Details

analyze9.0ms (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)

sample76.0ms (0.2%)

Algorithm

1×

intervals

Results

56.0ms	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)

simplify178.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

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

2.4b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize23.0ms (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))

rewrite398.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

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:

43.0ms	(.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)

series330.0ms (1%)

Error

2.3b

Counts

4 → 24

Calls

4 calls:

195.0ms	(.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)))))
69.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
26.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1858 to 1391 computations (25.1% saved)

simplify156.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4943	6637
1	4943	6637

prune399.0ms (1.2%)

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

0.6b

Counts

175 → 16

Compiler

Compiled 7912 to 3594 computations (54.6% saved)

localize22.0ms (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)
1.0b	(pow.f64 (exp.f64 x) x)

rewrite680.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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:

63.0ms	(.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))
4.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 11001 to 4719 computations (57.1% saved)

series360.0ms (1.1%)

Error

0.6b

Counts

4 → 24

Calls

4 calls:

213.0ms	(.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))
37.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1858 to 1267 computations (31.8% saved)

simplify114.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5039	11122

prune631.0ms (1.9%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	242	19	261
Fresh	11	4	15
Picked	1	0	1
Done	0	0	0
Total	254	23	277

Error

0.1b

Counts

277 → 23

Compiler

Compiled 12521 to 5606 computations (55.2% saved)

localize27.0ms (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)
1.0b	(pow.f64 (exp.f64 x) x)

rewrite2.0s (6.2%)

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:

145.0ms	(.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))))
4.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 30812 to 11707 computations (62% saved)

series394.0ms (1.2%)

Error

0.1b

Counts

4 → 18

Calls

4 calls:

311.0ms	(.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))))
43.0ms	(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)

simplify262.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

518 → 518

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4973	26823
1	4973	26823

prune1.7s (5.3%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	510	8	518
Fresh	3	19	22
Picked	0	1	1
Done	0	0	0
Total	513	28	541

Error

0.1b

Counts

541 → 28

Compiler

Compiled 31356 to 11999 computations (61.7% saved)

localize29.0ms (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 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 PI.f64)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)
1.0b	(pow.f64 (exp.f64 x) x)
1.0b	(pow.f64 (exp.f64 x) x)

rewrite1.1s (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

389×	`times-frac_binary64_2812`
230×	`add-sqr-sqrt_binary64_2828`
229×	`sqrt-prod_binary64_2822`
199×	`*-un-lft-identity_binary64_2806`
196×	`associate-r_binary64_2746`
194×	`add-cube-cbrt_binary64_2841`
62×	`unpow-prod-down_binary64_2885`
22×	`sqr-pow_binary64_2778`
13×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
10×	`unswap-sqr_binary64_2774`
9×	`pow1_binary64_2867`
8×	`pow-pow_binary64_2878`
6×	`pow-unpow_binary64_2883` `exp-prod_binary64_2858`
5×	`associate-l_binary64_2747`
4×	`add-log-exp_binary64_2845` `div-inv_binary64_2803`
3×	`div-exp_binary64_2857` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `cbrt-undiv_binary64_2840` `distribute-lft-out_binary64_2757`
2×	`pow-to-exp_binary64_2875` `pow-exp_binary64_2874` `flip3-+_binary64_2809` `frac-times_binary64_2816` `flip-+_binary64_2780` `associate-*l/_binary64_2749`
1×	`pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `pow-prod-down_binary64_2877` `associate-r/_binary64_2748` `-commutative_binary64_2737`

Counts

4 → 284

Calls

4 calls:

88.0ms	(.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 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 PI.f64)) (fabs.f64 x)))
4.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 16621 to 6953 computations (58.2% saved)

series322.0ms (1%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

195.0ms	(.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 (sqrt.f64 (pow.f64 (exp.f64 x) x)) (sqrt.f64 PI.f64)) (fabs.f64 x)))
44.0ms	(pow.f64 (exp.f64 x) x)
42.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 2412 to 1510 computations (37.4% saved)

simplify156.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4980	13909
1	4980	13909

prune805.0ms (2.5%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	301	7	308
Fresh	6	20	26
Picked	1	0	1
Done	0	1	1
Total	308	28	336

Error

0.0b

Counts

336 → 28

Compiler

Compiled 16662 to 6800 computations (59.2% saved)

regimes5.0s (15.5%)

Accuracy

Total 1.1b remaining (92.7%)

Threshold costs 0b (0%)

Compiler

Compiled 64097 to 39402 computations (38.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	113
1	49	113

end0.0ms (0%)

sample17.3s (53.2%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
97.0ms	8131×	pre	128	true
29.0ms	131×	body	128	invalid

Compiler

Compiled 21470 to 13201 computations (38.5% saved)

Details

analyze9.0ms (0%)

sample76.0ms (0.2%)

simplify178.0ms (0.5%)

prune9.0ms (0%)

localize23.0ms (0.1%)

rewrite398.0ms (1.2%)

series330.0ms (1%)

simplify156.0ms (0.5%)

prune399.0ms (1.2%)

localize22.0ms (0.1%)

rewrite680.0ms (2.1%)

series360.0ms (1.1%)

simplify114.0ms (0.3%)

prune631.0ms (1.9%)

localize27.0ms (0.1%)

rewrite2.0s (6.2%)

series394.0ms (1.2%)

simplify262.0ms (0.8%)

prune1.7s (5.3%)

localize29.0ms (0.1%)

rewrite1.1s (3.4%)

series322.0ms (1%)

simplify156.0ms (0.5%)

prune805.0ms (2.5%)

regimes5.0s (15.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample17.3s (53.2%)

Profiling