Details

analyze56.0ms (1.5%)

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)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
0.0ms	10×	body	128	nan
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 29 computations (0% saved)

simplify148.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	1572	18
1	1572	18

prune6.0ms (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 64 to 59 computations (7.8% saved)

localize9.0ms (0.2%)

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

rewrite44.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
15×	`associate-r_binary64`
14×	`pow1_binary64`
12×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cancel-sign-sub-inv_binary64` `prod-exp_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`distribute-lft-out_binary64` `associate-l_binary64` `sqrt-prod_binary64`
3×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `div-inv_binary64`
2×	`sub-neg_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `div-exp_binary64` `pow-flip_binary64` `associate--l+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r*_binary64` `flip3--_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 97

Calls

4 calls:

17.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
8.0ms	(*.f64 3 (sqrt.f64 x))
6.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
5.0ms	(/.f64 1 (*.f64 x 9))

series162.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
39.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
29.0ms	(*.f64 3 (sqrt.f64 x))
21.0ms	(/.f64 1 (*.f64 x 9))

simplify77.0ms (2%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4916	1407
1	4916	1407

prune483.0ms (12.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	98	11	109
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	100	11	111

Merged error: 0.0b

Counts

111 → 11

Compiler

Compiled 8204 to 6774 computations (17.4% saved)

localize12.0ms (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))

rewrite66.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

25.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
15.0ms	(+.f64 y (/.f64 (/.f64 1 x) 9))
7.0ms	(/.f64 (/.f64 1 x) 9)
6.0ms	(*.f64 3 (sqrt.f64 x))

series163.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
31.0ms	(+.f64 y (/.f64 (/.f64 1 x) 9))
29.0ms	(*.f64 3 (sqrt.f64 x))
20.0ms	(/.f64 (/.f64 1 x) 9)

simplify83.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4914	2203
1	4914	2203

prune206.0ms (5.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	151	12	163

Merged error: 0.0b

Counts

163 → 12

Compiler

Compiled 3758 to 2772 computations (26.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/9 x) y)
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
0.3b	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
0.4b	(/.f64 1/9 x)

rewrite48.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

16.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
15.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
8.0ms	(+.f64 (/.f64 1/9 x) y)
3.0ms	(/.f64 1/9 x)

series203.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
65.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
35.0ms	(+.f64 (/.f64 1/9 x) y)
24.0ms	(/.f64 1/9 x)

simplify77.0ms (2%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5073	1547

prune418.0ms (11.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	100	15	115

Merged error: 0b

Counts

115 → 15

Compiler

Compiled 7513 to 5964 computations (20.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 x 1/9))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1 (/.f64 x 1/9)) y))))
0.3b	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1 (/.f64 x 1/9)) y)))
0.4b	(/.f64 x 1/9)

rewrite81.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
65×	`*-un-lft-identity_binary64`
62×	`add-sqr-sqrt_binary64`
58×	`add-cube-cbrt_binary64`
21×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
16×	`associate-/r*_binary64`
12×	`pow1_binary64`
9×	`associate-l_binary64`
7×	`associate-r_binary64` `div-inv_binary64`
6×	`associate-r/_binary64` `associate-/l_binary64`
5×	`distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-exp_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 154

Calls

4 calls:

30.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1 (/.f64 x 1/9)) y))))
26.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1 (/.f64 x 1/9)) y)))
7.0ms	(/.f64 1 (/.f64 x 1/9))
3.0ms	(/.f64 x 1/9)

series185.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1 (/.f64 x 1/9)) y))))
64.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1 (/.f64 x 1/9)) y)))
23.0ms	(/.f64 1 (/.f64 x 1/9))
20.0ms	(/.f64 x 1/9)

simplify53.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5687	2355

prune187.0ms (5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	13	13
Picked	1	0	1
Done	0	1	1
Total	166	15	181

Merged error: 0b

Counts

181 → 15

Compiler

Compiled 3499 to 2504 computations (28.4% saved)

regimes69.0ms (1.8%)

Compiler: Compiled 708 to 586 computations (17.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	21
1	19	21

end0.0ms (0%)

sample892.0ms (23.7%)

Algorithm

1×

intervals

Results

367.0ms	8000×	body	128	valid
6.0ms	134×	body	128	nan
3.0ms	71×	body	128	invalid

Compiler

Compiled 398 to 332 computations (16.6% saved)

Details

analyze56.0ms (1.5%)

sample20.0ms (0.5%)

simplify148.0ms (3.9%)

prune6.0ms (0.1%)

localize9.0ms (0.2%)

rewrite44.0ms (1.2%)

series162.0ms (4.3%)

simplify77.0ms (2%)

prune483.0ms (12.8%)

localize12.0ms (0.3%)

rewrite66.0ms (1.8%)

series163.0ms (4.3%)

simplify83.0ms (2.2%)

prune206.0ms (5.5%)

localize9.0ms (0.2%)

rewrite48.0ms (1.3%)

series203.0ms (5.4%)

simplify77.0ms (2%)

prune418.0ms (11.1%)

localize10.0ms (0.3%)

rewrite81.0ms (2.1%)

series185.0ms (4.9%)

simplify53.0ms (1.4%)

prune187.0ms (5%)

regimes69.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample892.0ms (23.7%)

Profiling