Details

analyze1.3s (9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55
0	1	1
1	1	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)

sample222.0ms (1.5%)

Algorithm

1×

intervals

Results

62.0ms	132×	body	1024	nan
61.0ms	121×	body	1024	valid
25.0ms	61×	body	512	valid
19.0ms	58×	body	512	nan
12.0ms	12×	body	2048	valid
10.0ms	43×	body	256	valid
8.0ms	35×	body	256	nan
2.0ms	19×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55

prune13.0ms (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

61.9b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.8b	(/.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))))
7.0b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite455.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

61.9b

Rules

75×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
35×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`
18×	`difference-of-squares_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`unpow-prod-down_binary64`
8×	`pow1_binary64` `distribute-lft-out_binary64`
7×	`sqr-pow_binary64` `cancel-sign-sub-inv_binary64` `associate-/r*_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_binary64` `associate-r_binary64`
4×	`associate-/l*_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
3×	`div-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64`
2×	`flip3--_binary64` `flip--_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `pow-prod-down_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`diff-log_binary64` `sub-neg_binary64` `frac-2neg_binary64` `clear-num_binary64` `flip3-+_binary64` `flip-+_binary64`

Counts

4 → 141

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))))
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)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 6543 to 4377 computations (33.1% saved)

series382.0ms (2.6%)

Error

1.3b

Counts

4 → 12

Calls

4 calls:

190.0ms	(/.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))))
71.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
50.0ms	(*.f64 (/.f64 PI.f64 4) f)
46.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 1240 to 921 computations (25.7% saved)

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5172	5387

prune441.0ms (3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	3	154

Error

1.2b

Counts

154 → 3

Compiler

Compiled 6636 to 4451 computations (32.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))
0.3b	(.f64 f (.f64 PI.f64 1/2))
0.3b	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
0.4b	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))

rewrite156.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

33×	`add-exp-log_binary64`
23×	`add-cbrt-cube_binary64`
22×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
16×	`times-frac_binary64`
14×	`associate-r_binary64`
13×	`pow1_binary64`
11×	`prod-exp_binary64`
8×	`cbrt-unprod_binary64`
7×	`div-exp_binary64` `associate-l_binary64` `log-prod_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64`
3×	`div-inv_binary64` `associate-/l*_binary64`
2×	`unswap-sqr_binary64` `log-pow_binary64` `*-commutative_binary64`
1×	`associate-r/_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/r_binary64` `log-div_binary64`

Counts

4 → 94

Calls

4 calls:

10.0ms	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
6.0ms	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
5.0ms	(log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))
5.0ms	(.f64 f (.f64 PI.f64 1/2))

Compiler

Compiled 1805 to 1377 computations (23.7% saved)

series378.0ms (2.6%)

Error

1.0b

Counts

4 → 12

Calls

4 calls:

176.0ms	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
106.0ms	(log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))
44.0ms	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
41.0ms	(.f64 f (.f64 PI.f64 1/2))

Compiler

Compiled 420 to 356 computations (15.2% saved)

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5045	1497

prune140.0ms (0.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	93	13	106
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	94	15	109

Error

0.9b

Counts

109 → 15

Compiler

Compiled 1894 to 1352 computations (28.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
0.3b	(*.f64 PI.f64 f)
0.3b	(/.f64 4 (*.f64 PI.f64 f))
0.3b	(/.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) PI.f64)

rewrite125.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

21×	`add-sqr-sqrt_binary64`
19×	`add-exp-log_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
18×	`times-frac_binary64`
13×	`add-cbrt-cube_binary64`
11×	`pow1_binary64`
7×	`associate-/l*_binary64` `log-prod_binary64`
5×	`div-exp_binary64` `log-pow_binary64`
4×	`add-log-exp_binary64` `associate-/r*_binary64`
3×	`cbrt-undiv_binary64` `div-inv_binary64` `prod-exp_binary64` `associate-l_binary64` `associate-r_binary64` `rem-log-exp_binary64`
2×	`frac-2neg_binary64` `log-div_binary64` `clear-num_binary64` `cbrt-unprod_binary64`
1×	`div-sub_binary64` `pow-prod-down_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

6.0ms	(/.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) PI.f64)
4.0ms	(/.f64 4 (*.f64 PI.f64 f))
4.0ms	(*.f64 PI.f64 f)
4.0ms	(log.f64 (/.f64 4 (*.f64 PI.f64 f)))

Compiler

Compiled 1468 to 910 computations (38% saved)

series341.0ms (2.3%)

Error

0.9b

Counts

4 → 12

Calls

4 calls:

142.0ms	(/.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) PI.f64)
116.0ms	(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
41.0ms	(/.f64 4 (*.f64 PI.f64 f))
30.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 402 to 339 computations (15.7% saved)

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5068	1423

prune120.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	95	7	102
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	105	12	117

Error

0.8b

Counts

117 → 12

Compiler

Compiled 1720 to 1137 computations (33.9% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (/.f64 4 f))
0.2b	(+.f64 (neg.f64 (log.f64 PI.f64)) (log.f64 (/.f64 4 f)))
0.3b	(/.f64 (+.f64 (neg.f64 (log.f64 PI.f64)) (log.f64 (/.f64 4 f))) PI.f64)

rewrite165.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

67×	`*-un-lft-identity_binary64`
45×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
30×	`distribute-lft-out_binary64`
29×	`pow1_binary64` `log-prod_binary64`
26×	`log-pow_binary64`
20×	`distribute-rgt-neg-in_binary64`
13×	`associate-+r+_binary64`
9×	`associate-/l*_binary64`
8×	`add-exp-log_binary64`
5×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`log-div_binary64` `div-inv_binary64` `associate-/r*_binary64` `distribute-neg-in_binary64` `associate-+l+_binary64`
2×	`div-exp_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `div-sub_binary64` `associate-+r-_binary64` `flip3-+_binary64` `associate-/l/_binary64` `flip-+_binary64` `sum-log_binary64` `rem-log-exp_binary64`
1×	`cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `neg-log_binary64` `+-commutative_binary64`

Counts

3 → 115

Calls

3 calls:

10.0ms	(/.f64 (+.f64 (neg.f64 (log.f64 PI.f64)) (log.f64 (/.f64 4 f))) PI.f64)
10.0ms	(+.f64 (neg.f64 (log.f64 PI.f64)) (log.f64 (/.f64 4 f)))
3.0ms	(log.f64 (/.f64 4 f))

Compiler

Compiled 2259 to 1384 computations (38.7% saved)

series437.0ms (2.9%)

Error

0.8b

Counts

3 → 9

Calls

3 calls:

192.0ms	(/.f64 (+.f64 (neg.f64 (log.f64 PI.f64)) (log.f64 (/.f64 4 f))) PI.f64)
160.0ms	(+.f64 (neg.f64 (log.f64 PI.f64)) (log.f64 (/.f64 4 f)))
76.0ms	(log.f64 (/.f64 4 f))

Compiler

Compiled 369 to 314 computations (14.9% saved)

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5003	2236

prune135.0ms (0.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	124	12	136

Error

0.8b

Counts

136 → 12

Compiler

Compiled 2117 to 1350 computations (36.2% saved)

regimes979.0ms (6.6%)

Accuracy

Total 1.1b remaining (42.6%)

Threshold costs 0b (0%)

Compiler

Compiled 11574 to 9548 computations (17.5% 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%)

sample8.6s (57.9%)

Algorithm

1×

intervals

Results

2.0s	3937×	body	1024	valid
1.9s	3976×	body	1024	nan
708.0ms	1956×	body	512	valid
660.0ms	1988×	body	512	nan
487.0ms	461×	body	2048	valid
246.0ms	997×	body	256	valid
229.0ms	1003×	body	256	nan
86.0ms	649×	body	128	valid
3.0ms	4×	body	2048	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 1932 to 1596 computations (17.4% saved)

Details

analyze1.3s (9%)

sample222.0ms (1.5%)

simplify78.0ms (0.5%)

prune13.0ms (0.1%)

localize18.0ms (0.1%)

rewrite455.0ms (3.1%)

series382.0ms (2.6%)

simplify96.0ms (0.6%)

prune441.0ms (3%)

localize9.0ms (0.1%)

rewrite156.0ms (1.1%)

series378.0ms (2.6%)

simplify58.0ms (0.4%)

prune140.0ms (0.9%)

localize8.0ms (0.1%)

rewrite125.0ms (0.8%)

series341.0ms (2.3%)

simplify64.0ms (0.4%)

prune120.0ms (0.8%)

localize10.0ms (0.1%)

rewrite165.0ms (1.1%)

series437.0ms (2.9%)

simplify69.0ms (0.5%)

prune135.0ms (0.9%)

regimes979.0ms (6.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample8.6s (57.9%)

Profiling