Details

analyze1.1s (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)

sample227.0ms (1.2%)

Algorithm

1×

intervals

Results

65.0ms	127×	body	1024	nan
63.0ms	119×	body	1024	valid
26.0ms	69×	body	512	valid
20.0ms	53×	body	512	nan
15.0ms	13×	body	2048	valid
10.0ms	36×	body	256	valid
9.0ms	40×	body	256	nan
3.0ms	19×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify253.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4782	55
1	4782	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

Merged error: 62.0b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.6b	(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)))))
0.7b	(/.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))))
5.5b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite77.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
37×	`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`
11×	`add-cbrt-cube_binary64`
10×	`sqr-pow_binary64` `unpow-prod-down_binary64` `distribute-lft-out--_binary64`
7×	`associate-/r*_binary64` `pow1_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 → 147

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)

series2.1s (11.1%)

Counts

4 → 12

Calls

4 calls:

1.5s	(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)))))
452.0ms	(/.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))))
79.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
37.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify135.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4969	9836
1	4969	9836

prune604.0ms (3.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	153	6	159
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	6	160

Merged error: 1.8b

Counts

160 → 6

Compiler

Compiled 9154 to 6308 computations (31.1% saved)

localize216.0ms (1.1%)

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)))

rewrite89.0ms (0.5%)

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

simplify65.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	6065	3502

prune3.6s (19.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	74	6	80

Merged error: 1.8b

Counts

80 → 6

Compiler

Compiled 35763 to 26389 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)

rewrite43.0ms (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)
3.0ms	(pow.f64 PI.f64 3)
3.0ms	(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)

simplify39.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5213	1424

prune1.1s (5.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	78	6	84

Merged error: 1.8b

Counts

84 → 6

Compiler

Compiled 14967 to 11893 computations (20.5% saved)

localize93.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(exp.f64 (*.f64 (log.f64 PI.f64) 3))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

3.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 4)
2.0ms	(exp.f64 (*.f64 (log.f64 PI.f64) 3))
2.0ms	(pow.f64 PI.f64 4)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(exp.f64 (*.f64 (log.f64 PI.f64) 3))
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(pow.f64 PI.f64 4)

simplify111.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4761	462
1	4761	462

prune961.0ms (5.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	66	6	72

Merged error: 1.8b

Counts

72 → 6

Compiler

Compiled 12577 to 9979 computations (20.7% saved)

regimes124.0ms (0.7%)

Compiler: Compiled 919 to 695 computations (24.4% saved)

bsearch0.0ms (0%)

simplify25.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	1003	774
1	1003	774

end0.0ms (0%)

sample7.8s (41.4%)

Algorithm

1×

intervals

Results

2.0s	3848×	body	1024	valid
1.8s	3787×	body	1024	nan
750.0ms	2039×	body	512	valid
674.0ms	1987×	body	512	nan
541.0ms	491×	body	2048	valid
256.0ms	984×	body	256	valid
219.0ms	950×	body	256	nan
87.0ms	638×	body	128	valid
2.0ms	3×	body	2048	nan
0.0ms	2×	body	128	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 1432 to 1081 computations (24.5% saved)

Details

analyze1.1s (5.6%)

sample227.0ms (1.2%)

simplify253.0ms (1.3%)

prune8.0ms (0%)

localize20.0ms (0.1%)

rewrite77.0ms (0.4%)

series2.1s (11.1%)

simplify135.0ms (0.7%)

prune604.0ms (3.2%)

localize216.0ms (1.1%)

rewrite89.0ms (0.5%)

series0.0ms (0%)

simplify65.0ms (0.3%)

prune3.6s (19.2%)

localize84.0ms (0.4%)

rewrite43.0ms (0.2%)

series0.0ms (0%)

simplify39.0ms (0.2%)

prune1.1s (5.7%)

localize93.0ms (0.5%)

rewrite34.0ms (0.2%)

series0.0ms (0%)

simplify111.0ms (0.6%)

prune961.0ms (5.1%)

regimes124.0ms (0.7%)

bsearch0.0ms (0%)

simplify25.0ms (0.1%)

end0.0ms (0%)

sample7.8s (41.4%)

Profiling