Details

analyze1.1s (7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 38 to 31 computations (18.4% saved)

sample236.0ms (1.5%)

Algorithm

1×

intervals

Results

65.0ms	139×	body	1024	nan
56.0ms	108×	body	1024	valid
24.0ms	64×	body	512	nan
24.0ms	60×	body	512	valid
22.0ms	20×	body	2048	valid
11.0ms	45×	body	256	valid
8.0ms	36×	body	256	nan
3.0ms	23×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify178.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

62.0b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.4b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
1.7b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
8.3b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite580.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

62.0b

Rules

94×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
34×	`log-prod_binary64`
30×	`difference-of-squares_binary64`
15×	`distribute-lft-out_binary64`
14×	`add-exp-log_binary64`
13×	`unpow-prod-down_binary64` `associate-l_binary64`
11×	`add-cbrt-cube_binary64` `sqr-pow_binary64`
10×	`distribute-lft-out--_binary64`
7×	`pow1_binary64` `cancel-sign-sub-inv_binary64` `associate-/r*_binary64`
6×	`add-log-exp_binary64`
4×	`associate-/r/_binary64` `associate-/l*_binary64`
3×	`flip3--_binary64` `flip--_binary64` `div-exp_binary64` `div-inv_binary64` `associate-r_binary64`
2×	`cbrt-undiv_binary64` `associate-/l/_binary64` `rem-log-exp_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
1×	`diff-log_binary64` `sub-neg_binary64` `frac-2neg_binary64` `clear-num_binary64` `flip3-+_binary64` `flip-+_binary64` `log-pow_binary64` `log-div_binary64` `pow-prod-down_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 154

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
14.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
9.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 7895 to 5333 computations (32.5% saved)

series593.0ms (3.7%)

Error

2.4b

Counts

4 → 12

Calls

4 calls:

346.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
132.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
57.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
34.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 1363 to 1042 computations (23.6% saved)

simplify124.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5005	8522

prune479.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	160	6	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	6	167

Error

2.4b

Counts

167 → 6

Compiler

Compiled 7862 to 5333 computations (32.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(-.f64 (log.f64 (/.f64 2 (*.f64 PI.f64 1/2))) (log.f64 f))
0.4b	(.f64 (-.f64 (log.f64 (/.f64 2 (.f64 PI.f64 1/2))) (log.f64 f)) (/.f64 -4 PI.f64))
2.0b	(log.f64 (/.f64 2 (*.f64 PI.f64 1/2)))

rewrite157.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

2.1b

Rules

26×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64` `log-prod_binary64`
16×	`times-frac_binary64`
15×	`pow1_binary64`
14×	`add-exp-log_binary64`
13×	`associate-r_binary64`
10×	`log-pow_binary64`
8×	`add-cbrt-cube_binary64` `associate-l_binary64` `distribute-lft-out--_binary64`
7×	`associate--l+_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`div-inv_binary64` `prod-exp_binary64` `div-exp_binary64` `rem-log-exp_binary64` `add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `associate--r+_binary64`
2×	`log-div_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `unswap-sqr_binary64` `associate-*l/_binary64` `difference-of-squares_binary64`
1×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `-commutative_binary64` `diff-log_binary64` `sub-neg_binary64` `associate--l-_binary64`

Counts

3 → 91

Calls

3 calls:

13.0ms	(.f64 (-.f64 (log.f64 (/.f64 2 (.f64 PI.f64 1/2))) (log.f64 f)) (/.f64 -4 PI.f64))
9.0ms	(-.f64 (log.f64 (/.f64 2 (*.f64 PI.f64 1/2))) (log.f64 f))
4.0ms	(log.f64 (/.f64 2 (*.f64 PI.f64 1/2)))

Compiler

Compiled 1966 to 1423 computations (27.6% saved)

series266.0ms (1.7%)

Error

2.3b

Counts

3 → 6

Calls

3 calls:

150.0ms	(.f64 (-.f64 (log.f64 (/.f64 2 (.f64 PI.f64 1/2))) (log.f64 f)) (/.f64 -4 PI.f64))
109.0ms	(-.f64 (log.f64 (/.f64 2 (*.f64 PI.f64 1/2))) (log.f64 f))
0.0ms	(log.f64 (/.f64 2 (*.f64 PI.f64 1/2)))

Compiler

Compiled 240 to 211 computations (12.1% saved)

simplify84.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4959	1739
1	4959	1739

prune137.0ms (0.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	87	10	97
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	89	14	103

Error

2.1b

Counts

103 → 14

Compiler

Compiled 2151 to 1521 computations (29.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f)) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite184.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

2.1b

Rules

66×	`*-un-lft-identity_binary64`
57×	`times-frac_binary64`
54×	`add-sqr-sqrt_binary64`
38×	`add-cube-cbrt_binary64`
35×	`pow1_binary64`
33×	`sqrt-prod_binary64`
29×	`log-pow_binary64`
28×	`distribute-lft-out--_binary64`
13×	`log-prod_binary64`
9×	`add-exp-log_binary64`
8×	`associate-/l*_binary64`
7×	`difference-of-squares_binary64`
6×	`add-cbrt-cube_binary64` `associate-/r*_binary64`
4×	`add-log-exp_binary64`
2×	`div-inv_binary64` `div-exp_binary64` `rem-log-exp_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-/l/_binary64`
1×	`log-div_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `flip3--_binary64` `flip--_binary64`

Counts

4 → 127

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f)) (sqrt.f64 PI.f64))
3.0ms	(log.f64 (/.f64 4 PI.f64))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 2953 to 1616 computations (45.3% saved)

series155.0ms (1%)

Error

2.1b

Counts

4 → 3

Calls

4 calls:

151.0ms	(/.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f)) (sqrt.f64 PI.f64))
0.0ms	(log.f64 (/.f64 4 PI.f64))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 174 to 150 computations (13.8% saved)

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4962	2815
1	4962	2815

prune166.0ms (1.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	129	15	144

Error

2.1b

Counts

144 → 15

Compiler

Compiled 3310 to 1912 computations (42.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (-.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (.f64 2 (log.f64 (cbrt.f64 f)))) (log.f64 (cbrt.f64 f))) (/.f64 -4 PI.f64))
0.7b	(cbrt.f64 f)
0.7b	(cbrt.f64 f)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite139.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

2.1b

Rules

28×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
13×	`log-prod_binary64` `associate-r_binary64`
12×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`cbrt-prod_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
2×	`log-pow_binary64` `div-inv_binary64` `div-exp_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `flip3--_binary64` `frac-times_binary64` `flip--_binary64` `unswap-sqr_binary64` `associate-*l/_binary64` `distribute-lft-out--_binary64`
1×	`log-div_binary64` `pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `difference-of-squares_binary64` `-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

14.0ms	(.f64 (-.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (.f64 2 (log.f64 (cbrt.f64 f)))) (log.f64 (cbrt.f64 f))) (/.f64 -4 PI.f64))
3.0ms	(log.f64 (/.f64 4 PI.f64))
1.0ms	(cbrt.f64 f)
1.0ms	(cbrt.f64 f)

Compiler

Compiled 2353 to 1378 computations (41.4% saved)

series421.0ms (2.7%)

Error

2.1b

Counts

4 → 9

Calls

4 calls:

239.0ms	(.f64 (-.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (.f64 2 (log.f64 (cbrt.f64 f)))) (log.f64 (cbrt.f64 f))) (/.f64 -4 PI.f64))
85.0ms	(cbrt.f64 f)
85.0ms	(cbrt.f64 f)
0.0ms	(log.f64 (/.f64 4 PI.f64))

Compiler

Compiled 528 to 457 computations (13.4% saved)

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4969	1537
1	4969	1537

prune106.0ms (0.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	3	10	13
Picked	1	0	1
Done	0	1	1
Total	95	14	109

Error

2.1b

Counts

109 → 14

Compiler

Compiled 2024 to 1249 computations (38.3% saved)

regimes1.2s (7.5%)

Accuracy

Total 1.0b remaining (36%)

Threshold costs 0b (0%)

Compiler

Compiled 18630 to 14456 computations (22.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	19
1	22	19

end0.0ms (0%)

sample9.3s (58.7%)

Algorithm

1×

intervals

Results

2.0s	3904×	body	1024	valid
1.8s	3802×	body	1024	nan
720.0ms	1991×	body	512	valid
640.0ms	1870×	body	512	nan
548.0ms	516×	body	2048	valid
240.0ms	965×	body	256	valid
211.0ms	945×	body	256	nan
80.0ms	624×	body	128	valid
1.0ms	2×	body	2048	nan
0.0ms	1×	body	128	nan

Compiler

Compiled 3108 to 2414 computations (22.3% saved)

Details

analyze1.1s (7%)

sample236.0ms (1.5%)

simplify178.0ms (1.1%)

prune8.0ms (0.1%)

localize25.0ms (0.2%)

rewrite580.0ms (3.7%)

series593.0ms (3.7%)

simplify124.0ms (0.8%)

prune479.0ms (3%)

localize11.0ms (0.1%)

rewrite157.0ms (1%)

series266.0ms (1.7%)

simplify84.0ms (0.5%)

prune137.0ms (0.9%)

localize12.0ms (0.1%)

rewrite184.0ms (1.2%)

series155.0ms (1%)

simplify97.0ms (0.6%)

prune166.0ms (1.1%)

localize16.0ms (0.1%)

rewrite139.0ms (0.9%)

series421.0ms (2.7%)

simplify67.0ms (0.4%)

prune106.0ms (0.7%)

regimes1.2s (7.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample9.3s (58.7%)

Profiling