Details

analyze46.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
25%	25%	50%	4
25%	25%	50%	5
31.2%	18.7%	50%	6
34.3%	15.6%	50%	7
39%	10.9%	50%	8
40.6%	8.6%	50.8%	9
42.9%	5.9%	51.2%	10
43.7%	4.5%	51.8%	11
44.9%	3%	52.1%	12
45.3%	2.3%	52.4%	13
45.9%	1.5%	52.6%	14

Compiler

Compiled 15 to 14 computations (6.7% saved)

sample19.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 29 to 29 computations (0% saved)

simplify30.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	487	18
1	487	18

prune6.0ms (0.2%)

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: 0.2b

Counts

2 → 2

Compiler

Compiled 64 to 59 computations (7.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
19×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
15×	`add-cube-cbrt_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`times-frac_binary64`
9×	`add-log-exp_binary64` `pow1_binary64`
8×	`associate--l+_binary64`
6×	`associate-r_binary64` `associate-/l*_binary64`
5×	`distribute-lft-out--_binary64` `div-inv_binary64`
4×	`cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `sqrt-prod_binary64`
3×	`diff-log_binary64` `cbrt-unprod_binary64` `associate-l_binary64`
2×	`pow-prod-down_binary64` `associate-/r*_binary64` `sub-neg_binary64` `flip3--_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64`
1×	`associate--l-_binary64` `inv-pow_binary64` `difference-of-squares_binary64` `*-commutative_binary64`

Counts

4 → 103

Calls

4 calls:

16.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
6.0ms	(*.f64 3 (sqrt.f64 x))
6.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
5.0ms	(/.f64 1 (*.f64 x 9))

series193.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
59.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
33.0ms	(*.f64 3 (sqrt.f64 x))
21.0ms	(/.f64 1 (*.f64 x 9))

simplify82.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4942	1595
1	4942	1595

prune338.0ms (9.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	104	11	115
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	106	11	117

Merged error: 0.0b

Counts

117 → 11

Compiler

Compiled 5445 to 4386 computations (19.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
0.2b	(/.f64 1 (*.f64 x 9))
0.3b	(*.f64 y (/.f64 1/3 (sqrt.f64 x)))
0.4b	(/.f64 1/3 (sqrt.f64 x))

rewrite46.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`associate-r_binary64` `sqrt-prod_binary64`
19×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `pow1_binary64`
8×	`cancel-sign-sub-inv_binary64` `associate--l+_binary64`
7×	`associate-/r*_binary64`
6×	`associate-/l*_binary64`
4×	`cbrt-undiv_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
3×	`diff-log_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `associate-l*_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64`
1×	`associate--l-_binary64` `inv-pow_binary64` `*-commutative_binary64`

Counts

4 → 131

Calls

4 calls:

15.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
10.0ms	(*.f64 y (/.f64 1/3 (sqrt.f64 x)))
5.0ms	(/.f64 1 (*.f64 x 9))
4.0ms	(/.f64 1/3 (sqrt.f64 x))

series219.0ms (6%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(*.f64 y (/.f64 1/3 (sqrt.f64 x)))
64.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
53.0ms	(/.f64 1/3 (sqrt.f64 x))
22.0ms	(/.f64 1 (*.f64 x 9))

simplify82.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4933	1969
1	4933	1969

prune178.0ms (4.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	143	11	154

Merged error: 0.0b

Counts

154 → 11

Compiler

Compiled 3116 to 2228 computations (28.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite110.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64`
175×	`add-sqr-sqrt_binary64`
167×	`*-un-lft-identity_binary64`
156×	`add-cube-cbrt_binary64`
96×	`cancel-sign-sub-inv_binary64`
83×	`sqrt-prod_binary64`
20×	`div-inv_binary64`
17×	`add-exp-log_binary64`
16×	`associate-/l*_binary64`
14×	`add-cbrt-cube_binary64`
11×	`add-log-exp_binary64`
8×	`associate--l+_binary64`
7×	`associate-/r*_binary64` `pow1_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`diff-log_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64`
2×	`clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-flip_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `inv-pow_binary64`

Counts

4 → 273

Calls

4 calls:

57.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
8.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
7.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))
5.0ms	(/.f64 1 (*.f64 x 9))

series202.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
63.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
34.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))
20.0ms	(/.f64 1 (*.f64 x 9))

simplify111.0ms (3%)

Algorithm

1×	egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4942	5911
1	4942	5911

prune423.0ms (11.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	285	11	296

Merged error: 0.0b

Counts

296 → 11

Compiler

Compiled 6945 to 4709 computations (32.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite79.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

147×	`times-frac_binary64`
94×	`add-sqr-sqrt_binary64`
93×	`*-un-lft-identity_binary64`
88×	`add-cube-cbrt_binary64`
50×	`cancel-sign-sub-inv_binary64`
44×	`associate--l+_binary64`
18×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64` `associate-/l*_binary64`
11×	`div-inv_binary64`
9×	`add-log-exp_binary64`
6×	`pow1_binary64` `associate-r_binary64` `div-exp_binary64`
5×	`cbrt-undiv_binary64`
4×	`associate-/r*_binary64` `sqrt-prod_binary64`
3×	`diff-log_binary64` `associate-l_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate--l-_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `*-commutative_binary64`

Counts

4 → 183

Calls

4 calls:

40.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
7.0ms	(/.f64 (/.f64 1 x) 9)
6.0ms	(*.f64 3 (sqrt.f64 x))
6.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))

series192.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
62.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
29.0ms	(*.f64 3 (sqrt.f64 x))
20.0ms	(/.f64 (/.f64 1 x) 9)

simplify87.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5229	3249

prune338.0ms (9.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	4	4	8
Picked	0	1	1
Done	0	2	2
Total	197	9	206

Merged error: 0b

Counts

206 → 9

Compiler

Compiled 5545 to 4202 computations (24.2% saved)

regimes45.0ms (1.2%)

Compiler: Compiled 338 to 296 computations (12.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	21
1	79	21

end0.0ms (0%)

sample751.0ms (20.5%)

Algorithm

1×

intervals

Results

379.0ms	8000×	body	128	valid
4.0ms	94×	body	128	invalid

Compiler

Compiled 210 to 186 computations (11.4% saved)

Details

analyze46.0ms (1.3%)

sample19.0ms (0.5%)

simplify30.0ms (0.8%)

prune6.0ms (0.2%)

localize10.0ms (0.3%)

rewrite40.0ms (1.1%)

series193.0ms (5.3%)

simplify82.0ms (2.2%)

prune338.0ms (9.2%)

localize10.0ms (0.3%)

rewrite46.0ms (1.3%)

series219.0ms (6%)

simplify82.0ms (2.2%)

prune178.0ms (4.9%)

localize10.0ms (0.3%)

rewrite110.0ms (3%)

series202.0ms (5.5%)

simplify111.0ms (3%)

prune423.0ms (11.6%)

localize10.0ms (0.3%)

rewrite79.0ms (2.2%)

series192.0ms (5.3%)

simplify87.0ms (2.4%)

prune338.0ms (9.2%)

regimes45.0ms (1.2%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample751.0ms (20.5%)

Profiling