Details

analyze1.1s (5%)

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)

sample215.0ms (1%)

Algorithm

1×

intervals

Results

57.0ms	110×	body	1024	valid
51.0ms	109×	body	1024	nan
30.0ms	69×	body	512	valid
22.0ms	63×	body	512	nan
19.0ms	17×	body	2048	valid
10.0ms	39×	body	256	valid
9.0ms	37×	body	256	nan
3.0ms	21×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify177.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55

prune8.0ms (0%)

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)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.2b	(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)))))
1.2b	(/.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))))
7.9b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite65.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

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×	`associate-l_binary64` `unpow-prod-down_binary64`
11×	`sqr-pow_binary64` `add-cbrt-cube_binary64`
10×	`distribute-lft-out--_binary64`
7×	`associate-/r*_binary64` `pow1_binary64` `cancel-sign-sub-inv_binary64`
6×	`add-log-exp_binary64`
4×	`associate-/r/_binary64` `associate-/l*_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 154

Calls

4 calls:

13.0ms	(/.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	(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)))))
8.0ms	(-.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)

series1.3s (5.9%)

Counts

4 → 12

Calls

4 calls:

913.0ms	(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)))))
268.0ms	(/.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))))
58.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
18.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify142.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4959	9948
1	4959	9948

prune597.0ms (2.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	3	167

Error

1.8b

Counts

167 → 3

Compiler

Compiled 9223 to 6346 computations (31.2% saved)

localize82.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(pow.f64 PI.f64 3)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)

rewrite41.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`pow-unpow_binary64` `unpow-prod-down_binary64`
8×	`pow1_binary64` `add-exp-log_binary64`
5×	`add-cbrt-cube_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-exp_binary64`
3×	`cube-prod_binary64`
1×	`rem-cube-cbrt_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 74

Calls

4 calls:

2.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 3)
2.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 4)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 3)
0.0ms	(pow.f64 PI.f64 4)

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4869	1424
1	4869	1424

prune1.1s (5.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	78	3	81

Error

1.8b

Counts

81 → 3

Compiler

Compiled 15078 to 11968 computations (20.6% saved)

localize219.0ms (1%)

Local error

Found 4 expressions with local error:

1.6b	(pow.f64 (*.f64 PI.f64 1/2) 4)
1.6b	(pow.f64 (*.f64 PI.f64 1/2) 4)
1.6b	(pow.f64 (*.f64 PI.f64 1/2) 4)
2.0b	(log.f64 (/.f64 2 (*.f64 PI.f64 1/2)))

rewrite81.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64`
14×	`pow1_binary64`
9×	`*-un-lft-identity_binary64` `pow-unpow_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
7×	`log-prod_binary64`
6×	`pow-pow_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64`
3×	`pow-to-exp_binary64` `pow-prod-down_binary64` `rem-log-exp_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `times-frac_binary64`
2×	`div-exp_binary64`
1×	`log-pow_binary64` `div-inv_binary64` `log-div_binary64`

Counts

4 → 70

Calls

4 calls:

5.0ms	(log.f64 (/.f64 2 (*.f64 PI.f64 1/2)))
4.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
4.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
4.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(log.f64 (/.f64 2 (*.f64 PI.f64 1/2)))
0.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
0.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)
0.0ms	(pow.f64 (*.f64 PI.f64 1/2) 4)

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4944	3514
1	4944	3514

prune3.6s (16.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	74	3	77

Error

1.8b

Counts

77 → 3

Compiler

Compiled 35407 to 26118 computations (26.2% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (+.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f))))
1.0b	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f))))
1.1b	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (+.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f)))))
7.9b	(-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f)))

rewrite130.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

201×	`add-sqr-sqrt_binary64`
167×	`*-un-lft-identity_binary64`
145×	`sqrt-prod_binary64`
140×	`times-frac_binary64`
75×	`add-cube-cbrt_binary64`
72×	`difference-of-squares_binary64`
42×	`unpow-prod-down_binary64`
37×	`distribute-lft-out_binary64`
34×	`log-prod_binary64`
19×	`sqr-pow_binary64`
16×	`associate-/r*_binary64`
14×	`associate-/l*_binary64`
11×	`add-exp-log_binary64`
10×	`cancel-sign-sub-inv_binary64`
9×	`distribute-lft-out--_binary64`
8×	`add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `associate-/l/_binary64` `flip-+_binary64` `sqrt-div_binary64`
3×	`div-inv_binary64` `div-exp_binary64`
2×	`flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `log-pow_binary64` `log-div_binary64`

Counts

4 → 249

Calls

4 calls:

22.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f))))
17.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (+.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f)))))
16.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (+.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f))))
10.0ms	(-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f)))

series1.1s (5%)

Counts

4 → 12

Calls

4 calls:

454.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f))))
374.0ms	(log.f64 (/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (+.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f)))))
189.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (+.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f))))
66.0ms	(-.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f))) (pow.f64 (sqrt.f64 (exp.f64 -1/4)) (.f64 PI.f64 f)))

simplify214.0ms (1%)

Algorithm

1×	egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4997	21627
1	4997	21627

prune2.1s (9.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	261	0	261
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	261	3	264

Error

1.8b

Counts

264 → 3

Compiler

Compiled 23855 to 16735 computations (29.8% saved)

regimes837.0ms (3.9%)

Accuracy

Total 0.6b remaining (27.1%)

Threshold costs 0.6b (27.1%)

Compiler

Compiled 15024 to 11252 computations (25.1% saved)

bsearch0.0ms (0%)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	320	307
1	320	307

end0.0ms (0%)

sample8.3s (38.8%)

Algorithm

1×

intervals

Results

1.9s	3942×	body	1024	valid
1.7s	3883×	body	1024	nan
676.0ms	1939×	body	512	valid
639.0ms	1972×	body	512	nan
506.0ms	502×	body	2048	valid
235.0ms	957×	body	256	valid
214.0ms	973×	body	256	nan
83.0ms	660×	body	128	valid
1.0ms	1×	body	2048	nan
0.0ms	1×	body	128	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 2682 to 2020 computations (24.7% saved)

Details

analyze1.1s (5%)

sample215.0ms (1%)

simplify177.0ms (0.8%)

prune8.0ms (0%)

localize26.0ms (0.1%)

rewrite65.0ms (0.3%)

series1.3s (5.9%)

simplify142.0ms (0.7%)

prune597.0ms (2.8%)

localize82.0ms (0.4%)

rewrite41.0ms (0.2%)

series0.0ms (0%)

simplify60.0ms (0.3%)

prune1.1s (5.1%)

localize219.0ms (1%)

rewrite81.0ms (0.4%)

series0.0ms (0%)

simplify76.0ms (0.4%)

prune3.6s (16.6%)

localize29.0ms (0.1%)

rewrite130.0ms (0.6%)

series1.1s (5%)

simplify214.0ms (1%)

prune2.1s (9.6%)

regimes837.0ms (3.9%)

bsearch0.0ms (0%)

simplify8.0ms (0%)

end0.0ms (0%)

sample8.3s (38.8%)

Profiling