Details

analyze40.0ms (1%)

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)

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 29 to 29 computations (0% saved)

simplify189.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	487	18
1	487	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: 0.2b

Counts

2 → 2

Compiler

Compiled 64 to 59 computations (7.8% saved)

localize13.0ms (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 y (*.f64 3 (sqrt.f64 x)))
0.3b	(*.f64 3 (sqrt.f64 x))
0.5b	(/.f64 1 (*.f64 x 9))

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_14183` `add-exp-log_binary64_14221`
21×	`add-sqr-sqrt_binary64_14205`
16×	`add-cbrt-cube_binary64_14219`
15×	`add-cube-cbrt_binary64_14218`
14×	`cancel-sign-sub-inv_binary64_14149`
12×	`times-frac_binary64_14189`
9×	`pow1_binary64_14244` `add-log-exp_binary64_14222`
8×	`associate--l+_binary64_14120`
6×	`associate-/l_binary64_14128` `associate-r*_binary64_14123` `div-exp_binary64_14234`
5×	`prod-exp_binary64_14232` `div-inv_binary64_14180` `distribute-lft-out--_binary64_14135`
4×	`cbrt-undiv_binary64_14217` `sqrt-prod_binary64_14199`
3×	`associate-l_binary64_14124` `diff-log_binary64_14275` `cbrt-unprod_binary64_14216`
2×	`clear-num_binary64_14182` `sub-neg_binary64_14176` `flip--_binary64_14158` `flip3--_binary64_14187` `unswap-sqr_binary64_14151` `associate-/r*_binary64_14127` `1-exp_binary64_14227` `pow-flip_binary64_14257` `pow-prod-down_binary64_14254` `frac-2neg_binary64_14194` `rec-exp_binary64_14233` `frac-sub_binary64_14192`
1×	`inv-pow_binary64_14268` `*-commutative_binary64_14114` `associate--l-_binary64_14121` `difference-of-squares_binary64_14152`

Counts

4 → 105

Calls

4 calls:

15.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
6.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
6.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 1 (*.f64 x 9))

series187.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
60.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
28.0ms	(*.f64 3 (sqrt.f64 x))
20.0ms	(/.f64 1 (*.f64 x 9))

simplify68.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4986	1569
1	4986	1569

prune389.0ms (9.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	108	9	117
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	109	10	119

Merged error: 0.0b

Counts

119 → 10

Compiler

Compiled 6247 to 5116 computations (18.1% saved)

localize11.0ms (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))))
0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
0.3b	(*.f64 3 (sqrt.f64 x))
0.3b	(/.f64 (/.f64 1 x) 9)

rewrite75.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

147×	`times-frac_binary64_14189`
94×	`add-sqr-sqrt_binary64_14205`
93×	`*-un-lft-identity_binary64_14183`
88×	`add-cube-cbrt_binary64_14218`
50×	`cancel-sign-sub-inv_binary64_14149`
44×	`associate--l+_binary64_14120`
20×	`add-exp-log_binary64_14221`
16×	`add-cbrt-cube_binary64_14219` `associate-/l*_binary64_14128`
11×	`div-inv_binary64_14180`
9×	`add-log-exp_binary64_14222`
8×	`div-exp_binary64_14234`
6×	`associate-r_binary64_14123` `pow1_binary64_14244`
5×	`cbrt-undiv_binary64_14217`
4×	`associate-/r*_binary64_14127` `sqrt-prod_binary64_14199`
3×	`associate-l_binary64_14124` `diff-log_binary64_14275` `distribute-lft-out--_binary64_14135`
2×	`clear-num_binary64_14182` `sub-neg_binary64_14176` `flip--_binary64_14158` `prod-exp_binary64_14232` `flip3--_binary64_14187` `unswap-sqr_binary64_14151` `frac-2neg_binary64_14194` `frac-sub_binary64_14192` `cbrt-unprod_binary64_14216`
1×	`associate-/l/_binary64_14130` `*-commutative_binary64_14114` `associate--l-_binary64_14121` `difference-of-squares_binary64_14152` `1-exp_binary64_14227` `pow-prod-down_binary64_14254` `rec-exp_binary64_14233`

Counts

4 → 184

Calls

4 calls:

34.0ms	(-.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)))

series184.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
64.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
28.0ms	(*.f64 3 (sqrt.f64 x))
21.0ms	(/.f64 (/.f64 1 x) 9)

simplify84.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5216	3255

prune465.0ms (11.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	194	12	206

Merged error: 0b

Counts

206 → 12

Compiler

Compiled 7878 to 6198 computations (21.3% saved)

localize13.0ms (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)))
0.3b	(/.f64 (/.f64 y 3) (sqrt.f64 x))
0.5b	(/.f64 1 (*.f64 x 9))

rewrite109.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64_14189`
175×	`add-sqr-sqrt_binary64_14205`
167×	`*-un-lft-identity_binary64_14183`
156×	`add-cube-cbrt_binary64_14218`
96×	`cancel-sign-sub-inv_binary64_14149`
83×	`sqrt-prod_binary64_14199`
20×	`div-inv_binary64_14180` `add-exp-log_binary64_14221`
16×	`associate-/l*_binary64_14128`
14×	`add-cbrt-cube_binary64_14219`
11×	`add-log-exp_binary64_14222`
8×	`associate--l+_binary64_14120`
7×	`associate-/r*_binary64_14127` `difference-of-squares_binary64_14152` `div-exp_binary64_14234` `distribute-lft-out--_binary64_14135` `pow1_binary64_14244`
5×	`cbrt-undiv_binary64_14217`
4×	`diff-log_binary64_14275`
3×	`sub-neg_binary64_14176` `flip--_binary64_14158` `prod-exp_binary64_14232` `flip3--_binary64_14187`
2×	`clear-num_binary64_14182` `1-exp_binary64_14227` `pow-flip_binary64_14257` `frac-2neg_binary64_14194` `rec-exp_binary64_14233` `frac-sub_binary64_14192`
1×	`inv-pow_binary64_14268` `associate-/l/_binary64_14130` `associate--l-_binary64_14121` `pow-prod-down_binary64_14254` `cbrt-unprod_binary64_14216`

Counts

4 → 275

Calls

4 calls:

50.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
12.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))
9.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
5.0ms	(/.f64 1 (*.f64 x 9))

series199.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
65.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
34.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))
23.0ms	(/.f64 1 (*.f64 x 9))

simplify112.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

287 → 287

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4942	5923
1	4942	5923

prune407.0ms (10%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	286	1	287
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	287	12	299

Merged error: 0b

Counts

299 → 12

Compiler

Compiled 6771 to 4553 computations (32.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (/.f64 y 3) (/.f64 1 (sqrt.f64 x))))
0.2b	(/.f64 1 (sqrt.f64 x))
0.3b	(*.f64 (/.f64 y 3) (/.f64 1 (sqrt.f64 x)))
0.5b	(/.f64 1 (*.f64 x 9))

rewrite60.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_14205`
64×	`times-frac_binary64_14189`
47×	`*-un-lft-identity_binary64_14183`
43×	`add-cube-cbrt_binary64_14218`
41×	`add-exp-log_binary64_14221`
25×	`sqrt-prod_binary64_14199`
23×	`add-cbrt-cube_binary64_14219`
22×	`associate-r_binary64_14123`
14×	`div-exp_binary64_14234`
13×	`associate-l_binary64_14124`
11×	`prod-exp_binary64_14232` `pow1_binary64_14244`
10×	`unswap-sqr_binary64_14151`
9×	`add-log-exp_binary64_14222`
8×	`associate--l+_binary64_14120` `cancel-sign-sub-inv_binary64_14149` `frac-sub_binary64_14192`
7×	`cbrt-undiv_binary64_14217` `associate-/r*_binary64_14127`
6×	`associate-/l*_binary64_14128`
5×	`flip--_binary64_14158` `div-inv_binary64_14180` `flip3--_binary64_14187` `1-exp_binary64_14227` `pow-flip_binary64_14257` `rec-exp_binary64_14233` `cbrt-unprod_binary64_14216`
3×	`frac-times_binary64_14193` `associate-r/_binary64_14125` `associate-l/_binary64_14126` `diff-log_binary64_14275` `un-div-inv_binary64_14181`
2×	`clear-num_binary64_14182` `sub-neg_binary64_14176` `inv-pow_binary64_14268` `pow-prod-down_binary64_14254` `frac-2neg_binary64_14194`
1×	`sqrt-pow1_binary64_14201` `pow1/2_binary64_14263` `*-commutative_binary64_14114` `associate--l-_binary64_14121`

Counts

4 → 173

Calls

4 calls:

19.0ms	(*.f64 (/.f64 y 3) (/.f64 1 (sqrt.f64 x)))
13.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (/.f64 y 3) (/.f64 1 (sqrt.f64 x))))
5.0ms	(/.f64 1 (*.f64 x 9))
5.0ms	(/.f64 1 (sqrt.f64 x))

series209.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(*.f64 (/.f64 y 3) (/.f64 1 (sqrt.f64 x)))
62.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (/.f64 y 3) (/.f64 1 (sqrt.f64 x))))
51.0ms	(/.f64 1 (sqrt.f64 x))
22.0ms	(/.f64 1 (*.f64 x 9))

simplify94.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4930	2726
1	4930	2726

prune237.0ms (5.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	185	12	197

Merged error: 0b

Counts

197 → 12

Compiler

Compiled 4243 to 3096 computations (27% saved)

regimes54.0ms (1.3%)

Compiler: Compiled 436 to 382 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	67	21
1	67	21

end0.0ms (0%)

sample797.0ms (19.5%)

Algorithm

1×

intervals

Results

374.0ms	8000×	body	128	valid
5.0ms	103×	body	128	invalid

Compiler

Compiled 259 to 229 computations (11.6% saved)

Details

analyze40.0ms (1%)

sample24.0ms (0.6%)

simplify189.0ms (4.6%)

prune6.0ms (0.1%)

localize13.0ms (0.3%)

rewrite41.0ms (1%)

series187.0ms (4.6%)

simplify68.0ms (1.7%)

prune389.0ms (9.5%)

localize11.0ms (0.3%)

rewrite75.0ms (1.8%)

series184.0ms (4.5%)

simplify84.0ms (2.1%)

prune465.0ms (11.4%)

localize13.0ms (0.3%)

rewrite109.0ms (2.7%)

series199.0ms (4.9%)

simplify112.0ms (2.7%)

prune407.0ms (10%)

localize11.0ms (0.3%)

rewrite60.0ms (1.5%)

series209.0ms (5.1%)

simplify94.0ms (2.3%)

prune237.0ms (5.8%)

regimes54.0ms (1.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample797.0ms (19.5%)

Profiling