Details

analyze1.1s (8%)

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)

sample235.0ms (1.8%)

Algorithm

1×

intervals

Results

64.0ms	127×	body	1024	valid
59.0ms	125×	body	1024	nan
27.0ms	25×	body	2048	valid
23.0ms	69×	body	512	nan
19.0ms	54×	body	512	valid
11.0ms	39×	body	256	nan
8.0ms	34×	body	256	valid
2.0ms	16×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify178.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

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

62.3b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize18.0ms (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)
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))))
5.5b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite445.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

62.2b

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×	`sqr-pow_binary64` `cancel-sign-sub-inv_binary64` `associate-/r*_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_binary64` `associate-r_binary64`
4×	`associate-/l*_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
3×	`div-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64`
2×	`flip3--_binary64` `flip--_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `pow-prod-down_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`diff-log_binary64` `sub-neg_binary64` `frac-2neg_binary64` `clear-num_binary64` `flip3-+_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)

Compiler

Compiled 6543 to 4377 computations (33.1% saved)

series274.0ms (2.1%)

Error

2.2b

Counts

4 → 12

Calls

4 calls:

142.0ms	(/.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))))
51.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
33.0ms	(*.f64 (/.f64 PI.f64 4) f)
28.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 1240 to 921 computations (25.7% saved)

simplify95.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5172	5387

prune392.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	5	154

Error

2.1b

Counts

154 → 5

Compiler

Compiled 6728 to 4518 computations (32.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))
0.3b	(.f64 f (.f64 PI.f64 1/2))
0.3b	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
0.4b	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))

rewrite141.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

33×	`add-exp-log_binary64`
23×	`add-cbrt-cube_binary64`
22×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
16×	`times-frac_binary64`
14×	`associate-r_binary64`
13×	`pow1_binary64`
11×	`prod-exp_binary64`
8×	`cbrt-unprod_binary64`
7×	`div-exp_binary64` `associate-l_binary64` `log-prod_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64`
3×	`div-inv_binary64` `associate-/l*_binary64`
2×	`unswap-sqr_binary64` `log-pow_binary64` `*-commutative_binary64`
1×	`associate-r/_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/r_binary64` `log-div_binary64`

Counts

4 → 94

Calls

4 calls:

9.0ms	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
6.0ms	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
5.0ms	(log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))
5.0ms	(.f64 f (.f64 PI.f64 1/2))

Compiler

Compiled 1805 to 1377 computations (23.7% saved)

series266.0ms (2%)

Error

2.0b

Counts

4 → 12

Calls

4 calls:

117.0ms	(.f64 (log.f64 (/.f64 2 (.f64 f (*.f64 PI.f64 1/2)))) (/.f64 -4 PI.f64))
79.0ms	(log.f64 (/.f64 2 (.f64 f (.f64 PI.f64 1/2))))
30.0ms	(/.f64 2 (.f64 f (.f64 PI.f64 1/2)))
29.0ms	(.f64 f (.f64 PI.f64 1/2))

Compiler

Compiled 420 to 356 computations (15.2% saved)

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5045	1497

prune126.0ms (0.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	92	14	106
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	93	18	111

Error

1.8b

Counts

111 → 18

Compiler

Compiled 2008 to 1441 computations (28.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
0.3b	(*.f64 PI.f64 f)
0.3b	(/.f64 4 (*.f64 PI.f64 f))
0.3b	(/.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) PI.f64)

rewrite108.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

21×	`add-sqr-sqrt_binary64`
19×	`add-exp-log_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
18×	`times-frac_binary64`
13×	`add-cbrt-cube_binary64`
11×	`pow1_binary64`
7×	`associate-/l*_binary64` `log-prod_binary64`
5×	`div-exp_binary64` `log-pow_binary64`
4×	`add-log-exp_binary64` `associate-/r*_binary64`
3×	`cbrt-undiv_binary64` `div-inv_binary64` `prod-exp_binary64` `associate-l_binary64` `associate-r_binary64` `rem-log-exp_binary64`
2×	`frac-2neg_binary64` `log-div_binary64` `clear-num_binary64` `cbrt-unprod_binary64`
1×	`div-sub_binary64` `pow-prod-down_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

6.0ms	(/.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) PI.f64)
4.0ms	(/.f64 4 (*.f64 PI.f64 f))
4.0ms	(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
4.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 1468 to 910 computations (38% saved)

series219.0ms (1.6%)

Error

1.8b

Counts

4 → 12

Calls

4 calls:

91.0ms	(/.f64 (log.f64 (/.f64 4 (*.f64 PI.f64 f))) PI.f64)
71.0ms	(log.f64 (/.f64 4 (*.f64 PI.f64 f)))
28.0ms	(/.f64 4 (*.f64 PI.f64 f))
20.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 402 to 339 computations (15.7% saved)

simplify64.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5068	1423

prune111.0ms (0.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	6	11	17
Picked	1	0	1
Done	0	0	0
Total	106	14	120

Error

1.7b

Counts

120 → 14

Compiler

Compiled 1810 to 1205 computations (33.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 2)) f)
1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)

rewrite87.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

1.7b

Rules

9×	`add-exp-log_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
7×	`add-cbrt-cube_binary64`
4×	`pow1_binary64` `add-log-exp_binary64`
3×	`pow1/3_binary64` `times-frac_binary64` `associate-/r*_binary64`
2×	`div-exp_binary64` `cbrt-undiv_binary64`
1×	`prod-exp_binary64` `cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `associate-/l*_binary64`

Counts

4 → 54

Calls

4 calls:

6.0ms	(/.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 2)) f)
1.0ms	(cbrt.f64 2)
1.0ms	(cbrt.f64 2)
1.0ms	(cbrt.f64 2)

Compiler

Compiled 1331 to 1144 computations (14% saved)

series62.0ms (0.5%)

Error

1.7b

Counts

4 → 3

Calls

4 calls:

58.0ms	(/.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 2)) f)
0.0ms	(cbrt.f64 2)
0.0ms	(cbrt.f64 2)
0.0ms	(cbrt.f64 2)

Compiler

Compiled 171 to 158 computations (7.6% saved)

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5069	459

prune77.0ms (0.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	56	15	71

Error

1.7b

Counts

71 → 15

Compiler

Compiled 1303 to 1116 computations (14.4% saved)

regimes869.0ms (6.5%)

Accuracy

Total 1.1b remaining (41.1%)

Threshold costs 0b (0%)

Compiler

Compiled 11838 to 9626 computations (18.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	20
1	15	20

end0.0ms (0%)

sample8.3s (62.5%)

Algorithm

1×

intervals

Results

2.0s	3943×	body	1024	valid
1.7s	3787×	body	1024	nan
681.0ms	1947×	body	512	valid
626.0ms	1897×	body	512	nan
510.0ms	488×	body	2048	valid
240.0ms	993×	body	256	valid
210.0ms	960×	body	256	nan
81.0ms	629×	body	128	valid
2.0ms	3×	body	2048	nan
0.0ms	2×	body	128	nan
0.0ms	2×	body	128	overflowed

Compiler

Compiled 1977 to 1610 computations (18.6% saved)

Details

analyze1.1s (8%)

sample235.0ms (1.8%)

simplify178.0ms (1.3%)

prune15.0ms (0.1%)

localize18.0ms (0.1%)

rewrite445.0ms (3.3%)

series274.0ms (2.1%)

simplify95.0ms (0.7%)

prune392.0ms (2.9%)

localize9.0ms (0.1%)

rewrite141.0ms (1.1%)

series266.0ms (2%)

simplify58.0ms (0.4%)

prune126.0ms (0.9%)

localize8.0ms (0.1%)

rewrite108.0ms (0.8%)

series219.0ms (1.6%)

simplify64.0ms (0.5%)

prune111.0ms (0.8%)

localize14.0ms (0.1%)

rewrite87.0ms (0.6%)

series62.0ms (0.5%)

simplify60.0ms (0.4%)

prune77.0ms (0.6%)

regimes869.0ms (6.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample8.3s (62.5%)

Profiling