17/315 (* 62/2835 (pow eps 2))))))))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (sin eps) (* eps (cos eps))) 1))>
#<alt (* eps (- (/ (sin eps) (* eps (cos eps))) 1))>
#<alt (* eps (- (/ (sin eps) (* eps (cos eps))) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps)))))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps)))))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos 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 (* -1/362880 (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 eps)>
#<alt (* eps (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* eps (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* eps (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt (* -1/362880 (pow eps 7))>
#<alt (* (pow eps 7) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))>
#<alt (* (pow eps 7) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* (pow eps 7) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* -1/362880 (pow eps 7))>
#<alt (* -1 (* (pow eps 7) (- 1/362880 (* 1/5040 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 7) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (* 1/5040 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 7) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))))))>
#<alt 1/6>
#<alt (+ 1/6 (* -1/120 (pow eps 2)))>
#<alt (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120)))>
#<alt (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120)))>
#<alt (* -1/362880 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))>
#<alt (* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* -1/362880 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))>
#<alt (* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (+ (* 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) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (+ (* -1 (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* (pow eps 2) (cos eps)))) (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps))))>
#<alt (+ 1 (+ (* -1 (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* (pow eps 3) (pow (cos eps) 2)))) (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) 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 (/ 3 (pow eps 3))>
#<alt (/ (+ 3 (* -6/5 (pow eps 2))) (pow eps 3))>
#<alt (/ (+ 3 (* (pow eps 2) (- (* -1/175 (pow eps 2)) 6/5))) (pow eps 3))>
#<alt (/ (+ 3 (* (pow eps 2) (- (* (pow eps 2) (- (* -2/7875 (pow eps 2)) 1/175)) 6/5))) (pow eps 3))>
#<alt (/ -1 eps)>
#<alt (/ (- (* -1 (/ (sin eps) (* eps (cos eps)))) 1) 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))) (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2)))))) eps)>
#<alt (/ -1 eps)>
#<alt (* -1 (/ (+ 1 (/ (sin eps) (* eps (cos eps)))) eps))>
#<alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow (sin eps) 2) (* eps (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) eps))) eps))>
#<alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow (sin eps) 3) (* eps (pow (cos eps) 3))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (/ (sin eps) (cos eps))) eps))) eps))>
#<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 (/ 3 (pow eps 2))>
#<alt (/ (+ 3 (* -6/5 (pow eps 2))) (pow eps 2))>
#<alt (/ (+ 3 (* (pow eps 2) (- (* -1/175 (pow eps 2)) 6/5))) (pow eps 2))>
#<alt (/ (+ 3 (* (pow eps 2) (- (* (pow eps 2) (- (* -2/7875 (pow eps 2)) 1/175)) 6/5))) (pow eps 2))>
#<alt -1>
#<alt (- (* -1 (/ (sin eps) (* eps (cos eps)))) 1)>
#<alt (- (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2)))) (+ 1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (* -1 (/ (pow (sin eps) 3) (* (pow eps 3) (pow (cos eps) 3)))) (+ 1 (+ (/ (sin eps) (* eps (cos eps))) (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))>
#<alt -1>
#<alt (- (* -1 (/ (sin eps) (* eps (cos eps)))) 1)>
#<alt (- (* -1 (/ (- (/ (pow (sin eps) 2) (* eps (pow (cos eps) 2))) (* -1 (/ (sin eps) (cos eps)))) eps)) 1)>
#<alt (- (* -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)>
#<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 (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 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 (/ -6 (pow eps 3))>
#<alt (/ (- (* -3/10 (pow eps 2)) 6) (pow eps 3))>
#<alt (/ (- (* (pow eps 2) (- (* -11/1400 (pow eps 2)) 3/10)) 6) (pow eps 3))>
#<alt (/ (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/126000 (pow eps 2)) 11/1400)) 3/10)) 6) (pow eps 3))>
#<alt (/ -1 eps)>
#<alt (/ (- (* -1 (/ (sin eps) eps)) 1) eps)>
#<alt (/ (- (* -1 (/ (pow (sin eps) 2) (pow eps 2))) (+ 1 (/ (sin eps) eps))) eps)>
#<alt (/ (- (* -1 (/ (pow (sin eps) 3) (pow eps 3))) (+ 1 (+ (/ (sin eps) eps) (/ (pow (sin eps) 2) (pow eps 2))))) eps)>
#<alt (/ -1 eps)>
#<alt (* -1 (/ (+ 1 (/ (sin eps) eps)) eps))>
#<alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow (sin eps) 2) eps)) (sin eps)) eps))) eps))>
#<alt (* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow (sin eps) 3) eps) (* -1 (pow (sin eps) 2))) eps)) (sin eps)) eps))) eps))>

Calls

60 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	inf	(/ (* (* eps (+ 1/6 (* eps (* eps (+ -1/120 (* eps (* eps (+ 1/5040 (* (* eps eps) -1/362880))))))))) (* eps eps)) (- eps (tan eps)))
1.0ms	eps	@	inf	(- (/ (sin eps) (- (tan eps) eps)) (/ eps (- (tan eps) eps)))
1.0ms	eps	@	-inf	(- (/ (sin eps) (- (tan eps) eps)) (/ eps (- (tan eps) eps)))
1.0ms	eps	@	inf	(/ (/ 1 (- (tan eps) eps)) (/ -1 (- eps (sin eps))))
0.0ms	eps	@	-inf	(/ (sin eps) (- (tan eps) eps))

rewrite263.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2016×	`-lowering-.f32`
2016×	`-lowering-.f64`
1840×	`prod-diff`
1608×	`/-lowering-/.f32`
1608×	`/-lowering-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	170
1	157	158
2	789	152
3	4643	152
0	8069	152

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 998

Calls

Call 1

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

Outputs
(+.f64 (.f64 eps (.f64 eps #s(literal 9/40 binary64))) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) eps))
(+.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) eps) (.f64 eps (*.f64 eps #s(literal 9/40 binary64))))
(-.f64 (.f64 eps (.f64 eps #s(literal 9/40 binary64))) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (*.f64 eps eps)))
(-.f64 (.f64 eps (.f64 eps #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps))))
(fma.f64 eps (.f64 eps #s(literal 9/40 binary64)) (/.f64 (.f64 eps #s(literal -1/2 binary64)) eps))
(fma.f64 #s(literal 9/40 binary64) (.f64 eps eps) (/.f64 (.f64 eps #s(literal -1/2 binary64)) eps))
(fma.f64 (.f64 eps eps) #s(literal 9/40 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) eps))
(fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 eps (.f64 eps #s(literal 9/40 binary64))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 eps eps) (.f64 eps (.f64 eps #s(literal 9/40 binary64))))
(fma.f64 (.f64 eps #s(literal 9/40 binary64)) eps (/.f64 (.f64 eps #s(literal -1/2 binary64)) eps))
(.f64 eps (+.f64 (.f64 eps #s(literal 9/40 binary64)) (/.f64 #s(literal -1/2 binary64) eps)))
(.f64 (.f64 eps eps) (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(.f64 (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (*.f64 eps eps))
(.f64 (+.f64 (.f64 eps #s(literal 9/40 binary64)) (/.f64 #s(literal -1/2 binary64) eps)) eps)
(+.f64 (*.f64 eps #s(literal 9/40 binary64)) (/.f64 #s(literal -1/2 binary64) eps))
(+.f64 (/.f64 #s(literal -1/2 binary64) eps) (*.f64 eps #s(literal 9/40 binary64)))
(-.f64 (*.f64 eps #s(literal 9/40 binary64)) (/.f64 #s(literal 1/2 binary64) eps))
(-.f64 (.f64 eps #s(literal 9/40 binary64)) (.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)) eps))
(-.f64 (.f64 eps #s(literal 9/40 binary64)) (.f64 eps (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps))))
(-.f64 (.f64 eps #s(literal 9/40 binary64)) (/.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 eps eps)))
(fma.f64 eps #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) eps))
(fma.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 eps #s(literal 9/40 binary64)))
(fma.f64 #s(literal 9/40 binary64) eps (/.f64 #s(literal -1/2 binary64) eps))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) eps) (*.f64 eps #s(literal 9/40 binary64)))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)) eps (.f64 eps #s(literal 9/40 binary64)))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)) (*.f64 eps #s(literal 9/40 binary64)))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(.f64 (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))) eps)
(+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(+.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 9/40 binary64))
(-.f64 #s(literal 9/40 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 9/40 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 9/40 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps)) #s(literal 9/40 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -1/2 binary64) #s(literal 9/40 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 9/40 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 eps (/.f64 #s(literal -1/2 binary64) eps))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)))
(neg.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 eps eps)))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))))
(neg.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) eps) (-.f64 #s(literal 0 binary64) eps)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 eps (/.f64 #s(literal -1/2 binary64) eps))))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(/.f64 #s(literal 1 binary64) (/.f64 eps (/.f64 #s(literal -1/2 binary64) eps)))
(/.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps eps) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 eps eps)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal -2 binary64))
(/.f64 (/.f64 #s(literal -1/2 binary64) eps) eps)
(/.f64 (/.f64 #s(literal 1/2 binary64) eps) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 eps #s(literal -1/2 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) eps) #s(literal -1 binary64)) eps)
(pow.f64 (/.f64 eps (/.f64 #s(literal -1/2 binary64) eps)) #s(literal -1 binary64))
(.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)))
(.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(*.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 #s(literal 1 binary64) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)))
(*.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/2 binary64) eps))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))
(+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 eps (-.f64 (tan.f64 eps) eps)))))
(+.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps)) (+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 eps (-.f64 (tan.f64 eps) eps))))
(+.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps)) (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 eps (-.f64 (tan.f64 eps) eps)))))
(+.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps)) (*.f64 (+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 eps (-.f64 (tan.f64 eps) eps))) #s(literal 1 binary64)))
(+.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps)) (+.f64 (+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 eps (-.f64 (tan.f64 eps) eps))) (+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 eps (-.f64 (tan.f64 eps) eps)))))
(+.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps)) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (sin.f64 eps) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (sin.f64 eps))))
(+.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps)) (fma.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))))
(+.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps)) (fma.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) #s(literal -1 binary64) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps)))))
(+.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps)) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))))
(+.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps)) (fma.f64 #s(literal -1 binary64) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))))
(+.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps)) (fma.f64 (neg.f64 (/.f64 (-.f64 (tan.f64 eps) eps) (-.f64 (tan.f64 eps) eps))) (/.f64 eps (-.f64 (tan.f64 eps) eps)) (/.f64 (*.f64 eps (-.f64 (tan.f64 eps) eps)) (pow.f64 (-.f64 (tan.f64 eps) eps) #s(literal 2 binary64)))))
(+.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps)) (fma.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (-.f64 (tan.f64 eps) eps) (-.f64 (tan.f64 eps) eps)) (/.f64 (*.f64 eps (-.f64 (tan.f64 eps) eps)) (pow.f64 (-.f64 (tan.f64 eps) eps) #s(literal 2 binary64)))))
(+.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 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 eps (-.f64 (tan.f64 eps) eps)))))
(+.f64 (+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 eps (-.f64 (tan.f64 eps) eps))) (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps)))
(+.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (pow.f64 (-.f64 (tan.f64 eps) eps) #s(literal 2 binary64))) (neg.f64 (/.f64 (.f64 eps (-.f64 (tan.f64 eps) eps)) (pow.f64 (-.f64 (tan.f64 eps) eps) #s(literal 2 binary64)))))
(+.f64 (fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (neg.f64 (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps))))) (fma.f64 (neg.f64 (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (.f64 (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)))))
(+.f64 (fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps))))) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)))))
(+.f64 (fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 1 binary64))))) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (*.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal 1 binary64)))))
(+.f64 (fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -1 binary64))))) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) (.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (*.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -1 binary64)))))
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(+.f64 (fma.f64 #s(literal 1 binary64) eps (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (tan.f64 eps)) #s(literal -1 binary64)))) (fma.f64 (tan.f64 eps) #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (tan.f64 eps)) #s(literal -1 binary64))))
(+.f64 (fma.f64 #s(literal 1 binary64) eps (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 eps))) (-.f64 #s(literal 0 binary64) (sin.f64 eps))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 eps)))) (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 eps))) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))))
(+.f64 (fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) eps) (neg.f64 (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (sin.f64 eps)))) (fma.f64 (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal 1 binary64))) (sin.f64 eps) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (sin.f64 eps))))
(+.f64 (fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) eps) (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (tan.f64 eps)) #s(literal -1 binary64)))) (fma.f64 (tan.f64 eps) #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (tan.f64 eps)) #s(literal -1 binary64))))
(+.f64 (fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) eps) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 eps))) (-.f64 #s(literal 0 binary64) (sin.f64 eps))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 eps)))) (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 eps))) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))))
(-.f64 eps (tan.f64 eps))
(-.f64 #s(literal 0 binary64) (-.f64 (tan.f64 eps) eps))
(-.f64 (-.f64 #s(literal 0 binary64) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) eps))
(-.f64 (+.f64 eps #s(literal 0 binary64)) (tan.f64 eps))
(fma.f64 eps #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (tan.f64 eps)))
(fma.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 eps))) eps)
(fma.f64 (sin.f64 eps) (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 eps))) eps)
(fma.f64 (tan.f64 eps) #s(literal -1 binary64) eps)
(fma.f64 #s(literal 1 binary64) eps (-.f64 #s(literal 0 binary64) (tan.f64 eps)))
(fma.f64 #s(literal -1 binary64) (tan.f64 eps) eps)
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (tan.f64 eps)))
(fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (/.f64 #s(literal 1 binary64) (cos.f64 eps)) eps)
(neg.f64 (-.f64 (tan.f64 eps) eps))
(/.f64 (-.f64 (tan.f64 eps) eps) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)))
(/.f64 (-.f64 eps (tan.f64 eps)) #s(literal 1 binary64))
(*.f64 (-.f64 (tan.f64 eps) eps) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps)))
(*.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps))
(*.f64 (-.f64 eps (tan.f64 eps)) #s(literal 1 binary64))
(.f64 eps (.f64 eps #s(literal -1/362880 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/362880 binary64))
(.f64 #s(literal -1/362880 binary64) (.f64 eps eps))
(.f64 (.f64 eps #s(literal -1/362880 binary64)) eps)
(+.f64 eps (-.f64 #s(literal 0 binary64) (sin.f64 eps)))
(+.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) eps)
(+.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (*.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -1 binary64)) eps))
(+.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 #s(literal 1 binary64) eps (-.f64 #s(literal 0 binary64) eps)))
(+.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 #s(literal -1 binary64) (sin.f64 eps) (sin.f64 eps)))
(+.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal 1 binary64) (sin.f64 eps)))
(+.f64 (*.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))
(+.f64 (-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal 0 binary64)) eps)
(+.f64 (fma.f64 eps #s(literal 1 binary64) (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal -1 binary64)))) (fma.f64 (sin.f64 eps) #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal -1 binary64))))
(+.f64 (fma.f64 #s(literal 1 binary64) eps (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal -1 binary64)))) (fma.f64 (sin.f64 eps) #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal -1 binary64))))
(+.f64 (fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) eps) (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal -1 binary64)))) (fma.f64 (sin.f64 eps) #s(literal -1 binary64) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) #s(literal -1 binary64))))
(-.f64 eps (sin.f64 eps))
(-.f64 eps (/.f64 (sin.f64 eps) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 (sin.f64 eps) eps))
(-.f64 (-.f64 #s(literal 0 binary64) (sin.f64 eps)) (-.f64 #s(literal 0 binary64) eps))
(-.f64 (+.f64 eps #s(literal 0 binary64)) (sin.f64 eps))
(fma.f64 eps #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))
(fma.f64 eps #s(literal 1 binary64) (neg.f64 (/.f64 (sin.f64 eps) #s(literal 1 binary64))))
(fma.f64 (sin.f64 eps) #s(literal -1 binary64) eps)
(fma.f64 #s(literal 1 binary64) eps (-.f64 #s(literal 0 binary64) (sin.f64 eps)))
(fma.f64 #s(literal 1 binary64) eps (neg.f64 (/.f64 (sin.f64 eps) #s(literal 1 binary64))))
(fma.f64 #s(literal -1 binary64) (sin.f64 eps) eps)
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (sin.f64 eps)))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) eps) (neg.f64 (/.f64 (sin.f64 eps) #s(literal 1 binary64))))
(neg.f64 (-.f64 (sin.f64 eps) eps))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 eps (sin.f64 eps))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 eps) eps)))
(/.f64 (-.f64 (sin.f64 eps) eps) #s(literal -1 binary64))
(/.f64 (-.f64 eps (sin.f64 eps)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (sin.f64 eps))) #s(literal -1 binary64))
(pow.f64 (-.f64 eps (sin.f64 eps)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 eps (sin.f64 eps)))
(*.f64 #s(literal -1 binary64) (-.f64 (sin.f64 eps) eps))
(*.f64 (-.f64 (sin.f64 eps) eps) #s(literal -1 binary64))
(*.f64 (-.f64 eps (sin.f64 eps)) #s(literal 1 binary64))
(exp.f64 (*.f64 (log.f64 (-.f64 (sin.f64 eps) eps)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (-.f64 eps (sin.f64 eps))))
(neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (sin.f64 eps))))
(/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 eps) eps))
(/.f64 #s(literal -1 binary64) (-.f64 eps (sin.f64 eps)))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 eps) eps)) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (sin.f64 eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 eps) eps)) #s(literal 1 binary64))
(pow.f64 (-.f64 (sin.f64 eps) eps) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 eps) eps)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 eps (sin.f64 eps))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sin.f64 eps) eps)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (sin.f64 eps))) #s(literal -1 binary64))

simplify325.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

3496×	`-lowering-.f32`
3496×	`-lowering-.f64`
2302×	`+-lowering-+.f64`
2302×	`+-lowering-+.f32`
1544×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	494	2974
1	1565	2596
2	5027	2492
0	8204	2492

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
-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)))))
(/ -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 (pow eps 2))
(/ (- (* 9/40 (pow eps 2)) 1/2) (pow eps 2))
(/ (- (* 9/40 (pow eps 2)) 1/2) (pow eps 2))
(/ (- (* 9/40 (pow eps 2)) 1/2) (pow eps 2))
9/40
(- 9/40 (* 1/2 (/ 1 (pow eps 2))))
(- 9/40 (* 1/2 (/ 1 (pow eps 2))))
(- 9/40 (* 1/2 (/ 1 (pow eps 2))))
9/40
(- 9/40 (* 1/2 (/ 1 (pow eps 2))))
(- 9/40 (* 1/2 (/ 1 (pow eps 2))))
(- 9/40 (* 1/2 (/ 1 (pow eps 2))))
(/ -1/2 (pow eps 2))
(/ -1/2 (pow eps 2))
(/ -1/2 (pow eps 2))
(/ -1/2 (pow eps 2))
(/ -1/2 (pow eps 2))
(/ -1/2 (pow eps 2))
(/ -1/2 (pow eps 2))
(/ -1/2 (pow eps 2))
(/ -1/2 (pow eps 2))
(/ -1/2 (pow eps 2))
(/ -1/2 (pow eps 2))
(/ -1/2 (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)
1
(+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (+ (/ (sin eps) (* eps (cos eps))) (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2)))))) (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (+ (/ (sin eps) (* eps (cos eps))) (+ (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))) (/ (pow (sin eps) 3) (* (pow eps 3) (pow (cos eps) 3))))))) (+ (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps))) (/ (pow (sin eps) 3) (* (pow eps 3) (pow (cos eps) 2)))))
1
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (+ (* -1 (/ (pow (sin eps) 2) (* eps (pow (cos eps) 2)))) (/ (pow (sin eps) 2) (* eps (cos eps))))) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (+ (* -1 (/ (pow (sin eps) 3) (* eps (pow (cos eps) 2)))) (/ (pow (sin eps) 3) (* eps (pow (cos eps) 3)))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (cos eps)))) eps))) (/ (sin eps) (cos eps))) eps)))
(/ 3 (pow eps 2))
(/ (+ 3 (* -17/10 (pow eps 2))) (pow eps 2))
(/ (+ 3 (* (pow eps 2) (- (* 307/1400 (pow eps 2)) 17/10))) (pow eps 2))
(/ (+ 3 (* (pow eps 2) (- (* (pow eps 2) (+ 307/1400 (* -1247/126000 (pow eps 2)))) 17/10))) (pow eps 2))
(* -1 (/ (sin eps) eps))
(/ (+ (* -1 (sin eps)) (* -1 (/ (pow (sin eps) 2) (* eps (cos eps))))) eps)
(/ (- (+ (* -1 (sin eps)) (* -1 (/ (pow (sin eps) 3) (* (pow eps 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps)
(/ (- (+ (* -1 (sin eps)) (* -1 (/ (pow (sin eps) 4) (* (pow eps 3) (pow (cos eps) 3))))) (+ (/ (pow (sin eps) 2) (* eps (cos eps))) (/ (pow (sin eps) 3) (* (pow eps 2) (pow (cos eps) 2))))) eps)
(* -1 (/ (sin eps) eps))
(* -1 (/ (+ (sin eps) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))
(* -1 (/ (+ (sin eps) (* -1 (/ (- (* -1 (/ (pow (sin eps) 3) (* eps (pow (cos eps) 2)))) (/ (pow (sin eps) 2) (cos eps))) eps))) eps))
(* -1 (/ (+ (sin eps) (* -1 (/ (- (* -1 (/ (- (/ (pow (sin eps) 4) (* eps (pow (cos eps) 3))) (* -1 (/ (pow (sin eps) 3) (pow (cos eps) 2)))) eps)) (/ (pow (sin eps) 2) (cos eps))) eps))) eps))
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) (+ 1/3 (* 2/15 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))
(* (pow eps 3) (+ 1/3 (* (pow eps 2) (+ 2/15 (* (pow eps 2) (+ 17/315 (* 62/2835 (pow eps 2))))))))
(* -1 eps)
(* eps (- (/ (sin eps) (* eps (cos eps))) 1))
(* eps (- (/ (sin eps) (* eps (cos eps))) 1))
(* eps (- (/ (sin eps) (* eps (cos eps))) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps)))))))
(* -1 (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps)))))))
(* -1 (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos 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)
(* -1/362880 (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 eps)
(* eps (+ 1/6 (* -1/120 (pow eps 2))))
(* eps (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* eps (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(* -1/362880 (pow eps 7))
(* (pow eps 7) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(* (pow eps 7) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* (pow eps 7) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* -1/362880 (pow eps 7))
(* -1 (* (pow eps 7) (- 1/362880 (* 1/5040 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (* 1/5040 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))))))
1/6
(+ 1/6 (* -1/120 (pow eps 2)))
(+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120)))
(+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120)))
(* -1/362880 (pow eps 6))
(* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* (pow eps 6) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* -1/362880 (pow eps 6))
(* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* (pow eps 6) (- (+ (* 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) (/ (sin eps) (cos eps))) eps)))
(+ 1 (+ (* -1 (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* (pow eps 2) (cos eps)))) (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps))))
(+ 1 (+ (* -1 (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* (pow eps 3) (pow (cos eps) 2)))) (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) 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)))
(/ 3 (pow eps 3))
(/ (+ 3 (* -6/5 (pow eps 2))) (pow eps 3))
(/ (+ 3 (* (pow eps 2) (- (* -1/175 (pow eps 2)) 6/5))) (pow eps 3))
(/ (+ 3 (* (pow eps 2) (- (* (pow eps 2) (- (* -2/7875 (pow eps 2)) 1/175)) 6/5))) (pow eps 3))
(/ -1 eps)
(/ (- (* -1 (/ (sin eps) (* eps (cos eps)))) 1) 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))) (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2)))))) eps)
(/ -1 eps)
(* -1 (/ (+ 1 (/ (sin eps) (* eps (cos eps)))) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow (sin eps) 2) (* eps (pow (cos eps) 2)))) (/ (sin eps) (cos eps))) eps))) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow (sin eps) 3) (* eps (pow (cos eps) 3))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (/ (sin eps) (cos eps))) eps))) eps))
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))
(/ 3 (pow eps 2))
(/ (+ 3 (* -6/5 (pow eps 2))) (pow eps 2))
(/ (+ 3 (* (pow eps 2) (- (* -1/175 (pow eps 2)) 6/5))) (pow eps 2))
(/ (+ 3 (* (pow eps 2) (- (* (pow eps 2) (- (* -2/7875 (pow eps 2)) 1/175)) 6/5))) (pow eps 2))
-1
(- (* -1 (/ (sin eps) (* eps (cos eps)))) 1)
(- (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2)))) (+ 1 (/ (sin eps) (* eps (cos eps)))))
(- (* -1 (/ (pow (sin eps) 3) (* (pow eps 3) (pow (cos eps) 3)))) (+ 1 (+ (/ (sin eps) (* eps (cos eps))) (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))
-1
(- (* -1 (/ (sin eps) (* eps (cos eps)))) 1)
(- (* -1 (/ (- (/ (pow (sin eps) 2) (* eps (pow (cos eps) 2))) (* -1 (/ (sin eps) (cos 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)
(* -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 (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 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)))
(/ -6 (pow eps 3))
(/ (- (* -3/10 (pow eps 2)) 6) (pow eps 3))
(/ (- (* (pow eps 2) (- (* -11/1400 (pow eps 2)) 3/10)) 6) (pow eps 3))
(/ (- (* (pow eps 2) (- (* (pow eps 2) (- (* -17/126000 (pow eps 2)) 11/1400)) 3/10)) 6) (pow eps 3))
(/ -1 eps)
(/ (- (* -1 (/ (sin eps) eps)) 1) eps)
(/ (- (* -1 (/ (pow (sin eps) 2) (pow eps 2))) (+ 1 (/ (sin eps) eps))) eps)
(/ (- (* -1 (/ (pow (sin eps) 3) (pow eps 3))) (+ 1 (+ (/ (sin eps) eps) (/ (pow (sin eps) 2) (pow eps 2))))) eps)
(/ -1 eps)
(* -1 (/ (+ 1 (/ (sin eps) eps)) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow (sin eps) 2) eps)) (sin eps)) eps))) eps))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow (sin eps) 3) eps) (* -1 (pow (sin eps) 2))) eps)) (sin eps)) eps))) 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)))
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(- (* 9/40 (pow eps 2)) 1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(* 9/40 (pow eps 2))
(.f64 #s(literal 9/40 binary64) (.f64 eps eps))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(/ -1/2 eps)
(/.f64 #s(literal -1/2 binary64) eps)
(/ (- (* 9/40 (pow eps 2)) 1/2) eps)
(/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps))) eps)
(/ (- (* 9/40 (pow eps 2)) 1/2) eps)
(/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps))) eps)
(/ (- (* 9/40 (pow eps 2)) 1/2) eps)
(/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps))) eps)
(* 9/40 eps)
(*.f64 #s(literal 9/40 binary64) eps)
(* eps (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(* eps (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(* eps (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 eps (+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(* 9/40 eps)
(*.f64 #s(literal 9/40 binary64) eps)
(* -1 (* eps (- (* 1/2 (/ 1 (pow eps 2))) 9/40)))
(.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) #s(literal -9/40 binary64)) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (- (* 1/2 (/ 1 (pow eps 2))) 9/40)))
(.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) #s(literal -9/40 binary64)) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (- (* 1/2 (/ 1 (pow eps 2))) 9/40)))
(.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) #s(literal -9/40 binary64)) (-.f64 #s(literal 0 binary64) eps))
(/ -1/2 (pow eps 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(/ (- (* 9/40 (pow eps 2)) 1/2) (pow eps 2))
(+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(/ (- (* 9/40 (pow eps 2)) 1/2) (pow eps 2))
(+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(/ (- (* 9/40 (pow eps 2)) 1/2) (pow eps 2))
(+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
9/40
#s(literal 9/40 binary64)
(- 9/40 (* 1/2 (/ 1 (pow eps 2))))
(+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(- 9/40 (* 1/2 (/ 1 (pow eps 2))))
(+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(- 9/40 (* 1/2 (/ 1 (pow eps 2))))
(+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
9/40
#s(literal 9/40 binary64)
(- 9/40 (* 1/2 (/ 1 (pow eps 2))))
(+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(- 9/40 (* 1/2 (/ 1 (pow eps 2))))
(+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(- 9/40 (* 1/2 (/ 1 (pow eps 2))))
(+.f64 #s(literal 9/40 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(/ -1/2 (pow eps 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(/ -1/2 (pow eps 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(/ -1/2 (pow eps 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(/ -1/2 (pow eps 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(/ -1/2 (pow eps 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(/ -1/2 (pow eps 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(/ -1/2 (pow eps 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(/ -1/2 (pow eps 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(/ -1/2 (pow eps 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(/ -1/2 (pow eps 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(/ -1/2 (pow eps 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
(/ -1/2 (pow eps 2))
(/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))
-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 (.f64 eps eps) (+.f64 #s(literal -27/2800 binary64) (.f64 (.f64 eps eps) #s(literal 27/112000 binary64)))))))
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (sin eps) (* eps (cos eps)))))
(+.f64 (/.f64 (sin.f64 eps) (*.f64 eps (cos.f64 eps))) (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (+ (/ (sin eps) (* eps (cos eps))) (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2)))))) (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps))))
(+.f64 #s(literal 1 binary64) (+.f64 (/.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) (/.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (.f64 eps (cos.f64 eps)))) (-.f64 #s(literal 0 binary64) eps))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (+ (/ (sin eps) (* eps (cos eps))) (+ (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))) (/ (pow (sin eps) 3) (* (pow eps 3) (pow (cos eps) 3))))))) (+ (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps))) (/ (pow (sin eps) 3) (* (pow eps 3) (pow (cos eps) 2)))))
(+.f64 (+.f64 (/.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) (-.f64 (/.f64 (pow.f64 (/.f64 (sin.f64 eps) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 3 binary64))) (/.f64 (sin.f64 eps) eps))) (-.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (.f64 eps (*.f64 eps (cos.f64 eps)))) (/.f64 (pow.f64 (/.f64 (sin.f64 eps) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sin.f64 eps) (/.f64 (sin.f64 eps) (cos.f64 eps))) eps))
(+ 1 (* -1 (/ (- (+ (sin eps) (+ (* -1 (/ (pow (sin eps) 2) (* eps (pow (cos eps) 2)))) (/ (pow (sin eps) 2) (* eps (cos eps))))) (/ (sin eps) (cos eps))) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sin.f64 eps) (-.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) eps) (/.f64 (sin.f64 eps) (cos.f64 eps)))) eps))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (+ (* -1 (/ (pow (sin eps) 3) (* eps (pow (cos eps) 2)))) (/ (pow (sin eps) 3) (* eps (pow (cos eps) 3)))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (/ (pow (sin eps) 2) (cos eps)))) eps))) (/ (sin eps) (cos eps))) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 (sin.f64 eps) (/.f64 (+.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 3 binary64)) (.f64 eps (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (-.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps)))) eps)) (/.f64 (sin.f64 eps) (cos.f64 eps))) eps))
(/ 3 (pow eps 2))
(/.f64 #s(literal 3 binary64) (*.f64 eps eps))
(/ (+ 3 (* -17/10 (pow eps 2))) (pow eps 2))
(/.f64 (+.f64 #s(literal 3 binary64) (.f64 (.f64 eps eps) #s(literal -17/10 binary64))) (*.f64 eps eps))
(/ (+ 3 (* (pow eps 2) (- (* 307/1400 (pow eps 2)) 17/10))) (pow eps 2))
(/.f64 (+.f64 #s(literal 3 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -17/10 binary64) (.f64 (.f64 eps eps) #s(literal 307/1400 binary64))))) (*.f64 eps eps))
(/ (+ 3 (* (pow eps 2) (- (* (pow eps 2) (+ 307/1400 (* -1247/126000 (pow eps 2)))) 17/10))) (pow eps 2))
(/.f64 (+.f64 #s(literal 3 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal -17/10 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 307/1400 binary64) (.f64 eps (.f64 eps #s(literal -1247/126000 binary64))))))))) (*.f64 eps eps))
(* -1 (/ (sin eps) eps))
(-.f64 #s(literal 0 binary64) (/.f64 (sin.f64 eps) eps))
(/ (+ (* -1 (sin eps)) (* -1 (/ (pow (sin eps) 2) (* eps (cos eps))))) eps)
(/.f64 (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (*.f64 eps (cos.f64 eps)))) (-.f64 #s(literal 0 binary64) eps))
(/ (- (+ (* -1 (sin eps)) (* -1 (/ (pow (sin eps) 3) (* (pow eps 2) (pow (cos eps) 2))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps)
(/.f64 (-.f64 (/.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 eps (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (cos.f64 eps))) eps) (sin.f64 eps)) eps)
(/ (- (+ (* -1 (sin eps)) (* -1 (/ (pow (sin eps) 4) (* (pow eps 3) (pow (cos eps) 3))))) (+ (/ (pow (sin eps) 2) (* eps (cos eps))) (/ (pow (sin eps) 3) (* (pow eps 2) (pow (cos eps) 2))))) eps)
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eps
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(* 1/6 (pow eps 3))
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(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
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(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
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(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
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(*.f64 #s(literal -1/362880 binary64) (pow.f64 eps #s(literal 9 binary64)))
(* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
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(* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
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(* -1/362880 (pow eps 9))
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(* 1/6 eps)
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(* eps (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
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-1/2
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eps
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eps
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eps
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eval203.0ms (1.2%)

Compiler: Compiled 38633 to 2768 computations (92.8% saved)

prune141.0ms (0.8%)

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	1486	1	1487
Fresh	0	0	0
Picked	0	4	4
Done	0	5	5
Total	1486	10	1496

Accuracy

100.0%

Counts

1496 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	1.1%	(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (/.f64 #s(literal -1 binary64) (-.f64 eps (sin.f64 eps))))
✓	1.1%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
✓	1.2%	(/.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 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 eps)) (-.f64 eps (tan.f64 eps)))
✓	1.2%	(-.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 (tan.f64 eps) 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))
✓	99.7%	(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
▶	99.1%	(*.f64 eps (/.f64 #s(literal -1/2 binary64) eps))
✓	55.2%	(.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 132 to 85 computations (35.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal -1/2 binary64) eps)
✓	cost-diff	256	(*.f64 eps (/.f64 #s(literal -1/2 binary64) eps))

Rules

6×	`*-commutative`
4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`associate-/l*`
2×	`*-inverses`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	4	14
1	7	14
2	9	14
3	11	6
4	13	6
5	15	6
0	15	6

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* eps (/ -1/2 eps))
eps
(/ -1/2 eps)
-1/2

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

localize22.0ms (0.1%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal -1/2 binary64) eps)
✓	accuracy	99.8%	(*.f64 eps (/.f64 #s(literal -1/2 binary64) eps))

Results

17.0ms

256×

valid

Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 3.0ms (58.2% of total)

ival-mult: 2.0ms (38.8% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series1.0ms (0%)

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (* eps (/ -1/2 eps))>
#<alt (/ -1/2 eps)>

Outputs
#<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)>

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	eps	@	inf	(/ -1/2 eps)
0.0ms	eps	@	-inf	(/ -1/2 eps)
0.0ms	eps	@	0	(/ -1/2 eps)
0.0ms	eps	@	0	(* eps (/ -1/2 eps))
0.0ms	eps	@	inf	(* eps (/ -1/2 eps))

rewrite123.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

636×	`sum3-define`
510×	`+-lowering-+.f64`
510×	`+-lowering-+.f32`
414×	`--lowering--.f32`
414×	`--lowering--.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	16	8
2	67	4
3	251	4
4	550	4
5	1041	4
0	3243	4

Stop Event

1×	iter limit
1×	iter limit
1×	node limit

Counts

2 → 54

Calls

Call 1

Inputs
(* eps (/ -1/2 eps))
(/ -1/2 eps)

Outputs
#s(literal -1/2 binary64)
(+.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/2 binary64) eps))
(exp.f64 (log.f64 (/.f64 #s(literal -1/2 binary64) eps)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (/.f64 eps #s(literal -1/2 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1/2 binary64) eps))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) eps) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1/2 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) eps) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) eps) #s(literal -1 binary64) #s(literal 0 binary64))
(neg.f64 (/.f64 #s(literal 1/2 binary64) eps))
(/.f64 #s(literal -1/2 binary64) eps)
(/.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 1 binary64))
(/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) eps))
(/.f64 #s(literal 1 binary64) (/.f64 eps #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -2 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) eps) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) eps) (pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -2 binary64)))))
(/.f64 #s(literal -1 binary64) (/.f64 eps #s(literal 1/2 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 2 binary64))
(/.f64 (/.f64 #s(literal -1 binary64) eps) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1/2 binary64) eps) #s(literal -1 binary64))
(/.f64 (/.f64 #s(literal 1/2 binary64) eps) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))) (/.f64 eps #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -2 binary64))) eps)
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) eps))))
(pow.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 1 binary64))
(pow.f64 (/.f64 eps #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (E.f64) (log.f64 (/.f64 #s(literal -1/2 binary64) eps)))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 eps #s(literal -1/2 binary64))))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal 1 binary64)) (log.f64 (/.f64 eps #s(literal -1/2 binary64))))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal -1/2 binary64) eps)))
(*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) eps))
(*.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) eps))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) eps))
(*.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1/2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) eps) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) eps) (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -2 binary64)))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) eps))
(*.f64 (/.f64 #s(literal -1 binary64) eps) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) eps) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) eps) (exp.f64 (.f64 #s(literal -1 binary64) (log.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal 1/2 binary64) eps) #s(literal -1 binary64))
(*.f64 (/.f64 #s(literal 1/2 binary64) eps) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) eps))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal -2 binary64))) (/.f64 #s(literal 1 binary64) eps))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) eps))
(*.f64 (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 #s(literal -2 binary64)))) (/.f64 #s(literal 1 binary64) eps))
(.f64 (exp.f64 (.f64 #s(literal -1 binary64) (log.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) eps))

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`/-lowering-/.f32`
2×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	48
0	3	48

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
-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)

Outputs
-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)
(/.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)
(/.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)
(/.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)

eval9.0ms (0.1%)

Compiler: Compiled 537 to 145 computations (73% saved)

prune11.0ms (0.1%)

Pruning

10 alts after pruning (0 fresh and 10 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	0	0
Picked	0	1	1
Done	0	9	9
Total	78	10	88

Accuracy

100.0%

Counts

88 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	1.1%	(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (/.f64 #s(literal -1 binary64) (-.f64 eps (sin.f64 eps))))
✓	1.1%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
✓	1.2%	(/.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 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 eps)) (-.f64 eps (tan.f64 eps)))
✓	1.2%	(-.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 (tan.f64 eps) 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))
✓	99.7%	(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
✓	99.1%	(*.f64 eps (/.f64 #s(literal -1/2 binary64) eps))
✓	55.2%	(.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 285 to 147 computations (48.4% saved)

regimes17.0ms (0.1%)

Counts

11 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(*.f64 eps (/.f64 #s(literal -1/2 binary64) eps))
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #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 eps (+.f64 #s(literal 9/40 binary64) (.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 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)))
(/.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 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 eps)) (-.f64 eps (tan.f64 eps)))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (/.f64 #s(literal -1 binary64) (-.f64 eps (sin.f64 eps))))
(-.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 (tan.f64 eps) 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:

13.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
4.0ms	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)

regimes3.0ms (0%)

Counts

5 → 1

Calls

Call 1

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

2.0ms

eps

Results

Accuracy	Segments	Branch
99.8%	1	`eps`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

eps

Results

Accuracy	Segments	Branch
99.7%	1	`eps`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Accuracy

Total -0.1b remaining (-24%)

Threshold costs -0.1b (-24%)

Counts

2 → 1

Calls

Call 1

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

Outputs
#s(literal -1/2 binary64)

Calls

1 calls:

3.0ms

eps

Results

Accuracy	Segments	Branch
99.3%	1	`eps`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0%)

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)

soundness353.0ms (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	6919	432
0	8081	432

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 66 to 39 computations (40.9% saved)

preprocess42.0ms (0.2%)

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

analyze557.0ms (3.2%)

sample9.3s (53.1%)

preprocess94.0ms (0.5%)

explain622.0ms (3.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify51.0ms (0.3%)

localize305.0ms (1.7%)

series4.0ms (0%)

rewrite307.0ms (1.7%)

simplify279.0ms (1.6%)

eval41.0ms (0.2%)

prune51.0ms (0.3%)

simplify223.0ms (1.3%)

localize1.5s (8.6%)

series15.0ms (0.1%)

rewrite804.0ms (4.6%)

simplify559.0ms (3.2%)

eval162.0ms (0.9%)

prune91.0ms (0.5%)

simplify154.0ms (0.9%)

localize875.0ms (5%)

series17.0ms (0.1%)

rewrite263.0ms (1.5%)

simplify325.0ms (1.8%)

eval203.0ms (1.2%)

prune141.0ms (0.8%)

simplify4.0ms (0%)

localize22.0ms (0.1%)

series1.0ms (0%)

rewrite123.0ms (0.7%)

simplify5.0ms (0%)

eval9.0ms (0.1%)

prune11.0ms (0.1%)

regimes17.0ms (0.1%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes4.0ms (0%)

simplify7.0ms (0%)

soundness353.0ms (2%)

preprocess42.0ms (0.2%)

end0.0ms (0%)

Profiling