Metrics for sintan (problem 3.4.5)

analyze577.0ms (4.2%)

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: 321.0ms

...c/correct-round.rkt:119:19: 151.0ms (47% of total)

ival-sub: 44.0ms (13.7% of total)

ival-sin: 42.0ms (13.1% of total)

ival-<=: 33.0ms (10.3% of total)

ival-tan: 28.0ms (8.7% of total)

ival-div: 14.0ms (4.4% of total)

ival-and: 7.0ms (2.2% of total)

backward-pass: 2.0ms (0.6% of total)

sample9.1s (66.6%)

Results

6.0s	4110×	2	valid
1.8s	1293×	3	valid
848.0ms	2758×	1	valid
14.0ms	95×	0	valid

Precisions

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

ival-tan: 4.4s (54.3% of total)

ival-sin: 2.4s (30.4% of total)

backward-pass: 372.0ms (4.6% of total)

ival-sub: 317.0ms (3.9% of total)

...c/correct-round.rkt:119:19: 283.0ms (3.5% of total)

ival-div: 138.0ms (1.7% of total)

ival-<=: 102.0ms (1.3% of total)

ival-and: 16.0ms (0.2% of total)

Bogosity

preprocess97.0ms (0.7%)

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	41	30
2	94	27
3	278	27
4	729	27
5	1562	27
6	2756	27
7	2794	27
8	3163	27
9	3179	27
0	6	9
1	15	9
2	25	9
3	44	9
4	83	9
5	192	9
6	515	9
7	1106	9
8	2356	9
9	2548	9
10	2567	9
11	2575	9
0	2575	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 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) 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)))
(/ (- eps (fast-sin eps)) (- eps (fast-tan eps)))
(/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps))))
(/ (- eps (fast-sin eps)) (- eps (fast-tan eps)))
(neg (/ (- (neg eps) (sin (neg eps))) (- (neg eps) (tan (neg eps)))))
(/ (- eps (fast-sin eps)) (- (fast-tan eps) eps))

Symmetry

(abs eps)

explain635.0ms (4.6%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
159	0	-	2	(1.01373580920723e-103)	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`
99	0	-	0	-	`(-.f64 eps (sin.f64 eps))`
99	1	(2.4320288414483705e-108)	0	-	`(-.f64 eps (tan.f64 eps))`
0	0	-	0	-	`(sin.f64 eps)`
0	0	-	0	-	`eps`
0	0	-	0	-	`(tan.f64 eps)`

Results

435.0ms	248×	2	valid
90.0ms	70×	3	valid
55.0ms	188×	1	valid
1.0ms	6×	0	valid

Compiler

Compiled 58 to 20 computations (65.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 498.0ms

ival-tan: 301.0ms (60.4% of total)

ival-sin: 148.0ms (29.7% of total)

backward-pass: 23.0ms (4.6% of total)

ival-sub: 19.0ms (3.8% 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
▶	1.7%	(/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

518×	`fnmadd-define`
412×	`fnmsub-define`
406×	`fmsub-define`
352×	`fma-lowering-fma.f32`
352×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
1	14	22
2	22	22
3	40	22
4	80	22
5	190	22
6	581	22
7	1313	22
8	1990	22
9	2163	22
10	2182	22
11	2190	22
0	2190	22

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize460.0ms (3.4%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	66.3%	(-.f64 (sin.f64 eps) eps)
✓	accuracy	66.3%	(-.f64 (tan.f64 eps) eps)
✓	accuracy	38.9%	(/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps))

Results

356.0ms	124×	2	valid
46.0ms	35×	3	valid
45.0ms	94×	1	valid
0.0ms	3×	0	valid

Compiler

Compiled 24 to 7 computations (70.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 408.0ms

ival-tan: 241.0ms (59.1% of total)

ival-sin: 125.0ms (30.6% of total)

backward-pass: 29.0ms (7.1% of total)

ival-sub: 8.0ms (2% of total)

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

const: 0.0ms (0% of total)

series4.0ms (0%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/ (- (sin eps) eps) (- (tan eps) eps))>
#<alt (- (sin eps) eps)>
#<alt (sin eps)>
#<alt (- (tan eps) 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) (- (* 1/120 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (+ 1/120 (* (pow eps 2) (- (* 1/362880 (pow eps 2)) 1/5040)))) 1/6))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (sin eps) eps) 1))>
#<alt (* eps (- (/ (sin eps) eps) 1))>
#<alt (* eps (- (/ (sin eps) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (sin eps) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (sin eps) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (sin 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)))))))>

Calls

12 calls:

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

rewrite833.0ms (6.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3744×	`-lowering-.f32`
3744×	`-lowering-.f64`
3442×	`/-lowering-/.f32`
3442×	`/-lowering-/.f64`
1594×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
1	47	19
2	416	19
3	6351	19
0	8631	19

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 372

Calls

Call 1

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

Outputs
(+.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (tan.f64 eps) eps)) (fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps))) 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 0 binary64) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps))))) (/.f64 eps (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (*.f64 eps 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 0 binary64) (+.f64 eps (tan.f64 eps))) (/.f64 eps (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (*.f64 eps eps))) (/.f64 eps (-.f64 (tan.f64 eps) 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 #s(literal 1 binary64) (/.f64 eps (-.f64 eps (tan.f64 eps)))))
(+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (-.f64 #s(literal 0 binary64) eps)))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) (-.f64 #s(literal 0 binary64) eps)) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)))
(+.f64 (.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps)))) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps)))) (*.f64 eps (+.f64 eps (tan.f64 eps)))))
(+.f64 (.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps)))) (.f64 eps (+.f64 eps (tan.f64 eps)))) (.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (*.f64 eps eps)))) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))
(+.f64 (.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps)))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps))) (.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps)))) (.f64 eps (tan.f64 eps))))
(+.f64 (.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps))) eps) (.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps))) (tan.f64 eps)))
(+.f64 (.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps))) (tan.f64 eps)) (.f64 (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps))) eps))
(+.f64 (.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) #s(literal 1 binary64)) (.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 1 binary64)))
(+.f64 (.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (*.f64 eps eps))))))
(+.f64 (.f64 (.f64 eps (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (*.f64 eps eps))))))
(+.f64 (.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps)) (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))))) (.f64 (.f64 eps (tan.f64 eps)) (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))))))
(+.f64 (.f64 eps (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps)))) (.f64 (tan.f64 eps) (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps)))))
(+.f64 (.f64 (tan.f64 eps) (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps)))) (.f64 eps (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps)))))
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 (tan.f64 eps) eps) (-.f64 (sin.f64 eps) eps))) #s(literal -1 binary64)))
(-.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 (tan.f64 eps) eps)))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 eps (tan.f64 eps))) (/.f64 (-.f64 (sin.f64 eps) eps) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (-.f64 (+.f64 (.f64 eps (+.f64 eps (sin.f64 eps))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal 2 binary64)))))) (-.f64 (tan.f64 eps) eps)) (/.f64 (/.f64 (.f64 eps (.f64 eps eps)) (-.f64 (+.f64 (.f64 eps (+.f64 eps (sin.f64 eps))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal 2 binary64)))))) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 eps #s(literal 2 binary64))))) (+.f64 eps (sin.f64 eps))) (-.f64 (tan.f64 eps) eps)) (/.f64 (/.f64 (*.f64 eps eps) (+.f64 eps (sin.f64 eps))) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (.f64 (-.f64 (tan.f64 eps) eps) (-.f64 (+.f64 (.f64 eps (+.f64 eps (sin.f64 eps))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal 2 binary64))))))) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (-.f64 (tan.f64 eps) eps) (-.f64 (+.f64 (.f64 eps (+.f64 eps (sin.f64 eps))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal 2 binary64))))))))
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(/.f64 (.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 6 binary64)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 4 binary64)) (.f64 (.f64 eps eps) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps)))) (+.f64 eps (tan.f64 eps))))
(/.f64 (.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 4 binary64)) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps)) (+.f64 eps (tan.f64 eps))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (*.f64 eps (+.f64 eps (tan.f64 eps)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (*.f64 eps (+.f64 eps (tan.f64 eps)))))))
(/.f64 (neg.f64 (+.f64 (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (*.f64 eps eps))) (+.f64 eps (tan.f64 eps)))
(/.f64 (neg.f64 (+.f64 (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (*.f64 eps eps))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 eps (tan.f64 eps)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps))))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps))))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps)))))) (+.f64 (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps))))) (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps)))))) (.f64 (/.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps))))) (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (*.f64 eps (+.f64 eps (tan.f64 eps)))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (+.f64 eps (tan.f64 eps))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 eps eps) (+.f64 eps (tan.f64 eps))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (+.f64 eps (tan.f64 eps))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (+.f64 eps (tan.f64 eps)))) (+.f64 (.f64 (/.f64 (.f64 eps eps) (+.f64 eps (tan.f64 eps))) (/.f64 (.f64 eps eps) (+.f64 eps (tan.f64 eps)))) (.f64 (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (+.f64 eps (tan.f64 eps))) (/.f64 (*.f64 eps eps) (+.f64 eps (tan.f64 eps)))))))
(/.f64 (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (-.f64 (-.f64 #s(literal 0 binary64) eps) (tan.f64 eps)))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps))))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps)))))) (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps))))) (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps))))))) (+.f64 (/.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps))))) (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps)))))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (+.f64 eps (tan.f64 eps))) (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (+.f64 eps (tan.f64 eps)))) (.f64 (/.f64 (.f64 eps eps) (+.f64 eps (tan.f64 eps))) (/.f64 (.f64 eps eps) (+.f64 eps (tan.f64 eps))))) (+.f64 (/.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (+.f64 eps (tan.f64 eps))) (/.f64 (*.f64 eps eps) (+.f64 eps (tan.f64 eps)))))
(/.f64 (.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 9 binary64)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps)))))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (*.f64 eps eps)))) (pow.f64 (tan.f64 eps) #s(literal 6 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 6 binary64)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps)))))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (*.f64 eps eps))))
(/.f64 (.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 6 binary64)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 4 binary64)) (.f64 (.f64 eps eps) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (*.f64 eps eps)))))
(/.f64 (.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 4 binary64)) (.f64 eps (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps)) #s(literal -1 binary64))
(*.f64 (-.f64 (tan.f64 eps) eps) #s(literal 1 binary64))
(.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps))))))
(.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 (-.f64 #s(literal 0 binary64) eps) (tan.f64 eps))))))
(.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps))))) #s(literal 1 binary64)))
(.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps)))) (/.f64 (-.f64 (tan.f64 eps) eps) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (*.f64 eps (+.f64 eps (tan.f64 eps))))))
(.f64 (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps)))) (.f64 (-.f64 (tan.f64 eps) eps) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps)))))))
(*.f64 #s(literal 1 binary64) (-.f64 (tan.f64 eps) eps))
(.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))))
(.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))) #s(literal 1 binary64)))
(*.f64 (+.f64 eps (tan.f64 eps)) (/.f64 (-.f64 (tan.f64 eps) eps) (+.f64 eps (tan.f64 eps))))
(.f64 (+.f64 eps (tan.f64 eps)) (.f64 (-.f64 (tan.f64 eps) eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))))
(*.f64 #s(literal -1 binary64) (-.f64 eps (tan.f64 eps)))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps)))))))
(.f64 (+.f64 (neg.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 eps (tan.f64 eps)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps (+.f64 eps (tan.f64 eps))))) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps)))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps)) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (*.f64 eps eps))) (-.f64 (tan.f64 eps) eps))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 6 binary64)) (pow.f64 (.f64 eps (+.f64 eps (tan.f64 eps))) #s(literal 3 binary64)))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 4 binary64)) (.f64 (.f64 eps (+.f64 eps (tan.f64 eps))) (-.f64 (*.f64 eps (+.f64 eps (tan.f64 eps))) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps))) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 4 binary64)) (pow.f64 (.f64 eps (+.f64 eps (tan.f64 eps))) #s(literal 2 binary64)))) (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (*.f64 eps (+.f64 eps (tan.f64 eps)))))
(.f64 (/.f64 (-.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 3 binary64)) (.f64 eps (.f64 eps eps)))) (+.f64 (pow.f64 (tan.f64 eps) #s(literal 2 binary64)) (*.f64 eps (-.f64 eps (tan.f64 eps)))))

simplify287.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

4700×	`-lowering-.f32`
4700×	`-lowering-.f64`
1412×	`sum3-define`
1386×	`+-lowering-+.f64`
1386×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	543
1	445	476
2	1587	450
3	7166	448
0	8440	448

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) (- (* 1/120 (pow eps 2)) 1/6))
(* (pow eps 3) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))
(* (pow eps 3) (- (* (pow eps 2) (+ 1/120 (* (pow eps 2) (- (* 1/362880 (pow eps 2)) 1/5040)))) 1/6))
(* -1 eps)
(* eps (- (/ (sin eps) eps) 1))
(* eps (- (/ (sin eps) eps) 1))
(* eps (- (/ (sin eps) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (sin eps) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (sin eps) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (sin 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)))))))

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

eval77.0ms (0.6%)

Compiler: Compiled 12571 to 1216 computations (90.3% saved)

prune57.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	417	3	420
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	418	3	421

Accuracy

100.0%

Counts

421 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.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))
▶	99.8%	(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
▶	98.8%	#s(literal -1/2 binary64)

Status

Accuracy

Program

▶

100.0%

(+.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))

▶

99.8%

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

▶

98.8%

#s(literal -1/2 binary64)

Compiler

Compiled 24 to 17 computations (29.2% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Rules

118×	`fma-define`
104×	`fma-lowering-fma.f32`
104×	`fma-lowering-fma.f64`
76×	`-lowering-.f32`
76×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	50
1	31	47
2	80	47
3	140	47
4	158	47
5	162	47
6	164	47
0	164	47

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
-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)
eps
(+ 9/40 (* (* eps eps) -27/2800))
9/40
(* (* eps eps) -27/2800)
-27/2800
-1/2

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

localize130.0ms (1%)

Localize:

Found 7 expressions of interest:

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

Results

113.0ms

256×

valid

Compiler

Compiled 64 to 12 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

...c/correct-round.rkt:119:19: 37.0ms (61.7% of total)

ival-mult: 18.0ms (30% of total)

ival-add: 4.0ms (6.7% of total)

const: 0.0ms (0% of total)

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

series4.0ms (0%)

Counts

7 → 84

Calls

Call 1

Inputs
#<alt (+ (* 9/40 (* eps eps)) -1/2)>
#<alt (* 9/40 (* eps eps))>
#<alt (* eps eps)>
#<alt (+ (* (* eps eps) (+ 9/40 (* (* eps eps) -27/2800))) -1/2)>
#<alt (* (* eps eps) (+ 9/40 (* (* eps eps) -27/2800)))>
#<alt (+ 9/40 (* (* eps eps) -27/2800))>
#<alt (* (* eps eps) -27/2800)>

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

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	0	(+ (* 9/40 (* eps eps)) -1/2)
0.0ms	eps	@	inf	(+ (* (* eps eps) (+ 9/40 (* (* eps eps) -27/2800))) -1/2)
0.0ms	eps	@	inf	(* (* eps eps) (+ 9/40 (* (* eps eps) -27/2800)))
0.0ms	eps	@	inf	(+ (* 9/40 (* eps eps)) -1/2)
0.0ms	eps	@	inf	(* (* eps eps) -27/2800)

rewrite401.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4262×	`-lowering-.f32`
4262×	`-lowering-.f64`
2230×	`/-lowering-/.f32`
2230×	`/-lowering-/.f64`
1200×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	72	37
2	585	37
3	6898	37
0	8278	37

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 247

Calls

Call 1

Inputs
(+ (* 9/40 (* eps eps)) -1/2)
(* 9/40 (* eps eps))
(* eps eps)
(+ (* (* eps eps) (+ 9/40 (* (* eps eps) -27/2800))) -1/2)
(* (* eps eps) (+ 9/40 (* (* eps eps) -27/2800)))
(+ 9/40 (* (* eps eps) -27/2800))
(* (* eps eps) -27/2800)

Outputs
(+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))
(+.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) (+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) (+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (.f64 #s(literal 9/40 binary64) (.f64 eps eps)) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))) (/.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 9/40 binary64) (.f64 eps eps)))))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 #s(literal 9/40 binary64) eps) #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
(fma.f64 (*.f64 #s(literal 9/40 binary64) eps) eps #s(literal -1/2 binary64))
(neg.f64 (/.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps)))) #s(literal -1/8 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64)))))))
(neg.f64 (/.f64 (+.f64 (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) #s(literal 81/1600 binary64))) #s(literal -1/4 binary64)) (+.f64 (.f64 (.f64 eps eps) #s(literal -9/40 binary64)) #s(literal -1/2 binary64))))
(neg.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 729/64000 binary64) (.f64 eps (.f64 eps eps)))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) #s(literal 81/1600 binary64)) #s(literal -9/80 binary64))))))
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(.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)

simplify200.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

2482×	`-lowering-.f32`
2482×	`-lowering-.f64`
1766×	`/-lowering-/.f32`
1766×	`/-lowering-/.f64`
1722×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	520
1	76	422
2	181	422
3	474	400
4	1236	400
5	3267	400
0	8203	400

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

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)))))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(* 9/40 (pow eps 2))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -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
(+ 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))
(* -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))

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

eval67.0ms (0.5%)

Compiler: Compiled 12406 to 894 computations (92.8% saved)

prune53.0ms (0.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	367	0	367
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	367	3	370

Accuracy

100.0%

Counts

370 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

(+.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))

✓

99.8%

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

✓

98.8%

#s(literal -1/2 binary64)

Compiler

Compiled 64 to 36 computations (43.8% saved)

regimes5.0ms (0%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(+.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))

Calls

2 calls:

2.0ms	eps
2.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
100.0%	1	`eps`
100.0%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

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

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
99.8%	1	`eps`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)

Outputs
#s(literal -1/2 binary64)

Calls

1 calls:

1.0ms

eps

Results

Accuracy	Segments	Branch
98.8%	1	`eps`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
6×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	17	21

Stop Event

1×

saturated

Calls

Call 1

Inputs

(+.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))

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

soundness495.0ms (3.6%)

Rules

4700×	`-lowering-.f32`
4700×	`-lowering-.f64`
1412×	`sum3-define`
1386×	`+-lowering-+.f64`
1386×	`+-lowering-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	15	9
2	25	9
3	44	9
4	83	9
5	192	9
6	515	9
7	1106	9
8	2356	9
9	2548	9
10	2567	9
11	2575	9
0	2575	9
0	139	543
1	445	476
2	1587	450
3	7166	448
0	8440	448

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	saturated

Compiler

Compiled 76 to 46 computations (39.5% saved)

preprocess69.0ms (0.5%)

Remove: (abs eps)
Compiler: Compiled 196 to 114 computations (41.8% saved)

sintan (problem 3.4.5)

analyze577.0ms (4.2%)

sample9.1s (66.6%)

preprocess97.0ms (0.7%)

explain635.0ms (4.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify85.0ms (0.6%)

localize460.0ms (3.4%)

series4.0ms (0%)

rewrite833.0ms (6.1%)

simplify287.0ms (2.1%)

eval77.0ms (0.6%)

prune57.0ms (0.4%)

simplify11.0ms (0.1%)

localize130.0ms (1%)

series4.0ms (0%)

rewrite401.0ms (2.9%)

simplify200.0ms (1.5%)

eval67.0ms (0.5%)

prune53.0ms (0.4%)

regimes5.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify9.0ms (0.1%)

soundness495.0ms (3.6%)

preprocess69.0ms (0.5%)

end0.0ms (0%)

Profiling