Details

analyze210.0ms (0.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5512	47
0	1	1
1	1	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)

sample82.0ms (0.3%)

Algorithm

1×

intervals

Results

62.0ms	256×	body	128	valid
3.0ms	261×	pre	128	true
1.0ms	5×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify96.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5512	47

prune8.0ms (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)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)))))
0.4b	(/.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))

rewrite446.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

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` `distribute-lft-out_binary64_2416` `div-inv_binary64_2462` `associate-r_binary64_2405`
4×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `associate-/l*_binary64_2410` `unswap-sqr_binary64_2433`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
2×	`associate-/l/_binary64_2412` `frac-times_binary64_2475` `associate-*r/_binary64_2407`
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` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/r_binary64_2409` `pow-prod-down_binary64_2536` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `associate-l/_binary64_2408` `*-commutative_binary64_2396`

Counts

4 → 149

Calls

4 calls:

50.0ms	(.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)))))
9.0ms	(/.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)

series408.0ms (1.4%)

Error

2.4b

Counts

4 → 24

Calls

4 calls:

222.0ms	(.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)))))
106.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
27.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1858 to 1391 computations (25.1% saved)

simplify145.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4943	6637
1	4943	6637

prune427.0ms (1.4%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	154	19	173
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	155	20	175

Error

0.7b

Counts

175 → 20

Compiler

Compiled 8195 to 3780 computations (53.9% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.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)))))
0.4b	(/.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)

rewrite834.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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` `distribute-lft-out_binary64_2416` `div-inv_binary64_2462` `associate-r_binary64_2405`
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` `associate-/l/_binary64_2412` `frac-times_binary64_2475` `associate-*r/_binary64_2407`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/r_binary64_2409` `pow-prod-down_binary64_2536` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `associate-l/_binary64_2408` `*-commutative_binary64_2396`

Counts

4 → 237

Calls

4 calls:

87.0ms	(.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)))))
9.0ms	(/.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)

series465.0ms (1.6%)

Error

0.7b

Counts

4 → 24

Calls

4 calls:

251.0ms	(.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)))))
101.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
65.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1858 to 1267 computations (31.8% saved)

simplify111.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5039	11122

prune679.0ms (2.3%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	237	24	261
Fresh	17	2	19
Picked	1	0	1
Done	0	0	0
Total	255	26	281

Error

0.1b

Counts

281 → 26

Compiler

Compiled 12812 to 5764 computations (55% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))
0.4b	(/.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)

rewrite370.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

57×	`add-sqr-sqrt_binary64_2487`
52×	`times-frac_binary64_2471`
47×	`*-un-lft-identity_binary64_2465`
46×	`associate-l_binary64_2406`
38×	`add-cube-cbrt_binary64_2500`
27×	`sqrt-prod_binary64_2481`
23×	`unpow-prod-down_binary64_2544`
18×	`add-exp-log_binary64_2503`
14×	`add-cbrt-cube_binary64_2501`
9×	`sqr-pow_binary64_2437`
8×	`pow1_binary64_2526`
7×	`unswap-sqr_binary64_2433`
5×	`prod-exp_binary64_2514` `div-exp_binary64_2516` `distribute-lft-out_binary64_2416` `associate-r_binary64_2405`
4×	`pow-pow_binary64_2537` `add-log-exp_binary64_2504` `associate-/l*_binary64_2410`
3×	`pow-unpow_binary64_2542` `exp-prod_binary64_2517` `cbrt-undiv_binary64_2499` `cbrt-unprod_binary64_2498` `flip3-+_binary64_2468` `flip-+_binary64_2439`
2×	`pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `div-inv_binary64_2462` `associate-/l/_binary64_2412` `frac-times_binary64_2475` `associate-*r/_binary64_2407`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/r_binary64_2409` `pow-prod-down_binary64_2536` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `associate-l/_binary64_2408` `*-commutative_binary64_2396`

Counts

4 → 138

Calls

4 calls:

42.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))
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 5930 to 2892 computations (51.2% saved)

series342.0ms (1.2%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

173.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))))
80.0ms	(/.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 1746 to 1241 computations (28.9% saved)

simplify97.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5198	5296

prune375.0ms (1.3%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	2	23	25
Picked	1	0	1
Done	0	0	0
Total	162	26	188

Error

0.1b

Counts

188 → 26

Compiler

Compiled 7784 to 3951 computations (49.2% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite148.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

14×	`add-sqr-sqrt_binary64_2487`
12×	`add-cube-cbrt_binary64_2500` `*-un-lft-identity_binary64_2465`
8×	`pow1_binary64_2526` `pow-pow_binary64_2537`
6×	`unpow-prod-down_binary64_2544` `pow-unpow_binary64_2542` `exp-prod_binary64_2517` `sqrt-prod_binary64_2481`
4×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
2×	`pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `sqr-pow_binary64_2437` `pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478`

Counts

4 → 66

Calls

4 calls:

3.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 3204 to 1312 computations (59.1% saved)

series130.0ms (0.4%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow.f64 (exp.f64 x) x)
46.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1304 to 783 computations (40% saved)

simplify52.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5200	632

prune150.0ms (0.5%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	3	22	25
Picked	0	1	1
Done	0	0	0
Total	76	28	104

Error

0.1b

Counts

104 → 28

Compiler

Compiled 3710 to 1542 computations (58.4% saved)

regimes5.1s (17.2%)

Accuracy

Total 1.1b remaining (90.5%)

Threshold costs 0b (0%)

Compiler

Compiled 59378 to 37032 computations (37.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	92
1	43	92

end0.0ms (0%)

sample18.8s (63.5%)

Algorithm

1×

intervals

Results

2.0s	8000×	body	128	valid
115.0ms	8132×	pre	128	true
33.0ms	132×	body	128	invalid

Compiler

Compiled 19885 to 12402 computations (37.6% saved)

Details

analyze210.0ms (0.7%)

sample82.0ms (0.3%)

simplify96.0ms (0.3%)

prune8.0ms (0%)

localize30.0ms (0.1%)

rewrite446.0ms (1.5%)

series408.0ms (1.4%)

simplify145.0ms (0.5%)

prune427.0ms (1.4%)

localize27.0ms (0.1%)

rewrite834.0ms (2.8%)

series465.0ms (1.6%)

simplify111.0ms (0.4%)

prune679.0ms (2.3%)

localize33.0ms (0.1%)

rewrite370.0ms (1.3%)

series342.0ms (1.2%)

simplify97.0ms (0.3%)

prune375.0ms (1.3%)

localize39.0ms (0.1%)

rewrite148.0ms (0.5%)

series130.0ms (0.4%)

simplify52.0ms (0.2%)

prune150.0ms (0.5%)

regimes5.1s (17.2%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample18.8s (63.5%)

Profiling