Details

analyze40.0ms (0.7%)

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 (0.3%)

Algorithm

1×

intervals

Results

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

Compiler

Compiled 29 to 29 computations (0% saved)

simplify121.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	497	18
1	497	18

prune4.0ms (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

Error

0.2b

Counts

2 → 2

Compiler

Compiled 38 to 35 computations (7.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64_11369`
20×	`add-sqr-sqrt_binary64_11353`
17×	`*-un-lft-identity_binary64_11331`
16×	`add-cbrt-cube_binary64_11367`
13×	`add-cube-cbrt_binary64_11366`
9×	`pow1_binary64_11392` `times-frac_binary64_11337`
7×	`cancel-sign-sub-inv_binary64_11297`
6×	`div-exp_binary64_11382` `associate-/l_binary64_11276` `associate-r*_binary64_11271` `add-log-exp_binary64_11370`
5×	`prod-exp_binary64_11380`
4×	`div-inv_binary64_11328` `cbrt-undiv_binary64_11365` `sqrt-prod_binary64_11347`
3×	`cbrt-unprod_binary64_11364` `associate-l_binary64_11272`
2×	`distribute-lft-out--_binary64_11283` `difference-of-squares_binary64_11300` `1-exp_binary64_11375` `pow-flip_binary64_11405` `rec-exp_binary64_11381` `unswap-sqr_binary64_11299` `frac-2neg_binary64_11342` `associate-/r*_binary64_11275` `pow-prod-down_binary64_11402` `clear-num_binary64_11330`
1×	`*-commutative_binary64_11262` `sub-neg_binary64_11324` `flip3--_binary64_11335` `inv-pow_binary64_11416` `diff-log_binary64_11423` `flip--_binary64_11306`

Counts

4 → 93

Calls

4 calls:

7.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))
6.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
5.0ms	(/.f64 1 (*.f64 x 9))

series89.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
17.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))
16.0ms	(*.f64 3 (sqrt.f64 x))
15.0ms	(/.f64 1 (*.f64 x 9))

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4910	1027
1	4910	1027

prune129.0ms (2.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	96	9	105
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Error

0.0b

Counts

107 → 9

Compiler

Compiled 1947 to 1406 computations (27.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite96.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64_11337`
175×	`add-sqr-sqrt_binary64_11353`
167×	`*-un-lft-identity_binary64_11331`
156×	`add-cube-cbrt_binary64_11366`
96×	`cancel-sign-sub-inv_binary64_11297`
83×	`sqrt-prod_binary64_11347`
20×	`add-exp-log_binary64_11369` `div-inv_binary64_11328`
16×	`associate-/l*_binary64_11276`
14×	`add-cbrt-cube_binary64_11367`
11×	`add-log-exp_binary64_11370`
8×	`associate--l+_binary64_11268`
7×	`distribute-lft-out--_binary64_11283` `div-exp_binary64_11382` `difference-of-squares_binary64_11300` `pow1_binary64_11392` `associate-/r*_binary64_11275`
5×	`cbrt-undiv_binary64_11365`
4×	`diff-log_binary64_11423`
3×	`sub-neg_binary64_11324` `flip3--_binary64_11335` `prod-exp_binary64_11380` `flip--_binary64_11306`
2×	`1-exp_binary64_11375` `frac-sub_binary64_11340` `pow-flip_binary64_11405` `rec-exp_binary64_11381` `frac-2neg_binary64_11342` `clear-num_binary64_11330`
1×	`cbrt-unprod_binary64_11364` `associate-/l/_binary64_11278` `associate--l-_binary64_11269` `inv-pow_binary64_11416` `pow-prod-down_binary64_11402`

Counts

4 → 275

Calls

4 calls:

49.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
8.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
6.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))
4.0ms	(/.f64 1 (*.f64 x 9))

series109.0ms (2%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
36.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
18.0ms	(-.f64 1 (/.f64 1 (*.f64 x 9)))
11.0ms	(/.f64 1 (*.f64 x 9))

simplify111.0ms (2%)

Algorithm

1×	egg-herbie

Counts

287 → 287

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5142	5916

prune391.0ms (7.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	285	2	287
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	288	8	296

Error

0.0b

Counts

296 → 8

Compiler

Compiled 6259 to 4116 computations (34.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite101.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

852×	`times-frac_binary64_11337`
416×	`*-un-lft-identity_binary64_11331` `add-cube-cbrt_binary64_11366` `add-sqr-sqrt_binary64_11353`
156×	`sqrt-prod_binary64_11347`
100×	`associate-/r*_binary64_11275`
43×	`add-exp-log_binary64_11369`
25×	`add-cbrt-cube_binary64_11367`
24×	`div-inv_binary64_11328`
23×	`div-exp_binary64_11382`
12×	`associate-/l*_binary64_11276` `cbrt-undiv_binary64_11365`
8×	`pow1_binary64_11392`
6×	`associate-/r/_binary64_11277`
5×	`1-exp_binary64_11375` `rec-exp_binary64_11381`
4×	`add-log-exp_binary64_11370` `frac-2neg_binary64_11342` `clear-num_binary64_11330`
3×	`pow-flip_binary64_11405` `prod-exp_binary64_11380`
2×	`inv-pow_binary64_11416`
1×	`cbrt-unprod_binary64_11364` `pow-prod-down_binary64_11402`

Counts

4 → 485

Calls

4 calls:

18.0ms	(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))
8.0ms	(/.f64 3 (/.f64 y (sqrt.f64 x)))
4.0ms	(/.f64 y (sqrt.f64 x))
4.0ms	(/.f64 1 (*.f64 x 9))

series130.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))
39.0ms	(/.f64 y (sqrt.f64 x))
37.0ms	(/.f64 3 (/.f64 y (sqrt.f64 x)))
11.0ms	(/.f64 1 (*.f64 x 9))

simplify188.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4946	11034
1	4946	11034

prune805.0ms (14.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	496	1	497
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	497	8	505

Error

0.0b

Counts

505 → 8

Compiler

Compiled 12657 to 7701 computations (39.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite105.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

852×	`times-frac_binary64_11337`
416×	`*-un-lft-identity_binary64_11331` `add-cube-cbrt_binary64_11366` `add-sqr-sqrt_binary64_11353`
156×	`sqrt-prod_binary64_11347`
100×	`associate-/r*_binary64_11275`
43×	`add-exp-log_binary64_11369`
25×	`add-cbrt-cube_binary64_11367`
24×	`div-inv_binary64_11328`
23×	`div-exp_binary64_11382`
12×	`associate-/l*_binary64_11276` `cbrt-undiv_binary64_11365`
9×	`pow1_binary64_11392`
6×	`associate-/r/_binary64_11277`
5×	`1-exp_binary64_11375` `pow-flip_binary64_11405` `rec-exp_binary64_11381`
4×	`add-log-exp_binary64_11370` `frac-2neg_binary64_11342` `clear-num_binary64_11330`
3×	`prod-exp_binary64_11380`
2×	`inv-pow_binary64_11416`
1×	`cbrt-unprod_binary64_11364` `sqrt-pow1_binary64_11349` `pow1/2_binary64_11411` `pow-prod-down_binary64_11402`

Counts

4 → 487

Calls

4 calls:

18.0ms	(/.f64 y (/.f64 3 (/.f64 1 (sqrt.f64 x))))
9.0ms	(/.f64 3 (/.f64 1 (sqrt.f64 x)))
4.0ms	(/.f64 1 (sqrt.f64 x))
4.0ms	(/.f64 1 (*.f64 x 9))

series93.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(/.f64 y (/.f64 3 (/.f64 1 (sqrt.f64 x))))
25.0ms	(/.f64 1 (sqrt.f64 x))
17.0ms	(/.f64 3 (/.f64 1 (sqrt.f64 x)))
11.0ms	(/.f64 1 (*.f64 x 9))

simplify184.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

499 → 499

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4930	10671
1	4930	10671

prune991.0ms (18%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	498	1	499
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	500	7	507

Error

0.0b

Counts

507 → 7

Compiler

Compiled 12350 to 8473 computations (31.4% saved)

regimes399.0ms (7.3%)

Accuracy

Total 0.2b remaining (96.6%)

Threshold costs 0.2b (96.6%)

Compiler

Compiled 2105 to 1867 computations (11.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	21
1	69	21

end0.0ms (0%)

sample1.2s (22.7%)

Algorithm

1×

intervals

Results

362.0ms	8000×	body	128	valid
4.0ms	93×	body	128	invalid

Compiler

Compiled 734 to 653 computations (11% saved)

Details

analyze40.0ms (0.7%)

sample19.0ms (0.3%)

simplify121.0ms (2.2%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite28.0ms (0.5%)

series89.0ms (1.6%)

simplify69.0ms (1.2%)

prune129.0ms (2.4%)

localize9.0ms (0.2%)

rewrite96.0ms (1.7%)

series109.0ms (2%)

simplify111.0ms (2%)

prune391.0ms (7.1%)

localize11.0ms (0.2%)

rewrite101.0ms (1.8%)

series130.0ms (2.4%)

simplify188.0ms (3.4%)

prune805.0ms (14.6%)

localize13.0ms (0.2%)

rewrite105.0ms (1.9%)

series93.0ms (1.7%)

simplify184.0ms (3.4%)

prune991.0ms (18%)

regimes399.0ms (7.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (22.7%)

Profiling