Details

analyze106.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

Compiler

Compiled 15 to 14 computations (6.7% saved)

sample35.0ms (0.6%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
0.0ms	4×	body	128	nan
0.0ms	2×	body	128	invalid

Compiler

Compiled 29 to 29 computations (0% saved)

simplify449.0ms (7.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (280.0ms)

Iter	Nodes	Cost
0	1583	18
1	1583	18

prune8.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.3b

Counts

2 → 2

Compiler

Compiled 38 to 35 computations (7.9% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.3b	(/.f64 1 (*.f64 x 9))
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite86.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_10990`
22×	`add-exp-log_binary64_11028`
20×	`add-sqr-sqrt_binary64_11012`
16×	`add-cbrt-cube_binary64_11026`
15×	`associate-r_binary64_10930`
14×	`pow1_binary64_11051`
12×	`add-cube-cbrt_binary64_11025`
7×	`prod-exp_binary64_11039`
6×	`add-log-exp_binary64_11029` `cancel-sign-sub-inv_binary64_10956`
5×	`cbrt-unprod_binary64_11023` `distribute-rgt-in_binary64_10940` `pow-prod-down_binary64_11061` `distribute-lft-in_binary64_10939`
4×	`distribute-lft-out_binary64_10941` `sqrt-prod_binary64_11006` `div-exp_binary64_11041` `associate-l_binary64_10931`
3×	`distribute-lft-out--_binary64_10942` `times-frac_binary64_10996` `associate-/l*_binary64_10935` `div-inv_binary64_10987`
2×	`associate--l+_binary64_10927` `associate-r/_binary64_10932` `unswap-sqr_binary64_10958` `1-exp_binary64_11034` `pow-flip_binary64_11064` `sub-neg_binary64_10983` `difference-of-squares_binary64_10959` `rec-exp_binary64_11040` `-commutative_binary64_10921` `cbrt-undiv_binary64_11024`
1×	`flip3--_binary64_10994` `sum-log_binary64_11081` `flip--_binary64_10965` `clear-num_binary64_10989` `difference-of-sqr-1_binary64_10960` `flip3-+_binary64_10993` `associate-/r*_binary64_10934` `flip-+_binary64_10964` `+-commutative_binary64_10920` `frac-2neg_binary64_11001` `inv-pow_binary64_11075`

Counts

4 → 99

Calls

4 calls:

31.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
20.0ms	(/.f64 1 (*.f64 x 9))
11.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
10.0ms	(*.f64 3 (sqrt.f64 x))

series143.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
31.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
31.0ms	(*.f64 3 (sqrt.f64 x))
20.0ms	(/.f64 1 (*.f64 x 9))

simplify85.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5251	1423

prune233.0ms (3.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	103	10	113

Merged error: 0.0b

Counts

113 → 10

Compiler

Compiled 2151 to 1558 computations (27.6% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/9 x) y)
0.2b	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
0.2b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
0.4b	(/.f64 1/9 x)

rewrite92.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_10990`
20×	`add-sqr-sqrt_binary64_11012`
16×	`add-cube-cbrt_binary64_11025`
13×	`add-exp-log_binary64_11028` `add-cbrt-cube_binary64_11026`
11×	`pow1_binary64_11051`
9×	`times-frac_binary64_10996` `associate-l_binary64_10931`
6×	`associate-r/_binary64_10932` `add-log-exp_binary64_11029` `associate-r*_binary64_10930`
5×	`distribute-rgt-in_binary64_10940` `distribute-lft-in_binary64_10939`
4×	`prod-exp_binary64_11039` `distribute-lft-out_binary64_10941` `sqrt-prod_binary64_11006` `cbrt-unprod_binary64_11023` `pow-prod-down_binary64_11061`
3×	`associate-/l_binary64_10935` `flip3-+_binary64_10993` `associate-/r_binary64_10934` `flip-+_binary64_10964`
2×	`unswap-sqr_binary64_10958` `*-commutative_binary64_10921`
1×	`sum-log_binary64_11081` `clear-num_binary64_10989` `div-exp_binary64_11041` `+-commutative_binary64_10920` `frac-2neg_binary64_11001` `div-inv_binary64_10987` `cbrt-undiv_binary64_11024`

Counts

4 → 91

Calls

4 calls:

32.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
26.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
14.0ms	(+.f64 (/.f64 1/9 x) y)
6.0ms	(/.f64 1/9 x)

series163.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
51.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
19.0ms	(+.f64 (/.f64 1/9 x) y)
19.0ms	(/.f64 1/9 x)

simplify136.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4877	1561
1	4877	1561

prune212.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	104	9	113

Merged error: 0b

Counts

113 → 9

Compiler

Compiled 1961 to 1367 computations (30.3% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 (/.f64 1 x) 9))
0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
0.3b	(/.f64 (/.f64 1 x) 9)
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite128.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64_10996`
60×	`*-un-lft-identity_binary64_10990` `add-sqr-sqrt_binary64_11012`
52×	`add-cube-cbrt_binary64_11025`
20×	`add-exp-log_binary64_11028`
16×	`add-cbrt-cube_binary64_11026`
14×	`associate-r_binary64_10930`
13×	`associate-/l*_binary64_10935`
11×	`pow1_binary64_11051`
6×	`add-log-exp_binary64_11029` `div-exp_binary64_11041` `cancel-sign-sub-inv_binary64_10956`
5×	`distribute-rgt-in_binary64_10940` `div-inv_binary64_10987` `distribute-lft-in_binary64_10939`
4×	`prod-exp_binary64_11039` `sqrt-prod_binary64_11006` `cbrt-unprod_binary64_11023` `associate-l_binary64_10931` `pow-prod-down_binary64_11061`
3×	`associate-/r*_binary64_10934` `cbrt-undiv_binary64_11024`
2×	`associate--l+_binary64_10927` `distribute-lft-out--_binary64_10942` `associate-r/_binary64_10932` `distribute-lft-out_binary64_10941` `unswap-sqr_binary64_10958` `sub-neg_binary64_10983` `difference-of-squares_binary64_10959` `-commutative_binary64_10921`
1×	`flip3--_binary64_10994` `sum-log_binary64_11081` `associate-/l/_binary64_10937` `flip--_binary64_10965` `clear-num_binary64_10989` `difference-of-sqr-1_binary64_10960` `1-exp_binary64_11034` `flip3-+_binary64_10993` `flip-+_binary64_10964` `+-commutative_binary64_10920` `frac-2neg_binary64_11001` `rec-exp_binary64_11040`

Counts

4 → 141

Calls

4 calls:

47.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
34.0ms	(+.f64 y (/.f64 (/.f64 1 x) 9))
13.0ms	(/.f64 (/.f64 1 x) 9)
10.0ms	(*.f64 3 (sqrt.f64 x))

series147.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
29.0ms	(*.f64 3 (sqrt.f64 x))
29.0ms	(+.f64 y (/.f64 (/.f64 1 x) 9))
18.0ms	(/.f64 (/.f64 1 x) 9)

simplify161.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4918	2213
1	4918	2213

prune303.0ms (4.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	153	9	162

Merged error: 0b

Counts

162 → 9

Compiler

Compiled 3084 to 2210 computations (28.3% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))) 1))
0.3b	(*.f64 (sqrt.f64 x) 9)
0.3b	(*.f64 3 (sqrt.f64 x))
0.3b	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))

rewrite109.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64_10996`
51×	`add-sqr-sqrt_binary64_11012`
45×	`*-un-lft-identity_binary64_10990`
39×	`add-cube-cbrt_binary64_11025`
35×	`add-exp-log_binary64_11028`
26×	`sqrt-prod_binary64_11006`
25×	`add-cbrt-cube_binary64_11026`
22×	`associate-/l*_binary64_10935`
17×	`associate-r_binary64_10930`
13×	`pow1_binary64_11051`
12×	`div-exp_binary64_11041`
10×	`associate-l_binary64_10931`
9×	`prod-exp_binary64_11039`
7×	`cbrt-unprod_binary64_11023`
6×	`cbrt-undiv_binary64_11024` `cancel-sign-sub-inv_binary64_10956`
5×	`distribute-rgt-in_binary64_10940` `pow-prod-down_binary64_11061` `distribute-lft-in_binary64_10939`
4×	`add-log-exp_binary64_11029` `unswap-sqr_binary64_10958`
3×	`div-inv_binary64_10987` `*-commutative_binary64_10921`
2×	`associate--l+_binary64_10927` `distribute-lft-out--_binary64_10942` `associate-*r/_binary64_10932` `1-exp_binary64_11034` `sub-neg_binary64_10983` `difference-of-squares_binary64_10959` `rec-exp_binary64_11040`
1×	`flip3--_binary64_10994` `associate-/l/_binary64_10937` `flip--_binary64_10965` `clear-num_binary64_10989` `distribute-lft-out_binary64_10941` `difference-of-sqr-1_binary64_10960` `associate-/r*_binary64_10934` `frac-2neg_binary64_11001`

Counts

4 → 147

Calls

4 calls:

41.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))) 1))
20.0ms	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))
11.0ms	(*.f64 (sqrt.f64 x) 9)
10.0ms	(*.f64 3 (sqrt.f64 x))

series175.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))) 1))
28.0ms	(*.f64 (sqrt.f64 x) 9)
28.0ms	(*.f64 3 (sqrt.f64 x))
26.0ms	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))

simplify160.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4916	2285
1	4916	2285

prune311.0ms (4.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	159	9	168

Merged error: 0b

Counts

168 → 9

Compiler

Compiled 3423 to 2176 computations (36.4% saved)

regimes421.0ms (6.7%)

Compiler: Compiled 2363 to 2035 computations (13.9% saved)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	21
1	27	21

end0.0ms (0%)

sample2.5s (40.2%)

Algorithm

1×

intervals

Results

650.0ms	8000×	body	128	valid
13.0ms	158×	body	128	nan
6.0ms	69×	body	128	invalid

Compiler

Compiled 823 to 710 computations (13.7% saved)

Details

analyze106.0ms (1.7%)

sample35.0ms (0.6%)

simplify449.0ms (7.2%)

prune8.0ms (0.1%)

localize24.0ms (0.4%)

rewrite86.0ms (1.4%)

series143.0ms (2.3%)

simplify85.0ms (1.4%)

prune233.0ms (3.7%)

localize17.0ms (0.3%)

rewrite92.0ms (1.5%)

series163.0ms (2.6%)

simplify136.0ms (2.2%)

prune212.0ms (3.4%)

localize19.0ms (0.3%)

rewrite128.0ms (2%)

series147.0ms (2.3%)

simplify161.0ms (2.6%)

prune303.0ms (4.8%)

localize25.0ms (0.4%)

rewrite109.0ms (1.7%)

series175.0ms (2.8%)

simplify160.0ms (2.5%)

prune311.0ms (4.9%)

regimes421.0ms (6.7%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample2.5s (40.2%)

Profiling