Details

analyze1.0s (6.4%)

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)

sample225.0ms (1.4%)

Algorithm

1×

intervals

Results

64.0ms	137×	body	1024	nan
61.0ms	116×	body	1024	valid
28.0ms	78×	body	512	valid
21.0ms	66×	body	512	nan
18.0ms	15×	body	2048	valid
9.0ms	38×	body	256	nan
6.0ms	25×	body	256	valid
3.0ms	22×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify187.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	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: 61.3b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.2b	(*.f64 (/.f64 PI.f64 4) f)
1.7b	(/.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))))
5.4b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite62.0ms (0.4%)

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:

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))))
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)
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

series362.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

265.0ms	(/.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))))
59.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
19.0ms	(*.f64 (/.f64 PI.f64 4) f)
19.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify85.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5184	5751

prune413.0ms (2.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	3	154

Merged error: 2.1b

Counts

154 → 3

Compiler

Compiled 7035 to 4763 computations (32.3% saved)

localize81.0ms (0.5%)

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)

rewrite35.0ms (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 4)
2.0ms	(pow.f64 PI.f64 3)
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)

simplify45.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5373	1148

prune1.1s (6.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	78	3	81

Merged error: 2.1b

Counts

81 → 3

Compiler

Compiled 14055 to 11036 computations (21.5% saved)

localize94.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 (pow.f64 PI.f64 (*.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 4))

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`cbrt-prod_binary64`
16×	`unpow-prod-down_binary64`
13×	`pow1_binary64`
12×	`pow-unpow_binary64`
10×	`add-exp-log_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `pow1/3_binary64` `associate-l_binary64` `pow-exp_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
3×	`pow-pow_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 100

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
5.0ms	(pow.f64 (pow.f64 PI.f64 (*.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 4))
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 (pow.f64 PI.f64 (*.f64 (cbrt.f64 4) (cbrt.f64 4))) (cbrt.f64 4))
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
0.0ms	(pow.f64 PI.f64 4)

simplify75.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5185	1176

prune1.8s (11.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	104	3	107

Merged error: 2.1b

Counts

107 → 3

Compiler

Compiled 19874 to 15825 computations (20.4% saved)

localize97.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 2)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 PI.f64 4)
1.6b	(pow.f64 (pow.f64 PI.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))) (cbrt.f64 4))

rewrite38.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`unpow-prod-down_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`pow-unpow_binary64`
8×	`add-exp-log_binary64`
6×	`pow1_binary64` `cbrt-prod_binary64` `pow-exp_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64`
3×	`pow-pow_binary64`
1×	`pow1/3_binary64`

Counts

4 → 71

Calls

4 calls:

5.0ms	(pow.f64 (pow.f64 PI.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))) (cbrt.f64 4))
2.0ms	(pow.f64 PI.f64 4)
2.0ms	(pow.f64 PI.f64 4)
1.0ms	(cbrt.f64 2)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(pow.f64 (pow.f64 PI.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))) (cbrt.f64 4))
0.0ms	(pow.f64 PI.f64 4)
0.0ms	(cbrt.f64 2)
0.0ms	(pow.f64 PI.f64 4)

simplify47.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5093	1435

prune1.2s (7.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	75	3	78

Merged error: 2.1b

Counts

78 → 3

Compiler

Compiled 14037 to 11201 computations (20.2% saved)

regimes786.0ms (4.9%)

Compiler: Compiled 15216 to 12086 computations (20.6% saved)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	307	295
1	307	295

end0.0ms (0%)

sample8.3s (51.2%)

Algorithm

1×

intervals

Results

1.9s	3909×	body	1024	valid
1.8s	3927×	body	1024	nan
687.0ms	1964×	body	512	valid
613.0ms	1916×	body	512	nan
489.0ms	482×	body	2048	valid
237.0ms	992×	body	256	valid
202.0ms	930×	body	256	nan
84.0ms	653×	body	128	valid
1.0ms	1×	body	2048	nan
0.0ms	1×	body	128	nan

Compiler

Compiled 2706 to 2151 computations (20.5% saved)

Details

analyze1.0s (6.4%)

sample225.0ms (1.4%)

simplify187.0ms (1.2%)

prune8.0ms (0.1%)

localize17.0ms (0.1%)

rewrite62.0ms (0.4%)

series362.0ms (2.2%)

simplify85.0ms (0.5%)

prune413.0ms (2.6%)

localize81.0ms (0.5%)

rewrite35.0ms (0.2%)

series0.0ms (0%)

simplify45.0ms (0.3%)

prune1.1s (6.9%)

localize94.0ms (0.6%)

rewrite59.0ms (0.4%)

series0.0ms (0%)

simplify75.0ms (0.5%)

prune1.8s (11.2%)

localize97.0ms (0.6%)

rewrite38.0ms (0.2%)

series0.0ms (0%)

simplify47.0ms (0.3%)

prune1.2s (7.4%)

regimes786.0ms (4.9%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample8.3s (51.2%)

Profiling