Details

analyze177.0ms (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)

sample71.0ms (0.3%)

Algorithm

1×

intervals

Results

50.0ms	256×	body	128	valid
3.0ms	263×	pre	128	true
1.0ms	7×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify78.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5512	47

prune9.0ms (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)

localize21.0ms (0.1%)

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))

rewrite408.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

143×	`times-frac_binary64_2812`
97×	`add-sqr-sqrt_binary64_2828`
88×	`*-un-lft-identity_binary64_2806`
83×	`add-cube-cbrt_binary64_2841`
70×	`associate-l_binary64_2747`
43×	`sqrt-prod_binary64_2822`
15×	`add-cbrt-cube_binary64_2842`
13×	`add-exp-log_binary64_2844`
7×	`pow1_binary64_2867`
6×	`add-log-exp_binary64_2845` `associate-/r*_binary64_2750`
5×	`div-inv_binary64_2803` `associate-r_binary64_2746`
4×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `unswap-sqr_binary64_2774`
3×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `distribute-lft-out_binary64_2757` `associate-/l*_binary64_2751`
2×	`flip3-+_binary64_2809` `frac-times_binary64_2816` `flip-+_binary64_2780` `associate-*r/_binary64_2748`
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`

Counts

4 → 163

Calls

4 calls:

44.0ms	(.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)))))
5.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 7337 to 3085 computations (58% saved)

series319.0ms (1.3%)

Error

2.3b

Counts

4 → 24

Calls

4 calls:

187.0ms	(.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)))))
64.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
22.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1936 to 1445 computations (25.4% saved)

simplify93.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5169	7072

prune405.0ms (1.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	169	18	187
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	170	19	189

Error

0.8b

Counts

189 → 19

Compiler

Compiled 8793 to 3930 computations (55.3% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite718.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

319×	`times-frac_binary64_2812`
195×	`add-sqr-sqrt_binary64_2828`
172×	`*-un-lft-identity_binary64_2806`
167×	`add-cube-cbrt_binary64_2841`
142×	`associate-l_binary64_2747`
93×	`sqrt-prod_binary64_2822`
80×	`unpow-prod-down_binary64_2885`
28×	`sqr-pow_binary64_2778`
23×	`add-exp-log_binary64_2844`
15×	`add-cbrt-cube_binary64_2842`
10×	`div-exp_binary64_2857`
8×	`pow1_binary64_2867` `unswap-sqr_binary64_2774`
7×	`associate-/l*_binary64_2751`
6×	`associate-/r*_binary64_2750`
5×	`prod-exp_binary64_2855` `div-inv_binary64_2803` `associate-r_binary64_2746`
4×	`pow-pow_binary64_2878` `add-log-exp_binary64_2845` `cbrt-undiv_binary64_2840`
3×	`pow-unpow_binary64_2883` `exp-prod_binary64_2858` `pow-to-exp_binary64_2875` `pow-exp_binary64_2874` `cbrt-unprod_binary64_2839` `distribute-lft-out_binary64_2757`
2×	`flip3-+_binary64_2809` `frac-times_binary64_2816` `flip-+_binary64_2780` `associate-*r/_binary64_2748`
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`

Counts

4 → 281

Calls

4 calls:

59.0ms	(.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)))))
11.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64))
4.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 12785 to 5391 computations (57.8% saved)

series381.0ms (1.6%)

Error

0.7b

Counts

4 → 24

Calls

4 calls:

223.0ms	(.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)))))
80.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64))
39.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1936 to 1314 computations (32.1% saved)

simplify153.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4976	12315
1	4976	12315

prune696.0ms (2.9%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	278	27	305
Fresh	15	3	18
Picked	1	0	1
Done	0	0	0
Total	294	30	324

Error

0.2b

Counts

324 → 30

Compiler

Compiled 14731 to 6538 computations (55.6% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite785.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

56×	`*-un-lft-identity_binary64_2806`
45×	`add-sqr-sqrt_binary64_2828`
42×	`add-cube-cbrt_binary64_2841` `times-frac_binary64_2812`
27×	`sqrt-prod_binary64_2822`
24×	`unpow-prod-down_binary64_2885`
13×	`pow1_binary64_2867`
10×	`add-exp-log_binary64_2844`
9×	`frac-times_binary64_2816`
8×	`add-cbrt-cube_binary64_2842` `sqr-pow_binary64_2778` `frac-add_binary64_2814` `flip3-+_binary64_2809` `flip-+_binary64_2780`
7×	`associate-/l*_binary64_2751`
6×	`swap-sqr_binary64_2773` `distribute-lft-out_binary64_2757` `associate-/r*_binary64_2750`
4×	`pow-pow_binary64_2878` `add-log-exp_binary64_2845` `associate-l_binary64_2747` `associate-r_binary64_2746`
3×	`pow-unpow_binary64_2883` `exp-prod_binary64_2858` `associate-l/_binary64_2749` `associate-r/_binary64_2748` `div-exp_binary64_2857`
2×	`pow-to-exp_binary64_2875` `pow-exp_binary64_2874`
1×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `pow2_binary64_2887` `pow-prod-down_binary64_2877` `pow-prod-up_binary64_2876` `pow-plus_binary64_2869` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `pow-sqr_binary64_2779` `unswap-sqr_binary64_2774` `distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755` `*-commutative_binary64_2737` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803`

Counts

4 → 149

Calls

4 calls:

46.0ms	(.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))
6.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64))
3.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 12359 to 6905 computations (44.1% saved)

series299.0ms (1.3%)

Error

0.2b

Counts

4 → 24

Calls

4 calls:

104.0ms	(.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x))))
86.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64))
50.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 3284 to 2260 computations (31.2% saved)

simplify75.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5148	4738

prune770.0ms (3.2%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	168	5	173
Fresh	4	25	29
Picked	1	0	1
Done	0	0	0
Total	173	30	203

Error

0.2b

Counts

203 → 30

Compiler

Compiled 14487 to 8224 computations (43.2% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.5b	(.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) (+.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)

rewrite473.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

32×	`*-un-lft-identity_binary64_2806`
17×	`add-sqr-sqrt_binary64_2828`
14×	`add-cube-cbrt_binary64_2841`
13×	`pow1_binary64_2867`
11×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
9×	`frac-times_binary64_2816` `flip3-+_binary64_2809` `flip-+_binary64_2780`
8×	`frac-add_binary64_2814` `distribute-lft-out_binary64_2757`
6×	`swap-sqr_binary64_2773`
4×	`pow-pow_binary64_2878` `add-log-exp_binary64_2845` `associate-l_binary64_2747` `associate-r_binary64_2746` `times-frac_binary64_2812` `associate-/l*_binary64_2751`
3×	`unpow-prod-down_binary64_2885` `pow-unpow_binary64_2883` `exp-prod_binary64_2858` `sqrt-prod_binary64_2822` `associate-l/_binary64_2749` `associate-r/_binary64_2748`
2×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `associate-/l/_binary64_2753`
1×	`pow-to-exp_binary64_2875` `pow-exp_binary64_2874` `sqr-pow_binary64_2778` `pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `pow2_binary64_2887` `pow-prod-down_binary64_2877` `pow-prod-up_binary64_2876` `pow-plus_binary64_2869` `pow-sqr_binary64_2779` `unswap-sqr_binary64_2774` `distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755` `-commutative_binary64_2737` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803` `associate-/r_binary64_2750`

Counts

4 → 105

Calls

4 calls:

49.0ms	(.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) (+.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 8903 to 5074 computations (43% saved)

series287.0ms (1.2%)

Error

0.2b

Counts

4 → 24

Calls

4 calls:

95.0ms	(.f64 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))) (+.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))
49.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 3244 to 2233 computations (31.2% saved)

simplify93.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4899	3520
1	4899	3520

prune419.0ms (1.8%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	29	29
Picked	0	1	1
Done	0	0	0
Total	129	30	159

Error

0.2b

Counts

159 → 30

Compiler

Compiled 9278 to 5332 computations (42.5% saved)

regimes3.5s (14.5%)

Accuracy

Total 1.1b remaining (87.9%)

Threshold costs 0b (0%)

Compiler

Compiled 55229 to 33735 computations (38.9% 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%)

sample13.5s (56.8%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
93.0ms	8122×	pre	128	true
26.0ms	122×	body	128	invalid

Compiler

Compiled 18477 to 11293 computations (38.9% saved)

Details

analyze177.0ms (0.7%)

sample71.0ms (0.3%)

simplify78.0ms (0.3%)

prune9.0ms (0%)

localize21.0ms (0.1%)

rewrite408.0ms (1.7%)

series319.0ms (1.3%)

simplify93.0ms (0.4%)

prune405.0ms (1.7%)

localize24.0ms (0.1%)

rewrite718.0ms (3%)

series381.0ms (1.6%)

simplify153.0ms (0.6%)

prune696.0ms (2.9%)

localize29.0ms (0.1%)

rewrite785.0ms (3.3%)

series299.0ms (1.3%)

simplify75.0ms (0.3%)

prune770.0ms (3.2%)

localize27.0ms (0.1%)

rewrite473.0ms (2%)

series287.0ms (1.2%)

simplify93.0ms (0.4%)

prune419.0ms (1.8%)

regimes3.5s (14.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample13.5s (56.8%)

Profiling