Details

analyze2.5s (11.5%)

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)

sample446.0ms (2%)

Algorithm

1×

intervals

Results

121.0ms	123×	body	1024	valid
120.0ms	128×	body	1024	nan
54.0ms	78×	body	512	valid
47.0ms	71×	body	512	nan
30.0ms	13×	body	2048	valid
16.0ms	35×	body	256	nan
13.0ms	26×	body	256	valid
11.0ms	16×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify188.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (175.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55

prune15.0ms (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

62.8b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize42.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.2b	(*.f64 (/.f64 PI.f64 4) f)
1.5b	(/.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)))

rewrite107.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
35×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`
18×	`difference-of-squares_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`unpow-prod-down_binary64`
8×	`pow1_binary64` `distribute-lft-out_binary64`
7×	`associate-/r*_binary64` `sqr-pow_binary64` `cancel-sign-sub-inv_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `distribute-lft-out--_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
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 → 141

Calls

4 calls:

26.0ms	(/.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))))
16.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
14.0ms	(*.f64 (/.f64 PI.f64 4) f)
13.0ms	(*.f64 (/.f64 PI.f64 4) f)

series420.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

216.0ms	(/.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))))
91.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
61.0ms	(*.f64 (/.f64 PI.f64 4) f)
52.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 860 to 666 computations (22.6% saved)

simplify183.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5172	5387

prune738.0ms (3.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	149	4	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	4	154

Error

2.2b

Counts

154 → 4

Compiler

Compiled 6679 to 4478 computations (33% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite53.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`add-sqr-sqrt_binary64`
14×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
13×	`times-frac_binary64`
11×	`pow1_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `associate-/l*_binary64`
2×	`unswap-sqr_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `associate-r/_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

3 → 74

Calls

3 calls:

18.0ms	(.f64 (log.f64 (/.f64 2 (.f64 PI.f64 (*.f64 1/2 f)))) (/.f64 -4 PI.f64))
11.0ms	(/.f64 2 (.f64 PI.f64 (.f64 1/2 f)))
9.0ms	(.f64 PI.f64 (.f64 1/2 f))

series288.0ms (1.3%)

Counts

3 → 9

Calls

3 calls:

189.0ms	(.f64 (log.f64 (/.f64 2 (.f64 PI.f64 (*.f64 1/2 f)))) (/.f64 -4 PI.f64))
56.0ms	(.f64 PI.f64 (.f64 1/2 f))
43.0ms	(/.f64 2 (.f64 PI.f64 (.f64 1/2 f)))

Compiler

Compiled 206 to 188 computations (8.7% saved)

simplify137.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4966	1211
1	4966	1211

prune179.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	74	9	83
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	75	12	87

Error

1.9b

Counts

87 → 12

Compiler

Compiled 1523 to 1095 computations (28.1% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite33.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`times-frac_binary64`
5×	`pow1_binary64`
4×	`associate-/r_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

3 → 60

Calls

3 calls:

10.0ms	(/.f64 (.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) -4) PI.f64)
8.0ms	(/.f64 4 (*.f64 PI.f64 f))
7.0ms	(*.f64 PI.f64 f)

series289.0ms (1.3%)

Counts

3 → 9

Calls

3 calls:

191.0ms	(/.f64 (.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) -4) PI.f64)
60.0ms	(/.f64 4 (*.f64 PI.f64 f))
38.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 194 to 176 computations (9.3% saved)

simplify119.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4983	845
1	4983	845

prune129.0ms (0.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	68	13	81

Error

1.8b

Counts

81 → 13

Compiler

Compiled 1193 to 810 computations (32.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 f)
0.3b	(/.f64 4 (*.f64 PI.f64 f))
0.3b	(/.f64 1 (/.f64 PI.f64 (.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) -4)))
0.3b	(/.f64 PI.f64 (.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) -4))

rewrite58.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`times-frac_binary64`
37×	`add-exp-log_binary64`
28×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`add-cbrt-cube_binary64`
16×	`div-exp_binary64`
9×	`associate-/r_binary64` `cbrt-undiv_binary64` `associate-/l_binary64`
7×	`pow1_binary64` `div-inv_binary64`
6×	`prod-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64`
3×	`associate-r_binary64` `1-exp_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`pow-prod-down_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 116

Calls

4 calls:

14.0ms	(/.f64 PI.f64 (.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) -4))
14.0ms	(/.f64 1 (/.f64 PI.f64 (.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) -4)))
8.0ms	(/.f64 4 (*.f64 PI.f64 f))
7.0ms	(*.f64 PI.f64 f)

series538.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

265.0ms	(/.f64 PI.f64 (.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) -4))
181.0ms	(/.f64 1 (/.f64 PI.f64 (.f64 (log.f64 (/.f64 4 (.f64 PI.f64 f))) -4)))
50.0ms	(/.f64 4 (*.f64 PI.f64 f))
41.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 304 to 280 computations (7.9% saved)

simplify129.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4980	2261
1	4980	2261

prune214.0ms (1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	121	7	128
Fresh	4	7	11
Picked	1	0	1
Done	0	1	1
Total	126	15	141

Error

1.8b

Counts

141 → 15

Compiler

Compiled 2048 to 1387 computations (32.3% saved)

regimes753.0ms (3.4%)

Accuracy

Total 1.0b remaining (36.5%)

Threshold costs 0b (0%)

Compiler

Compiled 5094 to 4088 computations (19.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	17
1	12	17

end0.0ms (0%)

sample14.3s (65.2%)

Algorithm

1×

intervals

Results

3.8s	3871×	body	1024	valid
3.5s	3874×	body	1024	nan
1.4s	1967×	body	512	valid
1.2s	1894×	body	512	nan
1.1s	535×	body	2048	valid
472.0ms	985×	body	256	valid
429.0ms	991×	body	256	nan
160.0ms	642×	body	128	valid
1.0ms	1×	body	2048	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 851 to 685 computations (19.5% saved)

Details

analyze2.5s (11.5%)

sample446.0ms (2%)

simplify188.0ms (0.9%)

prune15.0ms (0.1%)

localize42.0ms (0.2%)

rewrite107.0ms (0.5%)

series420.0ms (1.9%)

simplify183.0ms (0.8%)

prune738.0ms (3.4%)

localize18.0ms (0.1%)

rewrite53.0ms (0.2%)

series288.0ms (1.3%)

simplify137.0ms (0.6%)

prune179.0ms (0.8%)

localize15.0ms (0.1%)

rewrite33.0ms (0.1%)

series289.0ms (1.3%)

simplify119.0ms (0.5%)

prune129.0ms (0.6%)

localize18.0ms (0.1%)

rewrite58.0ms (0.3%)

series538.0ms (2.5%)

simplify129.0ms (0.6%)

prune214.0ms (1%)

regimes753.0ms (3.4%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample14.3s (65.2%)

Profiling