Details

analyze50.0ms (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

sample19.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	80	valid
0.0ms	5×	body	80	nan
0.0ms	1×	body	80	invalid

simplify201.0ms (7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (198.0ms)

Iter	Nodes	Cost
0	4819	14
1	4819	14

prune9.0ms (0.3%)

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: 0.4b

Counts

2 → 1

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 1.0 (*.f64 x 9.0)))
0.2b	(.f64 (.f64 3.0 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1.0 (*.f64 x 9.0))) 1.0))
0.3b	(/.f64 1.0 (*.f64 x 9.0))
0.3b	(*.f64 3.0 (sqrt.f64 x))

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
11×	`pow1_binary64`
10×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`pow-prod-down_binary64` `associate-l_binary64` `sqrt-prod_binary64`
3×	`associate-/l*_binary64` `times-frac_binary64`
2×	`sub-neg_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `associate--l+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r*_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 82

Calls

4 calls:

14.0ms	(.f64 (.f64 3.0 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1.0 (*.f64 x 9.0))) 1.0))
6.0ms	(+.f64 y (/.f64 1.0 (*.f64 x 9.0)))
6.0ms	(*.f64 3.0 (sqrt.f64 x))
5.0ms	(/.f64 1.0 (*.f64 x 9.0))

series30.0ms (1%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(.f64 (.f64 3.0 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1.0 (*.f64 x 9.0))) 1.0))
6.0ms	(*.f64 3.0 (sqrt.f64 x))
5.0ms	(+.f64 y (/.f64 1.0 (*.f64 x 9.0)))
3.0ms	(/.f64 1.0 (*.f64 x 9.0))

simplify35.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5384	938

prune160.0ms (5.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	84	10	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Merged error: 0.0b

Counts

95 → 10

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 (/.f64 1.0 x) 9.0))
0.2b	(.f64 (.f64 3.0 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1.0 x) 9.0)) 1.0))
0.3b	(*.f64 3.0 (sqrt.f64 x))
0.3b	(/.f64 (/.f64 1.0 x) 9.0)

rewrite53.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
57×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
50×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
12×	`associate-r_binary64`
11×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`div-inv_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
3×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`sub-neg_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `associate--l+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 131

Calls

4 calls:

22.0ms	(.f64 (.f64 3.0 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1.0 x) 9.0)) 1.0))
14.0ms	(+.f64 y (/.f64 (/.f64 1.0 x) 9.0))
7.0ms	(/.f64 (/.f64 1.0 x) 9.0)
5.0ms	(*.f64 3.0 (sqrt.f64 x))

series32.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(.f64 (.f64 3.0 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1.0 x) 9.0)) 1.0))
6.0ms	(*.f64 3.0 (sqrt.f64 x))
5.0ms	(/.f64 (/.f64 1.0 x) 9.0)
5.0ms	(+.f64 y (/.f64 (/.f64 1.0 x) 9.0))

simplify46.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5548	1567

prune225.0ms (7.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	143	10	153

Merged error: 0.0b

Counts

153 → 10

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1.0 (sqrt.f64 x))
0.3b	(/.f64 1 (sqrt.f64 x))
0.3b	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1.0 (sqrt.f64 x)) 9.0))
0.3b	(/.f64 (/.f64 1.0 (sqrt.f64 x)) 9.0)

rewrite88.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

353×	`times-frac_binary64`
257×	`add-sqr-sqrt_binary64`
192×	`*-un-lft-identity_binary64`
184×	`add-cube-cbrt_binary64`
109×	`sqrt-prod_binary64`
70×	`associate-r_binary64`
54×	`add-exp-log_binary64`
34×	`add-cbrt-cube_binary64`
28×	`associate-/l*_binary64`
24×	`div-exp_binary64`
22×	`associate-l_binary64`
20×	`unswap-sqr_binary64`
15×	`associate-/r*_binary64`
14×	`cbrt-undiv_binary64`
12×	`prod-exp_binary64` `div-inv_binary64`
8×	`pow1_binary64`
6×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `1-exp_binary64` `rec-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64` `pow-flip_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `inv-pow_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 332

Calls

4 calls:

44.0ms	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1.0 (sqrt.f64 x)) 9.0))
9.0ms	(/.f64 (/.f64 1.0 (sqrt.f64 x)) 9.0)
5.0ms	(/.f64 1 (sqrt.f64 x))
5.0ms	(/.f64 1.0 (sqrt.f64 x))

series36.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(/.f64 (/.f64 1.0 (sqrt.f64 x)) 9.0)
10.0ms	(/.f64 1.0 (sqrt.f64 x))
9.0ms	(/.f64 1 (sqrt.f64 x))
5.0ms	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1.0 (sqrt.f64 x)) 9.0))

simplify105.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5056	3851

prune787.0ms (27.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	344	0	344
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	344	10	354

Merged error: 0.0b

Counts

354 → 10

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1.0 (*.f64 x 9.0))
0.3b	(*.f64 3.0 (sqrt.f64 x))
0.3b	(*.f64 3.0 (sqrt.f64 x))
0.4b	(.f64 (sqrt.f64 (.f64 3.0 (sqrt.f64 x))) (sqrt.f64 (*.f64 3.0 (sqrt.f64 x))))

rewrite34.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`pow1_binary64`
28×	`sqrt-pow1_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`pow-prod-down_binary64`
16×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`sqrt-prod_binary64`
10×	`pow1/2_binary64` `pow-prod-up_binary64` `associate-l_binary64`
6×	`pow-sqr_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64`
1×	`associate-/r*_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow2_binary64`

Counts

4 → 114

Calls

4 calls:

12.0ms	(.f64 (sqrt.f64 (.f64 3.0 (sqrt.f64 x))) (sqrt.f64 (*.f64 3.0 (sqrt.f64 x))))
6.0ms	(*.f64 3.0 (sqrt.f64 x))
6.0ms	(*.f64 3.0 (sqrt.f64 x))
5.0ms	(/.f64 1.0 (*.f64 x 9.0))

series24.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 (.f64 3.0 (sqrt.f64 x))) (sqrt.f64 (*.f64 3.0 (sqrt.f64 x))))
6.0ms	(*.f64 3.0 (sqrt.f64 x))
5.0ms	(*.f64 3.0 (sqrt.f64 x))
3.0ms	(/.f64 1.0 (*.f64 x 9.0))

simplify79.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4944	753
1	4944	753

prune174.0ms (6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	126	10	136

Merged error: 0.0b

Counts

136 → 10

regimes120.0ms (4.1%)

Accuracy

Total 0.4b remaining (88.7%)

Threshold costs 0.4b (88.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	16
1	28	16

end0.0ms (0%)

sample500.0ms (17.3%)

Algorithm

1×

intervals

Results

351.0ms	8000×	body	80	valid
6.0ms	144×	body	80	nan
4.0ms	85×	body	80	invalid

Details

analyze50.0ms (1.7%)

sample19.0ms (0.6%)

simplify201.0ms (7%)

prune9.0ms (0.3%)

localize9.0ms (0.3%)

rewrite32.0ms (1.1%)

series30.0ms (1%)

simplify35.0ms (1.2%)

prune160.0ms (5.5%)

localize10.0ms (0.3%)

rewrite53.0ms (1.8%)

series32.0ms (1.1%)

simplify46.0ms (1.6%)

prune225.0ms (7.8%)

localize12.0ms (0.4%)

rewrite88.0ms (3.1%)

series36.0ms (1.2%)

simplify105.0ms (3.6%)

prune787.0ms (27.3%)

localize12.0ms (0.4%)

rewrite34.0ms (1.2%)

series24.0ms (0.8%)

simplify79.0ms (2.8%)

prune174.0ms (6%)

regimes120.0ms (4.1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample500.0ms (17.3%)

Profiling