Details

analyze20.0ms (0%)

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)

sample167.0ms (0.3%)

Algorithm

1×

intervals

Results

124.0ms	256×	body	128	valid
7.0ms	259×	pre	128	true
1.0ms	3×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify311.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	5512	47

prune24.0ms (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

2.5b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize41.0ms (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))
0.4b	(.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)
2.4b	(exp.f64 (*.f64 x x))

rewrite685.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

129×	`times-frac_binary64_2812`
84×	`add-sqr-sqrt_binary64_2828`
79×	`*-un-lft-identity_binary64_2806`
70×	`add-cube-cbrt_binary64_2841` `associate-l_binary64_2747`
31×	`sqrt-prod_binary64_2822`
18×	`add-cbrt-cube_binary64_2842`
17×	`add-exp-log_binary64_2844`
7×	`pow1_binary64_2867`
6×	`add-log-exp_binary64_2845`
5×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `div-inv_binary64_2803` `associate-r_binary64_2746` `distribute-lft-out_binary64_2757`
4×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `unswap-sqr_binary64_2774` `associate-/l*_binary64_2751`
3×	`flip3-+_binary64_2809` `flip-+_binary64_2780`
2×	`frac-times_binary64_2816` `associate-*r/_binary64_2748` `associate-/l/_binary64_2753`
1×	`exp-to-pow_binary64_2868` `exp-prod_binary64_2858` `rem-exp-log_binary64_2846` `pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `pow-prod-down_binary64_2877` `distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755` `associate-l/_binary64_2749` `-commutative_binary64_2737` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `associate-/r*_binary64_2750`

Counts

4 → 149

Calls

4 calls:

94.0ms	(.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)))))
25.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
4.0ms	(exp.f64 (*.f64 x x))
3.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 6804 to 2952 computations (56.6% saved)

series614.0ms (1%)

Error

2.3b

Counts

4 → 24

Calls

4 calls:

358.0ms	(.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)))))
140.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
41.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1858 to 1391 computations (25.1% saved)

simplify260.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (155.0ms)

Iter	Nodes	Cost
0	4943	6637
1	4943	6637

prune620.0ms (1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	156	17	173
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	157	18	175

Error

0.7b

Counts

175 → 18

Compiler

Compiled 8043 to 3679 computations (54.3% saved)

localize44.0ms (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))
0.4b	(.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)))))
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite1.1s (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

281×	`times-frac_binary64_2812`
167×	`add-sqr-sqrt_binary64_2828`
148×	`*-un-lft-identity_binary64_2806`
142×	`associate-l_binary64_2747`
139×	`add-cube-cbrt_binary64_2841`
69×	`sqrt-prod_binary64_2822`
59×	`unpow-prod-down_binary64_2885`
24×	`add-exp-log_binary64_2844`
21×	`sqr-pow_binary64_2778`
18×	`add-cbrt-cube_binary64_2842`
9×	`div-exp_binary64_2857`
8×	`pow1_binary64_2867` `unswap-sqr_binary64_2774`
6×	`prod-exp_binary64_2855`
5×	`cbrt-undiv_binary64_2840` `div-inv_binary64_2803` `associate-r_binary64_2746` `distribute-lft-out_binary64_2757`
4×	`pow-pow_binary64_2878` `add-log-exp_binary64_2845` `cbrt-unprod_binary64_2839` `associate-/l*_binary64_2751`
3×	`pow-unpow_binary64_2883` `exp-prod_binary64_2858` `flip3-+_binary64_2809` `flip-+_binary64_2780`
2×	`pow-to-exp_binary64_2875` `pow-exp_binary64_2874` `frac-times_binary64_2816` `associate-*r/_binary64_2748` `associate-/l/_binary64_2753`
1×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `pow-prod-down_binary64_2877` `distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755` `associate-l/_binary64_2749` `-commutative_binary64_2737` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `associate-/r*_binary64_2750`

Counts

4 → 237

Calls

4 calls:

131.0ms	(.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)))))
19.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
7.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 11001 to 4719 computations (57.1% saved)

series579.0ms (1%)

Error

0.6b

Counts

4 → 24

Calls

4 calls:

340.0ms	(.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)))))
116.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
64.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1858 to 1267 computations (31.8% saved)

simplify187.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5039	11122

prune1.2s (2%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	233	28	261
Fresh	15	2	17
Picked	1	0	1
Done	0	0	0
Total	249	30	279

Error

0.2b

Counts

279 → 30

Compiler

Compiled 12879 to 5844 computations (54.6% saved)

localize54.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.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))) (sqrt.f64 (fabs.f64 x))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite3.1s (5.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

818×	`times-frac_binary64_2812`
613×	`sqrt-prod_binary64_2822`
461×	`add-sqr-sqrt_binary64_2828`
406×	`associate-r_binary64_2746`
390×	`*-un-lft-identity_binary64_2806`
385×	`add-cube-cbrt_binary64_2841`
171×	`unpow-prod-down_binary64_2885`
61×	`sqr-pow_binary64_2778`
21×	`unswap-sqr_binary64_2774`
19×	`add-exp-log_binary64_2844`
13×	`add-cbrt-cube_binary64_2842`
9×	`pow1_binary64_2867`
7×	`div-exp_binary64_2857` `div-inv_binary64_2803`
5×	`prod-exp_binary64_2855` `associate-l_binary64_2747`
4×	`pow-pow_binary64_2878` `add-log-exp_binary64_2845`
3×	`pow-unpow_binary64_2883` `exp-prod_binary64_2858` `cbrt-unprod_binary64_2839` `cbrt-undiv_binary64_2840` `distribute-lft-out_binary64_2757`
2×	`pow-to-exp_binary64_2875` `pow-exp_binary64_2874` `pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `flip3-+_binary64_2809` `frac-times_binary64_2816` `flip-+_binary64_2780` `associate-*l/_binary64_2749`
1×	`pow-prod-down_binary64_2877` `associate-r/_binary64_2748` `-commutative_binary64_2737`

Counts

4 → 500

Calls

4 calls:

276.0ms	(.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 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (fabs.f64 x))))
7.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 30812 to 11707 computations (62% saved)

series721.0ms (1.2%)

Error

0.2b

Counts

4 → 18

Calls

4 calls:

572.0ms	(.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 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (fabs.f64 x))))
72.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 2052 to 1383 computations (32.6% saved)

simplify504.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

518 → 518

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4973	26823
1	4973	26823

prune2.8s (4.6%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	509	9	518
Fresh	7	22	29
Picked	1	0	1
Done	0	0	0
Total	517	31	548

Error

0.1b

Counts

548 → 31

Compiler

Compiled 31592 to 12133 computations (61.6% saved)

localize47.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (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)
1.0b	(sqrt.f64 PI.f64)
1.1b	(pow.f64 (exp.f64 x) x)

rewrite551.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

61×	`times-frac_binary64_2812`
46×	`add-sqr-sqrt_binary64_2828`
37×	`associate-l_binary64_2747`
36×	`*-un-lft-identity_binary64_2806`
32×	`add-exp-log_binary64_2844`
31×	`add-cube-cbrt_binary64_2841`
18×	`add-cbrt-cube_binary64_2842`
13×	`unpow-prod-down_binary64_2885` `div-exp_binary64_2857`
11×	`prod-exp_binary64_2855`
9×	`pow1_binary64_2867`
6×	`sqrt-prod_binary64_2822`
5×	`sqr-pow_binary64_2778` `cbrt-unprod_binary64_2839` `cbrt-undiv_binary64_2840` `unswap-sqr_binary64_2774` `associate-r_binary64_2746`
4×	`pow-pow_binary64_2878` `add-log-exp_binary64_2845` `div-inv_binary64_2803`
3×	`pow-unpow_binary64_2883` `exp-prod_binary64_2858` `pow-to-exp_binary64_2875` `pow-exp_binary64_2874` `distribute-lft-out_binary64_2757`
2×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `flip3-+_binary64_2809` `frac-times_binary64_2816` `flip-+_binary64_2780` `associate-*r/_binary64_2748`
1×	`pow-prod-down_binary64_2877` `distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755` `associate-l/_binary64_2749` `-commutative_binary64_2737`

Counts

4 → 121

Calls

4 calls:

101.0ms	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (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)))))
7.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(sqrt.f64 PI.f64)
3.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 5992 to 2516 computations (58% saved)

series488.0ms (0.8%)

Error

0.1b

Counts

4 → 18

Calls

4 calls:

376.0ms	(.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (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)))))
67.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1478 to 952 computations (35.6% saved)

simplify150.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5228	5059

prune403.0ms (0.7%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	2	28	30
Picked	1	0	1
Done	0	0	0
Total	140	30	170

Error

0.1b

Counts

170 → 30

Compiler

Compiled 5851 to 2595 computations (55.6% saved)

regimes8.9s (14.9%)

Accuracy

Total 1.1b remaining (89.7%)

Threshold costs 0b (0%)

Compiler

Compiled 60056 to 36405 computations (39.4% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	92
1	43	92

end0.0ms (0%)

sample36.4s (60.7%)

Algorithm

1×

intervals

Results

3.3s	8000×	body	128	valid
169.0ms	8109×	pre	128	true
44.0ms	109×	body	128	invalid

Compiler

Compiled 20111 to 12193 computations (39.4% saved)

Details

analyze20.0ms (0%)

sample167.0ms (0.3%)

simplify311.0ms (0.5%)

prune24.0ms (0%)

localize41.0ms (0.1%)

rewrite685.0ms (1.1%)

series614.0ms (1%)

simplify260.0ms (0.4%)

prune620.0ms (1%)

localize44.0ms (0.1%)

rewrite1.1s (1.9%)

series579.0ms (1%)

simplify187.0ms (0.3%)

prune1.2s (2%)

localize54.0ms (0.1%)

rewrite3.1s (5.2%)

series721.0ms (1.2%)

simplify504.0ms (0.8%)

prune2.8s (4.6%)

localize47.0ms (0.1%)

rewrite551.0ms (0.9%)

series488.0ms (0.8%)

simplify150.0ms (0.3%)

prune403.0ms (0.7%)

regimes8.9s (14.9%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample36.4s (60.7%)

Profiling