Details

analyze1.3s (5.4%)

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)

sample220.0ms (1%)

Algorithm

1×

intervals

Results

67.0ms	146×	body	1024	nan
59.0ms	121×	body	1024	valid
24.0ms	60×	body	512	valid
20.0ms	61×	body	512	nan
16.0ms	16×	body	2048	valid
9.0ms	38×	body	256	valid
7.0ms	32×	body	256	nan
3.0ms	21×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify84.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

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

61.6b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.5b	(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)))))
1.0b	(/.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))))
6.6b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite68.0ms (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:

15.0ms	(/.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)

series1.3s (5.5%)

Counts

4 → 12

Calls

4 calls:

923.0ms	(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)))))
264.0ms	(/.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))))
64.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
22.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify148.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4959	9948
1	4959	9948

prune596.0ms (2.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	162	4	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	4	167

Error

1.7b

Counts

167 → 4

Compiler

Compiled 9293 to 6398 computations (31.2% saved)

localize212.0ms (0.9%)

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 (0.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4944	3514
1	4944	3514

prune3.7s (16.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	74	4	78

Error

1.7b

Counts

78 → 4

Compiler

Compiled 35663 to 26320 computations (26.2% saved)

localize84.0ms (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)

rewrite36.0ms (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:

3.0ms	(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 4)
0.0ms	(pow.f64 PI.f64 3)

simplify66.0ms (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 (4.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	78	4	82

Error

1.7b

Counts

82 → 4

Compiler

Compiled 14671 to 11664 computations (20.5% saved)

localize46.0ms (0.2%)

Local error

Found 4 expressions with local error:

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 (+.f64 (.f64 1/32 (.f64 (.f64 f f) (pow.f64 PI.f64 2))) (+.f64 (.f64 1/384 (.f64 (pow.f64 f 3) (pow.f64 PI.f64 3))) (.f64 PI.f64 (.f64 f 1/4)))) (+.f64 (.f64 1/6 (.f64 (pow.f64 f 3) (.f64 (pow.f64 PI.f64 3) -1/64))) (+.f64 (.f64 f (.f64 PI.f64 -1/4)) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (*.f64 f f) 1/16)))))))) (/.f64 -4 PI.f64))
1.0b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (+.f64 (.f64 1/32 (.f64 (.f64 f f) (pow.f64 PI.f64 2))) (+.f64 (.f64 1/384 (.f64 (pow.f64 f 3) (pow.f64 PI.f64 3))) (.f64 PI.f64 (.f64 f 1/4)))) (+.f64 (.f64 1/6 (.f64 (pow.f64 f 3) (.f64 (pow.f64 PI.f64 3) -1/64))) (+.f64 (.f64 f (.f64 PI.f64 -1/4)) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 f f) 1/16))))))))
1.0b	(pow.f64 PI.f64 3)
1.0b	(pow.f64 PI.f64 3)

rewrite82.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
41×	`add-sqr-sqrt_binary64`
30×	`log-prod_binary64` `times-frac_binary64`
28×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-r_binary64`
11×	`add-cbrt-cube_binary64`
10×	`pow1_binary64`
6×	`pow-unpow_binary64` `associate-/r/_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
5×	`distribute-lft-out_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `associate-l_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `frac-sub_binary64`
2×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `log-pow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `log-div_binary64` `flip--_binary64` `-commutative_binary64`

Counts

4 → 120

Calls

4 calls:

40.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (+.f64 (.f64 1/32 (.f64 (.f64 f f) (pow.f64 PI.f64 2))) (+.f64 (.f64 1/384 (.f64 (pow.f64 f 3) (pow.f64 PI.f64 3))) (.f64 PI.f64 (.f64 f 1/4)))) (+.f64 (.f64 1/6 (.f64 (pow.f64 f 3) (.f64 (pow.f64 PI.f64 3) -1/64))) (+.f64 (.f64 f (.f64 PI.f64 -1/4)) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 f f) 1/16))))))))
8.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (+.f64 (.f64 1/32 (.f64 (.f64 f f) (pow.f64 PI.f64 2))) (+.f64 (.f64 1/384 (.f64 (pow.f64 f 3) (pow.f64 PI.f64 3))) (.f64 PI.f64 (.f64 f 1/4)))) (+.f64 (.f64 1/6 (.f64 (pow.f64 f 3) (.f64 (pow.f64 PI.f64 3) -1/64))) (+.f64 (.f64 f (.f64 PI.f64 -1/4)) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (*.f64 f f) 1/16)))))))) (/.f64 -4 PI.f64))
3.0ms	(pow.f64 PI.f64 3)
2.0ms	(pow.f64 PI.f64 3)

series790.0ms (3.4%)

Counts

4 → 8

Calls

4 calls:

483.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (+.f64 (.f64 1/32 (.f64 (.f64 f f) (pow.f64 PI.f64 2))) (+.f64 (.f64 1/384 (.f64 (pow.f64 f 3) (pow.f64 PI.f64 3))) (.f64 PI.f64 (.f64 f 1/4)))) (+.f64 (.f64 1/6 (.f64 (pow.f64 f 3) (.f64 (pow.f64 PI.f64 3) -1/64))) (+.f64 (.f64 f (.f64 PI.f64 -1/4)) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (*.f64 f f) 1/16)))))))) (/.f64 -4 PI.f64))
306.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (+.f64 (.f64 1/32 (.f64 (.f64 f f) (pow.f64 PI.f64 2))) (+.f64 (.f64 1/384 (.f64 (pow.f64 f 3) (pow.f64 PI.f64 3))) (.f64 PI.f64 (.f64 f 1/4)))) (+.f64 (.f64 1/6 (.f64 (pow.f64 f 3) (.f64 (pow.f64 PI.f64 3) -1/64))) (+.f64 (.f64 f (.f64 PI.f64 -1/4)) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 f f) 1/16))))))))
0.0ms	(pow.f64 PI.f64 3)
0.0ms	(pow.f64 PI.f64 3)

simplify147.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5326	14523

prune858.0ms (3.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	119	9	128
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	120	12	132

Error

1.4b

Counts

132 → 12

Compiler

Compiled 13203 to 9246 computations (30% saved)

regimes1.8s (7.6%)

Accuracy

Total 0.7b remaining (32.8%)

Threshold costs 0.7b (32.8%)

Compiler

Compiled 34290 to 25268 computations (26.3% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	181	90
1	181	90

end0.0ms (0%)

sample10.3s (44.7%)

Algorithm

1×

intervals

Results

1.9s	3897×	body	1024	valid
1.8s	3966×	body	1024	nan
697.0ms	1996×	body	512	valid
645.0ms	1988×	body	512	nan
487.0ms	485×	body	2048	valid
238.0ms	967×	body	256	valid
214.0ms	978×	body	256	nan
86.0ms	655×	body	128	valid
1.0ms	2×	body	2048	nan
1.0ms	6×	body	128	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 5762 to 4245 computations (26.3% saved)

Details

analyze1.3s (5.4%)

sample220.0ms (1%)

simplify84.0ms (0.4%)

prune8.0ms (0%)

localize22.0ms (0.1%)

rewrite68.0ms (0.3%)

series1.3s (5.5%)

simplify148.0ms (0.6%)

prune596.0ms (2.6%)

localize212.0ms (0.9%)

rewrite81.0ms (0.4%)

series0.0ms (0%)

simplify76.0ms (0.3%)

prune3.7s (16.1%)

localize84.0ms (0.4%)

rewrite36.0ms (0.2%)

series0.0ms (0%)

simplify66.0ms (0.3%)

prune1.1s (4.9%)

localize46.0ms (0.2%)

rewrite82.0ms (0.4%)

series790.0ms (3.4%)

simplify147.0ms (0.6%)

prune858.0ms (3.7%)

regimes1.8s (7.6%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample10.3s (44.7%)

Profiling