Details

analyze1.1s (9%)

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)

sample217.0ms (1.8%)

Algorithm

1×

intervals

Results

61.0ms	130×	body	1024	nan
57.0ms	114×	body	1024	valid
24.0ms	69×	body	512	valid
23.0ms	61×	body	512	nan
12.0ms	12×	body	2048	valid
11.0ms	37×	body	256	valid
6.0ms	26×	body	256	nan
3.0ms	24×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify177.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

61.0b

Counts

2 → 1

Compiler

Compiled 69 to 54 computations (21.7% saved)

localize24.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(exp.f64 (neg.f64 (*.f64 (/.f64 PI.f64 4) f)))
0.0b	(exp.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b	(exp.f64 (*.f64 (/.f64 PI.f64 4) f))
0.0b	(+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))
0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.7b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))))
6.5b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))

rewrite51.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
50×	`times-frac_binary64`
34×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`distribute-lft-out_binary64` `sinh-undef_binary64` `cosh-undef_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-r*_binary64`
5×	`associate-/l*_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`cbrt-undiv_binary64` `cancel-sign-sub-inv_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

8 calls:

10.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
7.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)
0.0ms	(+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))

series275.0ms (2.3%)

Counts

4 → 18

Calls

4 calls:

140.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f)))))
74.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 PI.f64 4) f))))
32.0ms	(*.f64 (/.f64 PI.f64 4) f)
29.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 1012 to 808 computations (20.2% saved)

simplify115.0ms (1%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4856	5363
1	4856	5363

prune457.0ms (3.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	2	157

Error

1.2b

Counts

157 → 2

Compiler

Compiled 7157 to 5409 computations (24.4% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 PI.f64 f)
0.2b	(*.f64 PI.f64 f)
0.0b	(+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12))
0.0b	(log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12)))
0.2b	(*.f64 PI.f64 f)
0.3b	(/.f64 4 (*.f64 PI.f64 f))
0.4b	(.f64 (.f64 PI.f64 f) 1/12)
0.4b	(.f64 (/.f64 1 (/.f64 PI.f64 4)) (log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (.f64 PI.f64 f) 1/12))))

rewrite50.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
63×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
48×	`associate-l_binary64`
47×	`add-cube-cbrt_binary64`
35×	`add-exp-log_binary64`
25×	`add-cbrt-cube_binary64`
14×	`pow1_binary64`
12×	`prod-exp_binary64`
10×	`associate-r_binary64`
9×	`div-exp_binary64`
8×	`cbrt-unprod_binary64`
6×	`log-prod_binary64` `unswap-sqr_binary64`
5×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `div-inv_binary64`
4×	`add-log-exp_binary64`
3×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-/l_binary64` `-commutative_binary64`
2×	`1-exp_binary64` `rec-exp_binary64`
1×	`associate-/r_binary64` `log-pow_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64`

Counts

4 → 136

Calls

8 calls:

21.0ms	(.f64 (/.f64 1 (/.f64 PI.f64 4)) (log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (.f64 PI.f64 f) 1/12))))
5.0ms	(.f64 (.f64 PI.f64 f) 1/12)
4.0ms	(/.f64 4 (*.f64 PI.f64 f))
4.0ms	(*.f64 PI.f64 f)
0.0ms	(log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12)))

series188.0ms (1.6%)

Counts

4 → 15

Calls

4 calls:

105.0ms	(.f64 (/.f64 1 (/.f64 PI.f64 4)) (log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (.f64 PI.f64 f) 1/12))))
33.0ms	(.f64 (.f64 PI.f64 f) 1/12)
28.0ms	(/.f64 4 (*.f64 PI.f64 f))
22.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 588 to 493 computations (16.2% saved)

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4975	3342
1	4975	3342

prune233.0ms (1.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	142	9	151
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	142	11	153

Error

0.8b

Counts

153 → 11

Compiler

Compiled 4013 to 2654 computations (33.9% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 PI.f64 f)
0.2b	(*.f64 PI.f64 f)
0.0b	(+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12))
0.0b	(log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12)))
0.2b	(*.f64 PI.f64 f)
0.3b	(/.f64 4 (*.f64 PI.f64 f))
0.3b	(/.f64 (log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12))) (/.f64 PI.f64 4))
0.4b	(.f64 (.f64 PI.f64 f) 1/12)

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`times-frac_binary64`
60×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`pow1_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`associate-/r*_binary64` `log-pow_binary64`
7×	`associate-/l*_binary64` `div-inv_binary64`
6×	`associate-r_binary64`
5×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-l_binary64`
2×	`div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `flip-+_binary64`

Counts

4 → 143

Calls

8 calls:

12.0ms	(/.f64 (log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12))) (/.f64 PI.f64 4))
5.0ms	(.f64 (.f64 PI.f64 f) 1/12)
4.0ms	(/.f64 4 (*.f64 PI.f64 f))
4.0ms	(*.f64 PI.f64 f)
0.0ms	(log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12)))

series174.0ms (1.4%)

Counts

4 → 15

Calls

4 calls:

103.0ms	(/.f64 (log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12))) (/.f64 PI.f64 4))
27.0ms	(/.f64 4 (*.f64 PI.f64 f))
25.0ms	(.f64 (.f64 PI.f64 f) 1/12)
18.0ms	(*.f64 PI.f64 f)

Compiler

Compiled 552 to 457 computations (17.2% saved)

simplify121.0ms (1%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4741	4727
1	4741	4727

prune221.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	2	7	9
Picked	0	1	1
Done	1	0	1
Total	159	10	169

Error

0.8b

Counts

169 → 10

Compiler

Compiled 4327 to 2675 computations (38.2% saved)

localize17.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 PI.f64 f)
0.2b	(*.f64 PI.f64 f)
0.0b	(+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12))
0.0b	(log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12)))
0.3b	(.f64 (log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (.f64 PI.f64 f) 1/12))) (sqrt.f64 (/.f64 4 PI.f64)))
0.3b	(.f64 (sqrt.f64 (/.f64 1 (/.f64 PI.f64 4))) (.f64 (log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12))) (sqrt.f64 (/.f64 4 PI.f64))))
0.3b	(/.f64 4 (*.f64 PI.f64 f))
0.4b	(.f64 (.f64 PI.f64 f) 1/12)

rewrite57.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`times-frac_binary64`
59×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
52×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`associate-r_binary64`
17×	`pow1_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`pow-prod-down_binary64`
6×	`div-inv_binary64`
5×	`sqrt-div_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64`
3×	`unswap-sqr_binary64` `associate-/l_binary64` `-commutative_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64`
1×	`associate-/r_binary64` `log-pow_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 139

Calls

8 calls:

21.0ms	(.f64 (sqrt.f64 (/.f64 1 (/.f64 PI.f64 4))) (.f64 (log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12))) (sqrt.f64 (/.f64 4 PI.f64))))
9.0ms	(.f64 (log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (.f64 PI.f64 f) 1/12))) (sqrt.f64 (/.f64 4 PI.f64)))
5.0ms	(.f64 (.f64 PI.f64 f) 1/12)
4.0ms	(/.f64 4 (*.f64 PI.f64 f))
0.0ms	(log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12)))

series308.0ms (2.6%)

Counts

4 → 18

Calls

4 calls:

135.0ms	(.f64 (log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (.f64 PI.f64 f) 1/12))) (sqrt.f64 (/.f64 4 PI.f64)))
108.0ms	(.f64 (sqrt.f64 (/.f64 1 (/.f64 PI.f64 4))) (.f64 (log.f64 (+.f64 (/.f64 4 (.f64 PI.f64 f)) (.f64 (*.f64 PI.f64 f) 1/12))) (sqrt.f64 (/.f64 4 PI.f64))))
33.0ms	(.f64 (.f64 PI.f64 f) 1/12)
31.0ms	(/.f64 4 (*.f64 PI.f64 f))

Compiler

Compiled 924 to 797 computations (13.7% saved)

simplify100.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4919	4340
1	4919	4340

prune250.0ms (2.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	156	11	167

Error

0.8b

Counts

167 → 11

Compiler

Compiled 4744 to 3308 computations (30.3% saved)

simplify35.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	922	1744
1	922	1744

regimes323.0ms (2.7%)

Compiler: Compiled 4322 to 3342 computations (22.7% saved)

bsearch0.0ms (0%)

regimes21.0ms (0.2%)

Compiler: Compiled 126 to 106 computations (15.9% saved)

bsearch0.0ms (0%)

regimes11.0ms (0.1%)

Compiler: Compiled 37 to 37 computations (0% saved)

bsearch0.0ms (0%)

regimes9.0ms (0.1%)

Compiler: Compiled 15 to 17 computations (-13.3% saved)

bsearch0.0ms (0%)

regimes8.0ms (0.1%)

Accuracy

Total 1.6b remaining (83.1%)

Threshold costs 0b (0%)

Compiler

Compiled 4 to 6 computations (-50% saved)

bsearch4.0ms (0%)

Compiler: Compiled 50 to 45 computations (10% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	83
1	45	83

end0.0ms (0%)

sample7.3s (61.1%)

Algorithm

1×

intervals

Results

2.0s	3916×	body	1024	valid
1.8s	3865×	body	1024	nan
703.0ms	1992×	body	512	valid
640.0ms	1967×	body	512	nan
497.0ms	484×	body	2048	valid
237.0ms	962×	body	256	valid
216.0ms	966×	body	256	nan
83.0ms	646×	body	128	valid
1.0ms	2×	body	2048	nan
0.0ms	4×	body	128	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 1087 to 845 computations (22.3% saved)

Pareto

0.6507428958260418

Details

analyze1.1s (9%)

sample217.0ms (1.8%)

simplify177.0ms (1.5%)

prune6.0ms (0%)

localize24.0ms (0.2%)

rewrite51.0ms (0.4%)

series275.0ms (2.3%)

simplify115.0ms (1%)

prune457.0ms (3.8%)

localize13.0ms (0.1%)

rewrite50.0ms (0.4%)

series188.0ms (1.6%)

simplify77.0ms (0.6%)

prune233.0ms (1.9%)

localize13.0ms (0.1%)

rewrite40.0ms (0.3%)

series174.0ms (1.4%)

simplify121.0ms (1%)

prune221.0ms (1.8%)

localize17.0ms (0.1%)

rewrite57.0ms (0.5%)

series308.0ms (2.6%)

simplify100.0ms (0.8%)

prune250.0ms (2.1%)

simplify35.0ms (0.3%)

regimes323.0ms (2.7%)

bsearch0.0ms (0%)

regimes21.0ms (0.2%)

bsearch0.0ms (0%)

regimes11.0ms (0.1%)

bsearch0.0ms (0%)

regimes9.0ms (0.1%)

bsearch0.0ms (0%)

regimes8.0ms (0.1%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.3s (61.1%)

Profiling