Details

analyze2.3s (8.7%)

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)

sample439.0ms (1.6%)

Algorithm

1×

intervals

Results

145.0ms	163×	body	1024	nan
111.0ms	118×	body	1024	valid
43.0ms	60×	body	512	valid
36.0ms	58×	body	512	nan
35.0ms	18×	body	2048	valid
17.0ms	39×	body	256	valid
12.0ms	29×	body	256	nan
5.0ms	21×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify146.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55

prune14.0ms (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

62.1b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 f)
0.2b	(*.f64 PI.f64 f)
1.2b	(/.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))))
5.7b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite536.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

62.0b

Rules

57×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
10×	`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-l_binary64` `associate-r_binary64`
4×	`associate-/l*_binary64`
2×	`flip3--_binary64` `flip--_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `sub-neg_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `flip3-+_binary64` `flip-+_binary64`

Counts

4 → 113

Calls

4 calls:

24.0ms	(/.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))))
15.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
6.0ms	(*.f64 PI.f64 f)
6.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 5385 to 3566 computations (33.8% saved)

series358.0ms (1.3%)

Error

2.2b

Counts

4 → 12

Calls

4 calls:

195.0ms	(/.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))))
69.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
31.0ms	(*.f64 PI.f64 f)
31.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 1240 to 926 computations (25.3% saved)

simplify224.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (155.0ms)

Iter	Nodes	Cost
0	4882	4960
1	4882	4960

prune465.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	5	126

Error

2.1b

Counts

126 → 5

Compiler

Compiled 5621 to 3754 computations (33.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 f)
0.3b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))
0.4b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
1.2b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))

rewrite344.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

30×	`add-exp-log_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cbrt-cube_binary64`
18×	`add-cube-cbrt_binary64` `times-frac_binary64`
16×	`associate-r_binary64`
10×	`pow1_binary64`
9×	`prod-exp_binary64`
8×	`log-prod_binary64`
7×	`div-exp_binary64` `associate-l_binary64`
6×	`cbrt-unprod_binary64`
4×	`rem-log-exp_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
3×	`distribute-lft-out_binary64` `div-inv_binary64` `unswap-sqr_binary64`
2×	`log-pow_binary64` `pow-prod-down_binary64` `*-commutative_binary64` `associate-/l/_binary64`
1×	`log-div_binary64` `associate-r/_binary64` `frac-2neg_binary64` `clear-num_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-/r_binary64`

Counts

4 → 99

Calls

4 calls:

19.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))
10.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))
10.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
7.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 3626 to 2446 computations (32.5% saved)

series759.0ms (2.8%)

Error

1.9b

Counts

4 → 12

Calls

4 calls:

334.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
246.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2))))
107.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 f (.f64 PI.f64 1/2)))
41.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 858 to 670 computations (21.9% saved)

simplify109.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5274	3722

prune251.0ms (0.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	102	14	116

Error

1.7b

Counts

116 → 14

Compiler

Compiled 4028 to 2588 computations (35.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 f)
0.3b	(/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 f))
0.3b	(/.f64 (.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 f)))) -4) PI.f64)
1.2b	(log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (*.f64 PI.f64 f))))

rewrite305.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

26×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`
7×	`prod-exp_binary64` `times-frac_binary64`
6×	`div-exp_binary64`
5×	`associate-/l*_binary64`
4×	`rem-log-exp_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/r*_binary64`
3×	`cbrt-unprod_binary64` `associate-l_binary64` `associate-r_binary64`
2×	`pow-prod-down_binary64` `log-pow_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `distribute-lft-out_binary64` `associate-/l/_binary64`
1×	`associate-r/_binary64` `log-div_binary64` `log-prod_binary64` `flip3-+_binary64` `flip-+_binary64` `unswap-sqr_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

23.0ms	(/.f64 (.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 f)))) -4) PI.f64)
19.0ms	(/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 f))
12.0ms	(log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (*.f64 PI.f64 f))))
7.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 2756 to 1625 computations (41% saved)

series683.0ms (2.6%)

Error

1.7b

Counts

4 → 12

Calls

4 calls:

298.0ms	(/.f64 (.f64 (log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 f)))) -4) PI.f64)
251.0ms	(log.f64 (.f64 2 (/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (*.f64 PI.f64 f))))
82.0ms	(/.f64 (+.f64 (exp.f64 (.f64 1/4 (.f64 PI.f64 f))) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (.f64 PI.f64 f))
36.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 862 to 660 computations (23.4% saved)

simplify114.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5096	2575

prune241.0ms (0.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	92	13	105

Error

1.7b

Counts

105 → 13

Compiler

Compiled 3227 to 2003 computations (37.9% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite287.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

52×	`*-un-lft-identity_binary64`
42×	`add-sqr-sqrt_binary64` `times-frac_binary64`
32×	`add-cube-cbrt_binary64`
29×	`log-prod_binary64`
25×	`pow1_binary64`
22×	`log-pow_binary64`
20×	`distribute-lft-out--_binary64`
13×	`associate--l+_binary64`
8×	`add-exp-log_binary64` `associate-/l*_binary64`
5×	`add-cbrt-cube_binary64` `difference-of-squares_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`div-inv_binary64` `add-log-exp_binary64` `associate-/r*_binary64` `associate--r+_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--l-_binary64`

Counts

3 → 111

Calls

3 calls:

19.0ms	(/.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f)) PI.f64)
15.0ms	(-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f))
5.0ms	(log.f64 (/.f64 4 PI.f64))

Compiler

Compiled 2106 to 1368 computations (35% saved)

series366.0ms (1.4%)

Error

1.7b

Counts

3 → 6

Calls

3 calls:

212.0ms	(/.f64 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f)) PI.f64)
143.0ms	(-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f))
0.0ms	(log.f64 (/.f64 4 PI.f64))

Compiler

Compiled 240 to 211 computations (12.1% saved)

simplify121.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5003	2202

prune195.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	112	5	117
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	117	13	130

Error

1.7b

Counts

130 → 13

Compiler

Compiled 2039 to 1320 computations (35.3% saved)

regimes2.1s (7.8%)

Accuracy

Total 1.0b remaining (39.1%)

Threshold costs 1.0b (39.1%)

Compiler

Compiled 20766 to 15584 computations (25% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	41
1	26	41

end0.0ms (0%)

sample16.3s (60.9%)

Algorithm

1×

intervals

Results

3.5s	3964×	body	1024	valid
3.2s	3841×	body	1024	nan
1.2s	1918×	body	512	valid
1.1s	1908×	body	512	nan
843.0ms	485×	body	2048	valid
428.0ms	1020×	body	256	valid
390.0ms	1015×	body	256	nan
132.0ms	613×	body	128	valid
3.0ms	2×	body	2048	nan
1.0ms	4×	body	128	overflowed
0.0ms	2×	body	128	nan

Compiler

Compiled 3477 to 2611 computations (24.9% saved)

Details

analyze2.3s (8.7%)

sample439.0ms (1.6%)

simplify146.0ms (0.5%)

prune14.0ms (0.1%)

localize40.0ms (0.2%)

rewrite536.0ms (2%)

series358.0ms (1.3%)

simplify224.0ms (0.8%)

prune465.0ms (1.7%)

localize17.0ms (0.1%)

rewrite344.0ms (1.3%)

series759.0ms (2.8%)

simplify109.0ms (0.4%)

prune251.0ms (0.9%)

localize15.0ms (0.1%)

rewrite305.0ms (1.1%)

series683.0ms (2.6%)

simplify114.0ms (0.4%)

prune241.0ms (0.9%)

localize18.0ms (0.1%)

rewrite287.0ms (1.1%)

series366.0ms (1.4%)

simplify121.0ms (0.5%)

prune195.0ms (0.7%)

regimes2.1s (7.8%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample16.3s (60.9%)

Profiling