Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
74.9%	0%	25.1%	1

Compiler

Compiled 71 to 33 computations (53.5% saved)

sample1.4s (27.1%)

Infinites

29.6% of outputs are infinite.

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify101.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1509×	`associate-/l*_binary64`
766×	`distribute-rgt-out_binary64`
744×	`distribute-lft-out_binary64`
549×	`unswap-sqr_binary64`
497×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	32	75
1	74	59
2	239	41
3	928	37
4	1549	37
5	3195	37
6	3534	37
7	3698	33
8	2289	33
9	2775	33
10	2823	33
11	4807	33
12	5324	33

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
▶	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Status

Error

Program

0.4b

(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))

▶

0.1b

(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 272 to 147 computations (46% saved)

localize25.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
✓	0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
✓	0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
✓	1.0b	(sqrt.f64 (PI.f64))

series33.0ms (0.6%)

Counts

4 → 36

Calls

4 calls:

17.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
10.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
6.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 (PI.f64))

rewrite61.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`add-exp-log_binary64`
78×	`add-cbrt-cube_binary64`
75×	`prod-exp_binary64`
53×	`pow1_binary64`
45×	`cbrt-unprod_binary64`

Counts

4 → 153

Calls

4 calls:

29.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
10.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 (PI.f64))

simplify123.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

504×	`associate-/l*_binary64`
471×	`fma-def_binary64`
345×	`associate-/r*_binary64`
331×	`unswap-sqr_binary64`
310×	`associate-r_binary64`

Counts

189 → 194

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	217	2646
1	396	2039
2	1372	1782
3	2977	1752
4	4619	1719
5	4996	1719
6	4891	1719

prune491.0ms (9.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	280	2	282
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	280	4	284

Error

0.0b

Counts

284 → 4

Alt Table

Status	Error	Program
	0.4b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	0.8b	(fabs.f64 (.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
▶	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (*.f64 (pow.f64 (fabs.f64 x) 3) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 20509 to 7363 computations (64.1% saved)

localize31.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
	0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
	0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
	1.0b	(sqrt.f64 (PI.f64))

prune446.0ms (8.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	238	4	242

Error

0.0b

Counts

242 → 4

Alt Table

Status	Error	Program
▶	0.4b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
	0.8b	(fabs.f64 (.f64 (/.f64 1 (expm1.f64 (log1p.f64 (sqrt.f64 (PI.f64))))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
✓	0.1b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (*.f64 (pow.f64 (fabs.f64 x) 3) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))

Compiler

Compiled 16417 to 7653 computations (53.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))
✓	0.1b	(*.f64 2/3 (pow.f64 x 3))
✓	0.2b	(/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64)))
	1.0b	(sqrt.f64 (PI.f64))

series14.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

8.0ms

(/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64)))

4.0ms

(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))

3.0ms

(*.f64 2/3 (pow.f64 x 3))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
12×	`associate-r_binary64`

Counts

3 → 84

Calls

3 calls:

11.0ms

(/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64)))

4.0ms

(*.f64 2/3 (pow.f64 x 3))

0.0ms

(fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))

simplify135.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-l_binary64`
610×	`associate-r_binary64`
285×	`log-prod_binary64`
262×	`fma-def_binary64`
184×	`swap-sqr_binary64`

Counts

108 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	3342
1	305	3139
2	796	3025
3	3438	3025
4	4851	3025
5	4876	3025

prune159.0ms (3.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	1	0	1
Picked	0	1	1
Done	2	0	2
Total	132	3	135

Error

Counts

135 → 3

Alt Table

Status	Error	Program
	0.1b	(fabs.f64 (+.f64 (.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5))) (+.f64 (.f64 2/3 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 3))) (+.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) x)) (.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 7)))))))
✓	0.4b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))
▶	0.1b	(fabs.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (.f64 2/3 (pow.f64 x 3)))) (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5))))))

Compiler

Compiled 4235 to 3128 computations (26.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5))))
✓	0.1b	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (.f64 2/3 (pow.f64 x 3))))
✓	0.1b	(*.f64 1/5 (pow.f64 x 5))
	0.1b	(*.f64 2/3 (pow.f64 x 3))

series27.0ms (0.5%)

Counts

3 → 24

Calls

3 calls:

15.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5))))
9.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (.f64 2/3 (pow.f64 x 3))))
3.0ms	(*.f64 1/5 (pow.f64 x 5))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
35×	`associate-l_binary64`
32×	`sqrt-prod_binary64`
26×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`

Counts

3 → 105

Calls

3 calls:

10.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5))))
7.0ms	(.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (.f64 2/3 (pow.f64 x 3))))
4.0ms	(*.f64 1/5 (pow.f64 x 5))

simplify129.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

679×	`fma-def_binary64`
459×	`associate-/l*_binary64`
435×	`sqr-pow_binary64`
350×	`*-commutative_binary64`
223×	`exp-prod_binary64`

Counts

129 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	3232
1	306	2800
2	896	2788
3	1648	2788
4	2477	2788
5	4448	2788
6	5098	2788

prune260.0ms (5.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	182	3	185

Error

Counts

185 → 3

Alt Table

Status	Error	Program
	0.1b	(fabs.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (.f64 2/3 (pow.f64 x 3)))) (+.f64 (.f64 1/5 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 5))) (.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (pow.f64 x 7))))))
✓	0.1b	(fabs.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (.f64 2/3 (pow.f64 x 3)))) (.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (.f64 1/5 (pow.f64 x 5))))))
✓	0.4b	(fabs.f64 (/.f64 (fma.f64 1/21 (pow.f64 x 7) (fma.f64 1/5 (pow.f64 x 5) (fma.f64 2 x (*.f64 2/3 (pow.f64 x 3))))) (sqrt.f64 (PI.f64))))

Compiler

Compiled 6945 to 5542 computations (20.2% saved)

regimes1.5s (29%)

Accuracy

Total 0.1b remaining (78.9%)

Threshold costs 0.1b (78.9%)

Counts

171 → 1

Compiler

Compiled 53591 to 32733 computations (38.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	47
1	31	47
2	30	47

end114.0ms (2.2%)

Compiler: Compiled 153 to 128 computations (16.3% saved)

Details

analyze1.0ms (0%)

sample1.4s (27.1%)

simplify101.0ms (2%)

prune6.0ms (0.1%)

localize25.0ms (0.5%)

series33.0ms (0.6%)

rewrite61.0ms (1.2%)

simplify123.0ms (2.4%)

prune491.0ms (9.6%)

localize31.0ms (0.6%)

prune446.0ms (8.8%)

localize13.0ms (0.3%)

series14.0ms (0.3%)

rewrite20.0ms (0.4%)

simplify135.0ms (2.6%)

prune159.0ms (3.1%)

localize15.0ms (0.3%)

series27.0ms (0.5%)

rewrite27.0ms (0.5%)

simplify129.0ms (2.5%)

prune260.0ms (5.1%)

regimes1.5s (29%)

simplify2.0ms (0%)

end114.0ms (2.2%)

Profiling