Details

analyze1.2s (9.1%)

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)

sample206.0ms (1.5%)

Algorithm

1×

intervals

Results

60.0ms	125×	body	1024	valid
46.0ms	97×	body	1024	nan
25.0ms	62×	body	512	valid
22.0ms	19×	body	2048	valid
18.0ms	58×	body	512	nan
7.0ms	29×	body	256	valid
6.0ms	26×	body	256	nan
3.0ms	21×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify82.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

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

61.5b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize17.0ms (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)
2.0b	(/.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))))
5.6b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite438.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

61.4b

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))))
13.0ms	(-.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)

series270.0ms (2%)

Error

2.7b

Counts

4 → 12

Calls

4 calls:

129.0ms	(/.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))))
56.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
32.0ms	(*.f64 (/.f64 PI.f64 4) f)
31.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 1240 to 921 computations (25.7% saved)

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5172	5387

prune353.0ms (2.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	147	6	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	6	154

Error

2.7b

Counts

154 → 6

Compiler

Compiled 6780 to 4558 computations (32.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

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))

rewrite115.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

2.3b

Rules

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

Counts

3 → 74

Calls

3 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	(.f64 f (.f64 PI.f64 1/2))

Compiler

Compiled 1444 to 1095 computations (24.2% saved)

series181.0ms (1.3%)

Error

2.5b

Counts

3 → 9

Calls

3 calls:

113.0ms	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
30.0ms	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
30.0ms	(.f64 f (.f64 PI.f64 1/2))

Compiler

Compiled 309 to 261 computations (15.5% saved)

simplify56.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5859	1210

prune103.0ms (0.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	73	10	83
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	74	15	89

Error

2.3b

Counts

89 → 15

Compiler

Compiled 1659 to 1186 computations (28.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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)

rewrite88.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

2.3b

Rules

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

Counts

3 → 71

Calls

3 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)

Compiler

Compiled 1176 to 719 computations (38.9% saved)

series143.0ms (1%)

Error

2.3b

Counts

3 → 9

Calls

3 calls:

89.0ms	(/.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) PI.f64)
28.0ms	(/.f64 4 (*.f64 PI.f64 f))
19.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 291 to 244 computations (16.2% saved)

simplify56.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5451	1152

prune89.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Error

2.3b

Counts

95 → 13

Compiler

Compiled 1543 to 1028 computations (33.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64)))
0.3b	(/.f64 (-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64))) (neg.f64 PI.f64))
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite225.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

2.3b

Rules

105×	`*-un-lft-identity_binary64`
98×	`times-frac_binary64`
81×	`add-sqr-sqrt_binary64`
57×	`add-cube-cbrt_binary64`
53×	`pow1_binary64`
50×	`log-pow_binary64`
48×	`distribute-lft-out--_binary64`
29×	`log-prod_binary64`
27×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
13×	`associate--r+_binary64`
12×	`difference-of-squares_binary64`
10×	`associate-/r*_binary64`
9×	`neg-mul-1_binary64`
8×	`add-exp-log_binary64` `associate-/l*_binary64`
5×	`add-cbrt-cube_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`div-inv_binary64` `add-log-exp_binary64` `associate--l+_binary64`
2×	`log-div_binary64` `div-exp_binary64` `rem-log-exp_binary64` `flip3--_binary64` `associate-/l/_binary64` `flip--_binary64`
1×	`cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `diff-log_binary64` `sub-neg_binary64` `associate--r-_binary64`

Counts

3 → 174

Calls

3 calls:

10.0ms	(/.f64 (-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64))) (neg.f64 PI.f64))
7.0ms	(-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64)))
3.0ms	(log.f64 (/.f64 4 PI.f64))

Compiler

Compiled 3614 to 2188 computations (39.5% saved)

series249.0ms (1.8%)

Error

2.3b

Counts

3 → 6

Calls

3 calls:

137.0ms	(/.f64 (-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64))) (neg.f64 PI.f64))
108.0ms	(-.f64 (log.f64 f) (log.f64 (/.f64 4 PI.f64)))
0.0ms	(log.f64 (/.f64 4 PI.f64))

Compiler

Compiled 267 to 236 computations (11.6% saved)

simplify107.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4978	4222
1	4978	4222

prune184.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	181	12	193

Error

2.3b

Counts

193 → 12

Compiler

Compiled 3407 to 2049 computations (39.9% saved)

regimes859.0ms (6.3%)

Accuracy

Total 1.0b remaining (37.6%)

Threshold costs 0b (0%)

Compiler

Compiled 12282 to 9830 computations (20% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	21
1	28	21

end0.0ms (0%)

sample8.4s (61.9%)

Algorithm

1×

intervals

Results

1.9s	3888×	body	1024	valid
1.8s	3996×	body	1024	nan
687.0ms	1945×	body	512	valid
632.0ms	1942×	body	512	nan
538.0ms	524×	body	2048	valid
243.0ms	1012×	body	256	valid
205.0ms	940×	body	256	nan
79.0ms	631×	body	128	valid
2.0ms	3×	body	2048	nan

Compiler

Compiled 2051 to 1644 computations (19.8% saved)

Details

analyze1.2s (9.1%)

sample206.0ms (1.5%)

simplify82.0ms (0.6%)

prune8.0ms (0.1%)

localize17.0ms (0.1%)

rewrite438.0ms (3.2%)

series270.0ms (2%)

simplify92.0ms (0.7%)

prune353.0ms (2.6%)

localize11.0ms (0.1%)

rewrite115.0ms (0.8%)

series181.0ms (1.3%)

simplify56.0ms (0.4%)

prune103.0ms (0.8%)

localize8.0ms (0.1%)

rewrite88.0ms (0.6%)

series143.0ms (1%)

simplify56.0ms (0.4%)

prune89.0ms (0.7%)

localize10.0ms (0.1%)

rewrite225.0ms (1.7%)

series249.0ms (1.8%)

simplify107.0ms (0.8%)

prune184.0ms (1.3%)

regimes859.0ms (6.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample8.4s (61.9%)

Profiling