Details

analyze4.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 11 to 12 computations (-9.1% saved)

sample60.0ms (0.2%)

Algorithm

1×

intervals

Results

23.0ms	57×	body	1024	valid
9.0ms	144×	body	128	valid
9.0ms	36×	body	512	valid
3.0ms	7×	body	2048	valid
2.0ms	12×	body	256	valid

Compiler

Compiled 21 to 25 computations (-19% saved)

simplify488.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (184.0ms)

Iter	Nodes	Cost
0	4687	15
1	4687	15

prune4.0ms (0%)

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: 27.9b

Counts

2 → 1

Compiler

Compiled 20 to 22 computations (-10% saved)

localize13.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (exp.f64 (*.f64 -2 x)))
2.8b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

rewrite38.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_435`
8×	`*-un-lft-identity_binary64_414`
6×	`add-log-exp_binary64_450`
4×	`difference-of-squares_binary64_383`
3×	`times-frac_binary64_420`
2×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `difference-of-sqr-1_binary64_384`
1×	`flip3--_binary64_418` `distribute-lft-out--_binary64_368` `flip3-+_binary64_417` `diff-log_binary64_503` `+-commutative_binary64_346` `sub-neg_binary64_407` `flip-+_binary64_388` `distribute-lft-out_binary64_367` `flip--_binary64_389` `sum-log_binary64_502`

Counts

2 → 30

Calls

2 calls:

26.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
8.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

series185.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

162.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
23.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

simplify155.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4840	711
1	4840	711

prune87.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	34	2	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	2	37

Merged error: 0.0b

Counts

37 → 2

Compiler

Compiled 648 to 588 computations (9.3% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (exp.f64 (*.f64 -2 x)))
0.0b	(+.f64 1 (exp.f64 (*.f64 -2 x)))
0.0b	(/.f64 (-.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3) 1) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (*.f64 -2 x))))))
2.8b	(-.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 3) 1)

rewrite231.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

194×	`add-sqr-sqrt_binary64_435`
130×	`*-un-lft-identity_binary64_414`
124×	`times-frac_binary64_420`
72×	`difference-of-squares_binary64_383`
36×	`cube-prod_binary64_439` `unpow-prod-down_binary64_490` `difference-of-sqr-1_binary64_384`
32×	`add-cube-cbrt_binary64_446`
25×	`distribute-lft-out_binary64_367`
22×	`associate-/l*_binary64_361`
18×	`sqr-pow_binary64_386`
10×	`add-log-exp_binary64_450`
6×	`distribute-lft-out--_binary64_368` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
4×	`pow1_binary64_472` `associate-/r*_binary64_360`
3×	`flip3-+_binary64_417` `flip-+_binary64_388`
2×	`associate-/r/_binary64_362` `flip3--_binary64_418` `+-commutative_binary64_346` `flip--_binary64_389` `associate-/l/_binary64_363` `sum-log_binary64_502`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `div-inv_binary64_411` `cbrt-undiv_binary64_445` `sub-neg_binary64_407` `frac-2neg_binary64_425` `div-sub_binary64_419` `div-exp_binary64_462`

Counts

4 → 185

Calls

4 calls:

96.0ms	(/.f64 (-.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3) 1) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (*.f64 -2 x))))))
46.0ms	(-.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 3) 1)
14.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))
8.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

series1.7s (4.8%)

Counts

4 → 12

Calls

4 calls:

1.3s	(/.f64 (-.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3) 1) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (*.f64 -2 x))))))
349.0ms	(-.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 3) 1)
25.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))
22.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

simplify258.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5061	12309

prune1.5s (4.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	196	3	199

Merged error: 0.0b

Counts

199 → 3

Compiler

Compiled 10322 to 9412 computations (8.8% saved)

localize42.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (pow.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3) 3) (pow.f64 1 3)) (.f64 (+.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 6) (+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3))) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (.f64 -2 x)))))))
0.0b	(+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 3))
0.0b	(pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 6)
2.8b	(-.f64 (pow.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 3) 3) (pow.f64 1 3))

rewrite685.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

411×	`add-sqr-sqrt_binary64_435`
294×	`unpow-prod-down_binary64_490`
276×	`cube-prod_binary64_439`
252×	`difference-of-squares_binary64_383`
178×	`times-frac_binary64_420`
140×	`*-un-lft-identity_binary64_414`
97×	`sqr-pow_binary64_386`
94×	`associate-/l*_binary64_361`
18×	`distribute-lft-out--_binary64_368`
15×	`add-cube-cbrt_binary64_446`
12×	`add-exp-log_binary64_449`
10×	`associate-/r/_binary64_362`
9×	`add-cbrt-cube_binary64_447`
8×	`flip3-+_binary64_417` `add-log-exp_binary64_450` `flip-+_binary64_388`
5×	`pow1_binary64_472`
4×	`distribute-lft-out_binary64_367` `frac-times_binary64_424`
3×	`cube-mult_binary64_441` `pow-unpow_binary64_488` `difference-cubes_binary64_416` `div-exp_binary64_462`
2×	`flip3--_binary64_418` `associate-l/_binary64_359` `div-inv_binary64_411` `cbrt-undiv_binary64_445` `pow-exp_binary64_479` `flip--_binary64_389` `associate-/l/_binary64_363` `associate-r/_binary64_358`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `+-commutative_binary64_346` `pow-pow_binary64_483` `prod-exp_binary64_460` `pow-to-exp_binary64_480` `sub-neg_binary64_407` `frac-2neg_binary64_425` `cbrt-unprod_binary64_444` `sum-log_binary64_502` `div-sub_binary64_419` `associate-/r*_binary64_360`

Counts

4 → 361

Calls

4 calls:

287.0ms	(/.f64 (-.f64 (pow.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3) 3) (pow.f64 1 3)) (.f64 (+.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 6) (+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3))) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (.f64 -2 x)))))))
151.0ms	(-.f64 (pow.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 3) 3) (pow.f64 1 3))
36.0ms	(+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 3))
20.0ms	(pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 6)

series3.9s (10.9%)

Counts

4 → 12

Calls

4 calls:

2.9s	(/.f64 (-.f64 (pow.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3) 3) (pow.f64 1 3)) (.f64 (+.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 6) (+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3))) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (.f64 -2 x)))))))
460.0ms	(-.f64 (pow.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 3) 3) (pow.f64 1 3))
294.0ms	(+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 3))
288.0ms	(pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 6)

simplify484.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

373 → 373

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	5039	27280

prune5.1s (14.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	372	1	373
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	374	2	376

Merged error: 0.0b

Counts

376 → 2

Compiler

Compiled 27891 to 25642 computations (8.1% saved)

localize41.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (pow.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3) 3) (.f64 (+.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 6) (+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3))) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (.f64 -2 x)))))))
0.0b	(pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 6)
0.0b	(pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 6)
2.8b	(-.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3) 3) (.f64 (+.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 6) (+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3))) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (.f64 -2 x))))))) (/.f64 1 (.f64 (+.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 6) (+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3))) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (*.f64 -2 x))))))))

rewrite712.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

212×	`times-frac_binary64_420`
192×	`unpow-prod-down_binary64_490`
158×	`*-un-lft-identity_binary64_414`
156×	`cube-prod_binary64_439`
94×	`add-sqr-sqrt_binary64_435`
92×	`add-cube-cbrt_binary64_446`
90×	`associate-/l*_binary64_361`
44×	`associate-/r/_binary64_362`
38×	`add-exp-log_binary64_449`
30×	`distribute-lft-out_binary64_367`
28×	`flip3-+_binary64_417` `flip-+_binary64_388`
16×	`pow-exp_binary64_479` `div-exp_binary64_462`
15×	`div-inv_binary64_411`
12×	`frac-times_binary64_424`
10×	`distribute-rgt-out--_binary64_370`
9×	`add-cbrt-cube_binary64_447`
8×	`sqr-pow_binary64_386`
6×	`associate-l/_binary64_359` `pow1_binary64_472` `cube-mult_binary64_441` `pow-unpow_binary64_488` `prod-exp_binary64_460` `pow-to-exp_binary64_480` `unpow3_binary64_477` `add-log-exp_binary64_450` `associate-r/_binary64_358`
3×	`distribute-lft-out--_binary64_368`
2×	`cbrt-undiv_binary64_445` `pow-pow_binary64_483` `cube-div_binary64_440`
1×	`flip3--_binary64_418` `clear-num_binary64_413` `difference-of-squares_binary64_383` `diff-log_binary64_503` `frac-sub_binary64_423` `sub-neg_binary64_407` `frac-2neg_binary64_425` `flip--_binary64_389` `cbrt-unprod_binary64_444` `sub-div_binary64_421` `associate-/l/_binary64_363` `associate-/r*_binary64_360`

Counts

4 → 307

Calls

4 calls:

295.0ms	(-.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3) 3) (.f64 (+.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 6) (+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3))) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (.f64 -2 x))))))) (/.f64 1 (.f64 (+.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 6) (+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3))) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (*.f64 -2 x))))))))
172.0ms	(/.f64 (pow.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3) 3) (.f64 (+.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 6) (+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3))) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (.f64 -2 x)))))))
19.0ms	(pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 6)
18.0ms	(pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 6)

series8.4s (23.3%)

Counts

4 → 12

Calls

4 calls:

5.1s	(-.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3) 3) (.f64 (+.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 6) (+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3))) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (.f64 -2 x))))))) (/.f64 1 (.f64 (+.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 6) (+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3))) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (*.f64 -2 x))))))))
2.7s	(/.f64 (pow.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3) 3) (.f64 (+.f64 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 6) (+.f64 1 (pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x)))) 3))) (+.f64 1 (/.f64 (+.f64 2 (/.f64 4 (+.f64 1 (exp.f64 (.f64 -2 x))))) (+.f64 1 (exp.f64 (.f64 -2 x)))))))
271.0ms	(pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 6)
254.0ms	(pow.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 6)

simplify437.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

319 → 319

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5049	27010

prune8.2s (22.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	318	1	319
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	319	2	321

Merged error: 0.0b

Counts

321 → 2

Compiler

Compiled 37394 to 34148 computations (8.7% saved)

regimes341.0ms (1%)

Compiler: Compiled 1135 to 1055 computations (7% saved)

bsearch6.0ms (0%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

simplify14.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	225	360
1	225	360

end0.0ms (0%)

sample2.8s (7.8%)

Algorithm

1×

intervals

Results

775.0ms	1947×	body	1024	valid
286.0ms	4313×	body	128	valid
245.0ms	998×	body	512	valid
112.0ms	232×	body	2048	valid
78.0ms	510×	body	256	valid

Compiler

Compiled 466 to 429 computations (7.9% saved)

Details

analyze4.0ms (0%)

sample60.0ms (0.2%)

simplify488.0ms (1.4%)

prune4.0ms (0%)

localize13.0ms (0%)

rewrite38.0ms (0.1%)

series185.0ms (0.5%)

simplify155.0ms (0.4%)

prune87.0ms (0.2%)

localize31.0ms (0.1%)

rewrite231.0ms (0.6%)

series1.7s (4.8%)

simplify258.0ms (0.7%)

prune1.5s (4.1%)

localize42.0ms (0.1%)

rewrite685.0ms (1.9%)

series3.9s (10.9%)

simplify484.0ms (1.3%)

prune5.1s (14.3%)

localize41.0ms (0.1%)

rewrite712.0ms (2%)

series8.4s (23.3%)

simplify437.0ms (1.2%)

prune8.2s (22.8%)

regimes341.0ms (1%)

bsearch6.0ms (0%)

simplify14.0ms (0%)

end0.0ms (0%)

sample2.8s (7.8%)

Profiling