Details

analyze298.0ms (0.6%)

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)

sample142.0ms (0.3%)

Algorithm

1×

intervals

Results

106.0ms	256×	body	128	valid
5.0ms	258×	pre	128	true
1.0ms	2×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify142.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (131.0ms)

Iter	Nodes	Cost
0	5512	47

prune16.0ms (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)

localize41.0ms (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)))))
0.5b	(/.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))

rewrite682.0ms (1.3%)

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:

82.0ms	(.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)))))
18.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
3.0ms	(exp.f64 (*.f64 x x))
3.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 6804 to 2952 computations (56.6% saved)

series589.0ms (1.1%)

Error

2.5b

Counts

4 → 24

Calls

4 calls:

344.0ms	(.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)))))
131.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
43.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1858 to 1391 computations (25.1% saved)

simplify257.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (148.0ms)

Iter	Nodes	Cost
0	4943	6637
1	4943	6637

prune620.0ms (1.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	155	18	173
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	157	18	175

Error

0.7b

Counts

175 → 18

Compiler

Compiled 8074 to 3689 computations (54.3% saved)

localize39.0ms (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)))))
0.5b	(/.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 (2.2%)

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:

108.0ms	(.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)))))
17.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
6.0ms	(pow.f64 (exp.f64 x) x)
2.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 11001 to 4719 computations (57.1% saved)

series607.0ms (1.2%)

Error

0.6b

Counts

4 → 24

Calls

4 calls:

346.0ms	(.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)))))
128.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
66.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1858 to 1267 computations (31.8% saved)

simplify196.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5039	11122

prune1.3s (2.5%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	234	27	261
Fresh	14	3	17
Picked	1	0	1
Done	0	0	0
Total	249	30	279

Error

0.1b

Counts

279 → 30

Compiler

Compiled 12910 to 5815 computations (55% saved)

localize43.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.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)

rewrite232.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`*-un-lft-identity_binary64_2465`
13×	`add-sqr-sqrt_binary64_2487`
11×	`add-cube-cbrt_binary64_2500`
9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
7×	`pow1_binary64_2526`
6×	`sqrt-prod_binary64_2481`
4×	`pow-pow_binary64_2537` `add-log-exp_binary64_2504` `times-frac_binary64_2471` `associate-/l*_binary64_2410`
3×	`unpow-prod-down_binary64_2544` `pow-unpow_binary64_2542` `exp-prod_binary64_2517`
2×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `distribute-lft-out_binary64_2416` `associate-/l/_binary64_2412`
1×	`pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `sqr-pow_binary64_2437` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462` `flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-/r*_binary64_2409`

Counts

4 → 71

Calls

4 calls:

20.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
6.0ms	(pow.f64 (exp.f64 x) x)
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 2932 to 1330 computations (54.6% saved)

series210.0ms (0.4%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

116.0ms	(/.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)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1051 to 688 computations (34.5% saved)

simplify113.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5015	956

prune318.0ms (0.6%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	29	29
Picked	0	1	1
Done	0	0	0
Total	83	30	113

Error

0.1b

Counts

113 → 30

Compiler

Compiled 4746 to 2331 computations (50.9% saved)

localize45.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite1.9s (3.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

558×	`times-frac_binary64_2471`
319×	`add-sqr-sqrt_binary64_2487`
280×	`sqrt-prod_binary64_2481` `associate-r_binary64_2405`
275×	`*-un-lft-identity_binary64_2465`
266×	`add-cube-cbrt_binary64_2500`
115×	`unpow-prod-down_binary64_2544`
41×	`sqr-pow_binary64_2437`
24×	`add-exp-log_binary64_2503`
18×	`add-cbrt-cube_binary64_2501`
15×	`unswap-sqr_binary64_2433`
9×	`div-exp_binary64_2516`
8×	`pow1_binary64_2526` `div-inv_binary64_2462`
6×	`prod-exp_binary64_2514`
5×	`cbrt-undiv_binary64_2499` `distribute-lft-out_binary64_2416` `associate-l_binary64_2406`
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-*l/_binary64_2408`
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` `associate-r/_binary64_2407` `*-commutative_binary64_2396`

Counts

4 → 380

Calls

4 calls:

192.0ms	(.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (sqrt.f64 (fabs.f64 x))))
17.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
6.0ms	(pow.f64 (exp.f64 x) x)
2.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 20970 to 8571 computations (59.1% saved)

series632.0ms (1.2%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

369.0ms	(.f64 (+.f64 1 (+.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)) (/.f64 15/8 (pow.f64 x 6)))) (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64)) (sqrt.f64 (fabs.f64 x))))
127.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
68.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 2201 to 1419 computations (35.5% saved)

simplify358.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

404 → 404

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4977	19153
1	4977	19153

prune1.7s (3.3%)

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	394	10	404
Fresh	7	21	28
Picked	1	0	1
Done	0	1	1
Total	402	32	434

Error

0.1b

Counts

434 → 32

Compiler

Compiled 20494 to 8141 computations (60.3% saved)

regimes7.8s (15.2%)

Accuracy

Total 1.2b remaining (91.3%)

Threshold costs 0b (0%)

Compiler

Compiled 59615 to 36660 computations (38.5% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	63
1	34	63

end0.0ms (0%)

sample31.9s (62.3%)

Algorithm

1×

intervals

Results

3.2s	8000×	body	128	valid
164.0ms	8105×	pre	128	true
41.0ms	105×	body	128	invalid

Compiler

Compiled 19946 to 12271 computations (38.5% saved)

Details

analyze298.0ms (0.6%)

sample142.0ms (0.3%)

simplify142.0ms (0.3%)

prune16.0ms (0%)

localize41.0ms (0.1%)

rewrite682.0ms (1.3%)

series589.0ms (1.1%)

simplify257.0ms (0.5%)

prune620.0ms (1.2%)

localize39.0ms (0.1%)

rewrite1.1s (2.2%)

series607.0ms (1.2%)

simplify196.0ms (0.4%)

prune1.3s (2.5%)

localize43.0ms (0.1%)

rewrite232.0ms (0.5%)

series210.0ms (0.4%)

simplify113.0ms (0.2%)

prune318.0ms (0.6%)

localize45.0ms (0.1%)

rewrite1.9s (3.7%)

series632.0ms (1.2%)

simplify358.0ms (0.7%)

prune1.7s (3.3%)

regimes7.8s (15.2%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample31.9s (62.3%)

Profiling