Details

analyze10.0ms (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)

sample72.0ms (0.5%)

Algorithm

1×

intervals

Results

55.0ms	256×	body	128	valid
4.0ms	261×	pre	128	true
1.0ms	5×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify176.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5512	47

prune9.0ms (0.1%)

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

Merged error: 2.6b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
0.4b	(.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)
2.5b	(exp.f64 (*.f64 x x))

rewrite93.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

53.0ms	(.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)))))
6.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

series315.0ms (2.1%)

Counts

4 → 24

Calls

4 calls:

213.0ms	(.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)))))
71.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
30.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1126 to 921 computations (18.2% saved)

simplify121.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5012	7205

prune455.0ms (3.1%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	162	25	187
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	164	25	189

Merged error: 0.2b

Counts

189 → 25

Compiler

Compiled 9071 to 4263 computations (53% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite145.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

238×	`add-exp-log_binary64_2503`
174×	`times-frac_binary64_2471`
135×	`div-exp_binary64_2516`
100×	`add-sqr-sqrt_binary64_2487`
99×	`prod-exp_binary64_2514`
98×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
97×	`associate-l_binary64_2406`
87×	`sqrt-prod_binary64_2481`
58×	`add-cbrt-cube_binary64_2501`
36×	`1-exp_binary64_2509`
21×	`cbrt-undiv_binary64_2499` `cbrt-unprod_binary64_2498`
12×	`rec-exp_binary64_2515` `pow1_binary64_2526`
10×	`pow-exp_binary64_2533` `pow-to-exp_binary64_2534`
9×	`frac-times_binary64_2475`
7×	`associate-*r/_binary64_2407`
5×	`associate-*l/_binary64_2408`
4×	`flip3-+_binary64_2468` `add-log-exp_binary64_2504` `flip-+_binary64_2439` `div-inv_binary64_2462` `pow-pow_binary64_2537`
3×	`unpow-prod-down_binary64_2544` `exp-prod_binary64_2517` `pow-prod-down_binary64_2536` `pow-unpow_binary64_2542`
2×	`pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`
1×	`-commutative_binary64_2396` `sqr-pow_binary64_2437` `associate-r*_binary64_2405`

Counts

4 → 231

Calls

4 calls:

91.0ms	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 PI.f64))) 1) (.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (fabs.f64 x))))
4.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series323.0ms (2.2%)

Counts

4 → 18

Calls

4 calls:

263.0ms	(.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 PI.f64))) 1) (.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (fabs.f64 x))))
59.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 966 to 777 computations (19.6% saved)

simplify205.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4936	12405
1	4936	12405

prune619.0ms (4.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	241	8	249
Fresh	6	18	24
Picked	1	0	1
Done	0	0	0
Total	248	26	274

Merged error: 0.2b

Counts

274 → 26

Compiler

Compiled 12496 to 6329 computations (49.4% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite89.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`sqrt-prod_binary64_2481` `add-sqr-sqrt_binary64_2487`
72×	`times-frac_binary64_2471`
67×	`associate-r_binary64_2405`
55×	`*-un-lft-identity_binary64_2465`
50×	`add-cube-cbrt_binary64_2500`
33×	`unpow-prod-down_binary64_2544`
13×	`add-exp-log_binary64_2503` `sqr-pow_binary64_2437`
10×	`unswap-sqr_binary64_2433`
9×	`add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
5×	`associate-l_binary64_2406`
4×	`add-log-exp_binary64_2504` `pow-pow_binary64_2537` `prod-exp_binary64_2514`
3×	`div-exp_binary64_2516` `exp-prod_binary64_2517` `distribute-lft-out_binary64_2416` `pow-unpow_binary64_2542`
2×	`flip3-+_binary64_2468` `associate-*l/_binary64_2408` `frac-times_binary64_2475` `pow1/2_binary64_2545` `flip-+_binary64_2439` `pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483` `cbrt-unprod_binary64_2498`
1×	`-commutative_binary64_2396` `associate-r/_binary64_2407` `cbrt-undiv_binary64_2499` `div-inv_binary64_2462` `pow-prod-down_binary64_2536`

Counts

4 → 148

Calls

4 calls:

57.0ms	(.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))) (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))))
4.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series199.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))) (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))))
60.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 608 to 483 computations (20.6% saved)

simplify114.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4973	5864
1	4973	5864

prune362.0ms (2.4%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	154	6	160
Fresh	5	20	25
Picked	1	0	1
Done	0	0	0
Total	160	26	186

Merged error: 0.2b

Counts

186 → 26

Compiler

Compiled 8565 to 4041 computations (52.8% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite337.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

544×	`times-frac_binary64_2471`
409×	`add-sqr-sqrt_binary64_2487`
309×	`sqrt-prod_binary64_2481`
267×	`*-un-lft-identity_binary64_2465`
222×	`add-cube-cbrt_binary64_2500`
205×	`associate-r_binary64_2405`
96×	`unpow-prod-down_binary64_2544`
49×	`associate-l_binary64_2406`
44×	`unswap-sqr_binary64_2433`
40×	`sqr-pow_binary64_2437`
39×	`add-exp-log_binary64_2503`
27×	`distribute-lft-out_binary64_2416`
25×	`add-cbrt-cube_binary64_2501`
19×	`div-exp_binary64_2516`
10×	`prod-exp_binary64_2514`
9×	`cbrt-undiv_binary64_2499` `pow1_binary64_2526`
6×	`cbrt-unprod_binary64_2498`
5×	`div-inv_binary64_2462`
4×	`add-log-exp_binary64_2504` `pow-pow_binary64_2537`
3×	`pow-exp_binary64_2533` `pow-to-exp_binary64_2534` `exp-prod_binary64_2517` `pow-unpow_binary64_2542`
2×	`pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`
1×	`associate-l/_binary64_2408` `-commutative_binary64_2396` `frac-times_binary64_2475` `associate-*r/_binary64_2407` `pow-prod-down_binary64_2536`

Counts

4 → 372

Calls

4 calls:

242.0ms	(.f64 (/.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))) (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (fabs.f64 x)))
4.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series299.0ms (2%)

Counts

4 → 18

Calls

4 calls:

237.0ms	(.f64 (/.f64 (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))) (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (fabs.f64 x)))
62.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 934 to 745 computations (20.2% saved)

simplify225.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

390 → 390

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4995	23531
1	4995	23531

prune1.0s (6.8%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	375	15	390
Fresh	11	14	25
Picked	0	1	1
Done	0	0	0
Total	386	30	416

Merged error: 0.1b

Counts

416 → 30

Compiler

Compiled 20111 to 8083 computations (59.8% saved)

regimes1.7s (11.8%)

Compiler: Compiled 26972 to 17142 computations (36.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	57
1	30	57

end0.0ms (0%)

sample7.8s (52.6%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
115.0ms	8119×	pre	128	true
25.0ms	119×	body	128	invalid

Compiler

Compiled 9061 to 5762 computations (36.4% saved)

Details

analyze10.0ms (0.1%)

sample72.0ms (0.5%)

simplify176.0ms (1.2%)

prune9.0ms (0.1%)

localize23.0ms (0.2%)

rewrite93.0ms (0.6%)

series315.0ms (2.1%)

simplify121.0ms (0.8%)

prune455.0ms (3.1%)

localize30.0ms (0.2%)

rewrite145.0ms (1%)

series323.0ms (2.2%)

simplify205.0ms (1.4%)

prune619.0ms (4.2%)

localize24.0ms (0.2%)

rewrite89.0ms (0.6%)

series199.0ms (1.3%)

simplify114.0ms (0.8%)

prune362.0ms (2.4%)

localize24.0ms (0.2%)

rewrite337.0ms (2.3%)

series299.0ms (2%)

simplify225.0ms (1.5%)

prune1.0s (6.8%)

regimes1.7s (11.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.8s (52.6%)

Profiling