Details

analyze18.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 106 to 71 computations (33% saved)

sample93.0ms (0.3%)

Algorithm

1×

intervals

Results

65.0ms	256×	body	128	valid
3.0ms	260×	pre	128	true
1.0ms	4×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify179.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5512	47

prune10.0ms (0%)

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

2.6b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.5b	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
1.0b	(sqrt.f64 PI.f64)
2.6b	(exp.f64 (*.f64 x x))

rewrite500.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

129×	`times-frac_binary64_2471`
84×	`add-sqr-sqrt_binary64_2487`
79×	`*-un-lft-identity_binary64_2465`
70×	`add-cube-cbrt_binary64_2500` `associate-l_binary64_2406`
31×	`sqrt-prod_binary64_2481`
18×	`add-cbrt-cube_binary64_2501`
17×	`add-exp-log_binary64_2503`
7×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504`
5×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `div-inv_binary64_2462` `associate-r_binary64_2405` `distribute-lft-out_binary64_2416`
4×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `unswap-sqr_binary64_2433` `associate-/l*_binary64_2410`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
2×	`frac-times_binary64_2475` `associate-*r/_binary64_2407` `associate-/l/_binary64_2412`
1×	`exp-to-pow_binary64_2527` `exp-prod_binary64_2517` `rem-exp-log_binary64_2505` `pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `pow-prod-down_binary64_2536` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `associate-l/_binary64_2408` `-commutative_binary64_2396` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/r*_binary64_2409`

Counts

4 → 149

Calls

4 calls:

64.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 6804 to 2952 computations (56.6% saved)

series379.0ms (1.3%)

Error

2.5b

Counts

4 → 24

Calls

4 calls:

210.0ms	(.f64 (/.f64 (/.f64 (exp.f64 (.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))))
84.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
33.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1858 to 1391 computations (25.1% saved)

simplify151.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4943	6637
1	4943	6637

prune413.0ms (1.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	157	16	173
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	159	16	175

Error

0.8b

Counts

175 → 16

Compiler

Compiled 7862 to 3575 computations (54.5% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.5b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite736.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

281×	`times-frac_binary64_2471`
167×	`add-sqr-sqrt_binary64_2487`
148×	`*-un-lft-identity_binary64_2465`
142×	`associate-l_binary64_2406`
139×	`add-cube-cbrt_binary64_2500`
69×	`sqrt-prod_binary64_2481`
59×	`unpow-prod-down_binary64_2544`
24×	`add-exp-log_binary64_2503`
21×	`sqr-pow_binary64_2437`
18×	`add-cbrt-cube_binary64_2501`
9×	`div-exp_binary64_2516`
8×	`pow1_binary64_2526` `unswap-sqr_binary64_2433`
6×	`prod-exp_binary64_2514`
5×	`cbrt-undiv_binary64_2499` `div-inv_binary64_2462` `associate-r_binary64_2405` `distribute-lft-out_binary64_2416`
4×	`pow-pow_binary64_2537` `add-log-exp_binary64_2504` `cbrt-unprod_binary64_2498` `associate-/l*_binary64_2410`
3×	`pow-unpow_binary64_2542` `exp-prod_binary64_2517` `flip3-+_binary64_2468` `flip-+_binary64_2439`
2×	`pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `frac-times_binary64_2475` `associate-*r/_binary64_2407` `associate-/l/_binary64_2412`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `pow-prod-down_binary64_2536` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `associate-l/_binary64_2408` `-commutative_binary64_2396` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/r*_binary64_2409`

Counts

4 → 237

Calls

4 calls:

91.0ms	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
3.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 11001 to 4719 computations (57.1% saved)

series390.0ms (1.4%)

Error

0.7b

Counts

4 → 24

Calls

4 calls:

229.0ms	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (fabs.f64 x)) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
72.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
47.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1858 to 1267 computations (31.8% saved)

simplify115.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5039	11122

prune676.0ms (2.4%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	239	22	261
Fresh	12	3	15
Picked	1	0	1
Done	0	0	0
Total	252	25	277

Error

0.2b

Counts

277 → 25

Compiler

Compiled 12656 to 5690 computations (55% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite276.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

16×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487` `*-un-lft-identity_binary64_2465` `pow-pow_binary64_2537`
12×	`unpow-prod-down_binary64_2544` `pow-unpow_binary64_2542` `exp-prod_binary64_2517`
8×	`pow1_binary64_2526`
4×	`pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqr-pow_binary64_2437`

Counts

4 → 80

Calls

4 calls:

4.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)

Compiler

Compiled 4960 to 2396 computations (51.7% saved)

series280.0ms (1%)

Error

0.2b

Counts

4 → 24

Calls

4 calls:

61.0ms	(pow.f64 (exp.f64 x) x)
61.0ms	(pow.f64 (exp.f64 x) x)
49.0ms	(pow.f64 (exp.f64 x) x)
44.0ms	(pow.f64 (exp.f64 x) x)

Compiler

Compiled 3336 to 1994 computations (40.2% saved)

simplify60.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5177	940

prune389.0ms (1.4%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	1	23	24
Picked	1	0	1
Done	0	0	0
Total	104	25	129

Error

0.2b

Counts

129 → 25

Compiler

Compiled 7645 to 3926 computations (48.6% saved)

localize46.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(pow.f64 (exp.f64 x) (*.f64 x 1/2))
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite296.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

16×	`pow-pow_binary64_2537`
15×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487` `*-un-lft-identity_binary64_2465`
12×	`unpow-prod-down_binary64_2544` `exp-prod_binary64_2517`
10×	`pow-unpow_binary64_2542`
8×	`pow1_binary64_2526`
4×	`pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqr-pow_binary64_2437`

Counts

4 → 78

Calls

4 calls:

4.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) (*.f64 x 1/2))
3.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)

Compiler

Compiled 5553 to 2983 computations (46.3% saved)

series321.0ms (1.1%)

Error

0.2b

Counts

4 → 24

Calls

4 calls:

70.0ms	(pow.f64 (exp.f64 x) (*.f64 x 1/2))
64.0ms	(pow.f64 (exp.f64 x) x)
57.0ms	(pow.f64 (exp.f64 x) x)
54.0ms	(pow.f64 (exp.f64 x) x)

Compiler

Compiled 3848 to 2403 computations (37.6% saved)

simplify121.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4933	964
1	4933	964

prune361.0ms (1.3%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	2	22	24
Picked	1	0	1
Done	0	0	0
Total	102	25	127

Error

0.2b

Counts

127 → 25

Compiler

Compiled 7101 to 3854 computations (45.7% saved)

regimes4.5s (15.8%)

Accuracy

Total 1.1b remaining (89.9%)

Threshold costs 0b (0%)

Compiler

Compiled 55565 to 34071 computations (38.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	50
1	31	50

end0.0ms (0%)

sample18.2s (63.5%)

Algorithm

1×

intervals

Results

2.0s	8000×	body	128	valid
116.0ms	8130×	pre	128	true
32.0ms	130×	body	128	invalid

Compiler

Compiled 18589 to 11405 computations (38.6% saved)

Details

analyze18.0ms (0.1%)

sample93.0ms (0.3%)

simplify179.0ms (0.6%)

prune10.0ms (0%)

localize25.0ms (0.1%)

rewrite500.0ms (1.7%)

series379.0ms (1.3%)

simplify151.0ms (0.5%)

prune413.0ms (1.4%)

localize24.0ms (0.1%)

rewrite736.0ms (2.6%)

series390.0ms (1.4%)

simplify115.0ms (0.4%)

prune676.0ms (2.4%)

localize33.0ms (0.1%)

rewrite276.0ms (1%)

series280.0ms (1%)

simplify60.0ms (0.2%)

prune389.0ms (1.4%)

localize46.0ms (0.2%)

rewrite296.0ms (1%)

series321.0ms (1.1%)

simplify121.0ms (0.4%)

prune361.0ms (1.3%)

regimes4.5s (15.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample18.2s (63.5%)

Profiling