Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 70 to 33 computations (52.9% saved)

sample45.0ms (1.7%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify216.0ms (8.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	5050	41

prune9.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 2

Compiler

Compiled 119 to 75 computations (37% saved)

localize17.0ms (0.7%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 1/21 (pow.f64 x 6))
0.1b	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
0.0b	(+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4)))
0.0b	(/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64))
0.1b	(*.f64 1/21 (pow.f64 x 6))
0.1b	(*.f64 1/5 (pow.f64 x 4))
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)

rewrite27.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_3169`
19×	`add-exp-log_binary64_3185`
15×	`associate-r_binary64_3087`
13×	`add-cbrt-cube_binary64_3183`
12×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
10×	`pow1_binary64_3208`
9×	`prod-exp_binary64_3196` `associate-l_binary64_3088`
8×	`unpow-prod-down_binary64_3226`
7×	`unswap-sqr_binary64_3115`
5×	`cbrt-unprod_binary64_3180`
4×	`sqr-pow_binary64_3119` `add-log-exp_binary64_3186`
3×	`*-commutative_binary64_3078` `pow-prod-down_binary64_3218` `sqrt-prod_binary64_3163`
2×	`pow-exp_binary64_3215` `pow-to-exp_binary64_3216`
1×	`rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227`

Counts

4 → 82

Calls

8 calls:

6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 1/5 (pow.f64 x 4))
6.0ms	(*.f64 1/21 (pow.f64 x 6))
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64))

series101.0ms (3.9%)

Counts

4 → 9

Calls

4 calls:

38.0ms	(*.f64 1/21 (pow.f64 x 6))
32.0ms	(*.f64 1/5 (pow.f64 x 4))
30.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 468 to 402 computations (14.1% saved)

simplify53.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5031	773

prune159.0ms (6.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	90	3	93

Error

0.1b

Counts

93 → 3

Compiler

Compiled 2748 to 1858 computations (32.4% saved)

localize20.0ms (0.8%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 1/21 (pow.f64 x 6))
0.1b	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64)))))
0.0b	(+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4)))
0.0b	(/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))
0.1b	(*.f64 1/5 (pow.f64 x 4))
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite25.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_3169`
14×	`add-exp-log_binary64_3185`
11×	`add-cbrt-cube_binary64_3183` `pow1_binary64_3208`
10×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
8×	`associate-r_binary64_3087`
6×	`prod-exp_binary64_3196` `associate-l_binary64_3088` `sqrt-prod_binary64_3163`
4×	`unpow-prod-down_binary64_3226` `unswap-sqr_binary64_3115` `cbrt-unprod_binary64_3180` `add-log-exp_binary64_3186`
3×	`pow-prod-down_binary64_3218`
2×	`*-commutative_binary64_3078` `sqr-pow_binary64_3119` `rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227`
1×	`pow-exp_binary64_3215` `pow-to-exp_binary64_3216`

Counts

4 → 70

Calls

8 calls:

6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 1/5 (pow.f64 x 4))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))

series62.0ms (2.4%)

Counts

4 → 6

Calls

4 calls:

31.0ms	(*.f64 1/5 (pow.f64 x 4))
30.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 372 to 294 computations (21% saved)

simplify84.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4836	603
1	4836	603

prune119.0ms (4.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	76	3	79

Error

0.1b

Counts

79 → 3

Compiler

Compiled 2641 to 1546 computations (41.5% saved)

localize20.0ms (0.8%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (sqrt.f64 (.f64 (pow.f64 x 6) 1/21)) (sqrt.f64 (*.f64 (pow.f64 x 6) 1/21)))
0.1b	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (pow.f64 x 6) 1/21)) (sqrt.f64 (.f64 (pow.f64 x 6) 1/21))) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
0.0b	(+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4)))
0.0b	(/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (pow.f64 x 6) 1/21)) (sqrt.f64 (.f64 (pow.f64 x 6) 1/21))) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64))
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)
10.7b	(sqrt.f64 (*.f64 (pow.f64 x 6) 1/21))
10.7b	(sqrt.f64 (*.f64 (pow.f64 x 6) 1/21))

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1_binary64_3208`
9×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
8×	`add-sqr-sqrt_binary64_3169`
6×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
5×	`sqrt-prod_binary64_3163`
4×	`add-log-exp_binary64_3186`
3×	`pow-prod-down_binary64_3218` `prod-exp_binary64_3196` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `cbrt-unprod_binary64_3180` `associate-l_binary64_3088`
1×	`-commutative_binary64_3078` `unswap-sqr_binary64_3115` `associate-r*_binary64_3087` `rem-sqrt-square_binary64_3160`

Counts

4 → 52

Calls

8 calls:

6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(sqrt.f64 (*.f64 (pow.f64 x 6) 1/21))
4.0ms	(sqrt.f64 (*.f64 (pow.f64 x 6) 1/21))
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (pow.f64 x 6) 1/21)) (sqrt.f64 (.f64 (pow.f64 x 6) 1/21))) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64))

series128.0ms (4.9%)

Counts

4 → 9

Calls

4 calls:

49.0ms	(sqrt.f64 (*.f64 (pow.f64 x 6) 1/21))
43.0ms	(sqrt.f64 (*.f64 (pow.f64 x 6) 1/21))
36.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 620 to 536 computations (13.5% saved)

simplify92.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4967	521
1	4967	521

prune113.0ms (4.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	61	3	64

Error

0.1b

Counts

64 → 3

Compiler

Compiled 2255 to 1631 computations (27.7% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	100	330
1	100	330

regimes23.0ms (0.9%)

Compiler: Compiled 211 to 159 computations (24.6% saved)

bsearch0.0ms (0%)

regimes10.0ms (0.4%)

Accuracy

Total 0.0b remaining (30.2%)

Threshold costs 0.0b (30.2%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 27 to 24 computations (11.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	42
1	32	42

end0.0ms (0%)

sample1.2s (47.5%)

Algorithm

1×

intervals

Results

745.0ms	8000×	body	128	valid
95.0ms	8002×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 306 to 215 computations (29.7% saved)

Pareto

0.0

Details

analyze6.0ms (0.2%)

sample45.0ms (1.7%)

simplify216.0ms (8.3%)

prune9.0ms (0.4%)

localize17.0ms (0.7%)

rewrite27.0ms (1%)

series101.0ms (3.9%)

simplify53.0ms (2.1%)

prune159.0ms (6.1%)

localize20.0ms (0.8%)

rewrite25.0ms (1%)

series62.0ms (2.4%)

simplify84.0ms (3.2%)

prune119.0ms (4.6%)

localize20.0ms (0.8%)

rewrite22.0ms (0.8%)

series128.0ms (4.9%)

simplify92.0ms (3.5%)

prune113.0ms (4.4%)

simplify6.0ms (0.2%)

regimes23.0ms (0.9%)

bsearch0.0ms (0%)

regimes10.0ms (0.4%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (47.5%)

Profiling