Details

analyze920.0ms (5.6%)

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)

sample258.0ms (1.6%)

Algorithm

1×

intervals

Results

75.0ms	105×	body	1280	valid
52.0ms	82×	body	1280	nan
39.0ms	76×	body	640	valid
35.0ms	76×	body	640	nan
18.0ms	47×	body	320	valid
12.0ms	35×	body	320	nan
5.0ms	11×	body	160	nan
5.0ms	20×	body	160	valid
1.0ms	8×	body	80	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify229.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4783	55
1	4783	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

Merged error: 61.8b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize19.0ms (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))))
6.0b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite241.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
61×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`
18×	`difference-of-squares_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `distribute-lft-out_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `distribute-lft-out--_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64` `insert-posit16`
3×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`

Counts

4 → 138

Calls

4 calls:

200.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
17.0ms	(/.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))))
8.0ms	(*.f64 (/.f64 PI.f64 4) f)
8.0ms	(*.f64 (/.f64 PI.f64 4) f)

series454.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

260.0ms	(/.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))))
114.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
40.0ms	(*.f64 (/.f64 PI.f64 4) f)
40.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify129.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4956	5403
1	4956	5403

prune395.0ms (2.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	4	151

Merged error: 1.1b

Counts

151 → 4

Compiler

Compiled 6651 to 4452 computations (33.1% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (*.f64 PI.f64 f) 3)
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 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (*.f64 (pow.f64 f 5) (pow.f64 PI.f64 5))))))) (/.f64 -4 PI.f64))
0.7b	(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 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 PI.f64 5)))))))
1.0b	(pow.f64 PI.f64 5)

rewrite41.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
22×	`times-frac_binary64`
18×	`log-prod_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
12×	`pow1_binary64` `add-cbrt-cube_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `unpow-prod-down_binary64` `insert-posit16`
3×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `prod-exp_binary64` `pow-exp_binary64`
2×	`pow-to-exp_binary64` `pow-prod-down_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `cube-prod_binary64` `log-div_binary64` `flip-+_binary64` `unpow3_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 105

Calls

4 calls:

18.0ms	(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 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 PI.f64 5)))))))
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 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (*.f64 (pow.f64 f 5) (pow.f64 PI.f64 5))))))) (/.f64 -4 PI.f64))
5.0ms	(pow.f64 (*.f64 PI.f64 f) 3)
3.0ms	(pow.f64 PI.f64 5)

series1.3s (8.1%)

Counts

4 → 10

Calls

4 calls:

767.0ms	(.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 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (*.f64 (pow.f64 f 5) (pow.f64 PI.f64 5))))))) (/.f64 -4 PI.f64))
503.0ms	(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 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 f 5) (pow.f64 PI.f64 5)))))))
71.0ms	(pow.f64 (*.f64 PI.f64 f) 3)
0.0ms	(pow.f64 PI.f64 5)

simplify170.0ms (1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	5072	7624

prune452.0ms (2.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	9	115
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	108	11	119

Merged error: 0.7b

Counts

119 → 11

Compiler

Compiled 7634 to 5137 computations (32.7% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 (.f64 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5))))))
0.3b	(pow.f64 (*.f64 PI.f64 f) 3)
0.7b	(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 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5)))))))
1.0b	(pow.f64 PI.f64 5)

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64`
18×	`log-prod_binary64`
13×	`add-exp-log_binary64`
9×	`pow1_binary64` `add-cbrt-cube_binary64`
7×	`distribute-lft-out_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `unpow-prod-down_binary64` `associate-/l*_binary64` `insert-posit16`
3×	`flip3-+_binary64` `associate-/r*_binary64` `pow-pow_binary64` `flip-+_binary64` `pow-exp_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `rem-log-exp_binary64` `sqr-pow_binary64` `rem-cube-cbrt_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `cube-prod_binary64` `log-div_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 107

Calls

4 calls:

20.0ms	(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 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5)))))))
19.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 (.f64 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5))))))
5.0ms	(pow.f64 (*.f64 PI.f64 f) 3)
3.0ms	(pow.f64 PI.f64 5)

series790.0ms (4.8%)

Counts

4 → 10

Calls

4 calls:

491.0ms	(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 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5)))))))
236.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 (.f64 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5))))))
63.0ms	(pow.f64 (*.f64 PI.f64 f) 3)
0.0ms	(pow.f64 PI.f64 5)

simplify166.0ms (1%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4994	7576
1	4994	7576

prune448.0ms (2.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	117	11	128

Merged error: 0.7b

Counts

128 → 11

Compiler

Compiled 7829 to 5299 computations (32.3% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (+.f64 (.f64 (.f64 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5))))))
0.7b	(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 (.f64 (.f64 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5)))))))
1.0b	(pow.f64 PI.f64 5)
1.7b	(log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
42×	`times-frac_binary64`
38×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
34×	`log-prod_binary64`
32×	`sqrt-prod_binary64`
11×	`add-exp-log_binary64`
8×	`pow1_binary64` `distribute-lft-out_binary64`
7×	`associate-/l*_binary64`
6×	`add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `log-pow_binary64` `associate-/r/_binary64` `insert-posit16` `flip-+_binary64` `sqrt-div_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `rem-log-exp_binary64` `unpow-prod-down_binary64` `log-div_binary64`
2×	`associate-/l/_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64`

Counts

4 → 126

Calls

4 calls:

21.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (+.f64 (.f64 (.f64 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5))))))
19.0ms	(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 (.f64 (.f64 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5)))))))
8.0ms	(log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
3.0ms	(pow.f64 PI.f64 5)

series880.0ms (5.3%)

Counts

4 → 10

Calls

4 calls:

369.0ms	(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 (.f64 (.f64 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5)))))))
288.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))) (+.f64 (.f64 (.f64 PI.f64 f) 1/2) (+.f64 (.f64 1/192 (pow.f64 (.f64 PI.f64 f) 3)) (.f64 1/61440 (.f64 (pow.f64 PI.f64 5) (pow.f64 f 5))))))
223.0ms	(log.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
0.0ms	(pow.f64 PI.f64 5)

simplify142.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4946	10237
1	4946	10237

prune658.0ms (4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	136	11	147

Merged error: 0.7b

Counts

147 → 11

Compiler

Compiled 10852 to 7472 computations (31.1% saved)

regimes62.0ms (0.4%)

Compiler: Compiled 711 to 516 computations (27.4% saved)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	41	70
1	41	70

end0.0ms (0%)

sample8.5s (51.4%)

Algorithm

1×

intervals

Results

2.3s	3363×	body	1280	valid
1.8s	2911×	body	1280	nan
1.2s	2517×	body	640	valid
1.1s	2386×	body	640	nan
455.0ms	1222×	body	320	valid
394.0ms	1147×	body	320	nan
170.0ms	637×	body	160	valid
53.0ms	231×	body	160	nan
35.0ms	261×	body	80	valid
0.0ms	4×	body	80	overflowed

Compiler

Compiled 789 to 577 computations (26.9% saved)

Details

analyze920.0ms (5.6%)

sample258.0ms (1.6%)

simplify229.0ms (1.4%)

prune8.0ms (0.1%)

localize19.0ms (0.1%)

rewrite241.0ms (1.5%)

series454.0ms (2.8%)

simplify129.0ms (0.8%)

prune395.0ms (2.4%)

localize29.0ms (0.2%)

rewrite41.0ms (0.2%)

series1.3s (8.1%)

simplify170.0ms (1%)

prune452.0ms (2.7%)

localize29.0ms (0.2%)

rewrite51.0ms (0.3%)

series790.0ms (4.8%)

simplify166.0ms (1%)

prune448.0ms (2.7%)

localize34.0ms (0.2%)

rewrite59.0ms (0.4%)

series880.0ms (5.3%)

simplify142.0ms (0.9%)

prune658.0ms (4%)

regimes62.0ms (0.4%)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample8.5s (51.4%)

Profiling