Details

Time bar (total: 3.6min)

analyze286.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
0%0%100%2
0%0%100%3
0%0%100%4
0%0%100%5
0%0%100%6
0%0%100%7
0%0%100%8
0%0%100%9
0%0%100%10
0%0%100%11
0%0%100%12
0%0%100%13
0%0%100%14
Compiler

Compiled 30 to 24 computations (20% saved)

sample59.0ms (0%)

Algorithm
1×intervals
Results
12.0ms290×pre128true
12.0ms120×body256valid
6.0ms42×body512valid
5.0ms94×body128valid
2.0ms34×body128nan
Compiler

Compiled 50 to 47 computations (6% saved)

simplify469.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
2 → 2
Iterations

Useful iterations: 0 (373.0ms)

IterNodesCost
0183425
1183425

prune5.0ms (0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New022
Fresh022
Picked000
Done000
Total044
Error
47.1b
Counts
4 → 3
Compiler

Compiled 17 to 14 computations (17.6% saved)

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

26.0b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
26.0b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)

rewrite47.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
21×add-sqr-sqrt_binary64_441
14×*-un-lft-identity_binary64_419
9×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
8×add-log-exp_binary64_458 add-cube-cbrt_binary64_454
6×times-frac_binary64_425 difference-of-squares_binary64_388 sqrt-prod_binary64_435 associate-/l*_binary64_364
5×pow1_binary64_480
4×flip3--_binary64_423 flip--_binary64_394 cancel-sign-sub-inv_binary64_385
3×distribute-lft-out--_binary64_371
2×sqrt-div_binary64_436 sub-neg_binary64_412 diff-log_binary64_511 div-exp_binary64_470 cbrt-undiv_binary64_453 associate-/l/_binary64_366
1×clear-num_binary64_418 pow1/2_binary64_499 div-inv_binary64_416 prod-exp_binary64_468 cbrt-unprod_binary64_452 frac-2neg_binary64_430 sqrt-pow1_binary64_437 associate-/r*_binary64_363 rem-sqrt-square_binary64_432 div-sub_binary64_424
Counts
4 → 74
Calls

8 calls:

13.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
12.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
10.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series704.0ms (0.3%)

Counts
4 → 72
Calls

4 calls:

235.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b) (*.f64 a 2))
175.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) b)
174.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
119.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 1950 to 1660 computations (14.9% saved)

simplify98.0ms (0%)

Algorithm
1×egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
052073272

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

26.0b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
26.0b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

rewrite47.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
19×*-un-lft-identity_binary64_419
10×add-log-exp_binary64_458
9×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
8×add-sqr-sqrt_binary64_441
7×add-cube-cbrt_binary64_454
6×distribute-lft-out_binary64_370
5×times-frac_binary64_425 pow1_binary64_480 associate-/l*_binary64_364
3×distribute-rgt-neg-in_binary64_377 sqrt-prod_binary64_435
2×flip3-+_binary64_422 sqrt-div_binary64_436 associate-+l-_binary64_354 sum-log_binary64_510 flip3--_binary64_423 flip-+_binary64_393 flip--_binary64_394 div-exp_binary64_470 cbrt-undiv_binary64_453 associate-/l/_binary64_366 neg-sub0_binary64_414
1×clear-num_binary64_418 sub-neg_binary64_412 pow1/2_binary64_499 div-inv_binary64_416 prod-exp_binary64_468 cbrt-unprod_binary64_452 frac-2neg_binary64_430 diff-log_binary64_511 sqrt-pow1_binary64_437 cancel-sign-sub-inv_binary64_385 associate-/r*_binary64_363 rem-sqrt-square_binary64_432 neg-log_binary64_512 +-commutative_binary64_349 div-sub_binary64_424
Counts
4 → 70
Calls

8 calls:

19.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
10.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series716.0ms (0.3%)

Counts
4 → 72
Calls

4 calls:

237.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
179.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
176.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
124.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 2001 to 1711 computations (14.5% saved)

simplify71.0ms (0%)

Algorithm
1×egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
051673105

prune1.5s (0.7%)

Pruning

87 alts after pruning (85 fresh and 2 done)

PrunedKeptTotal
New20484288
Fresh011
Picked000
Done022
Total20487291
Error
0.0b
Counts
291 → 87
Compiler

Compiled 5601 to 3580 computations (36.1% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
0.3b
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

rewrite73.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
45×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
34×times-frac_binary64_425
32×*-un-lft-identity_binary64_419 add-sqr-sqrt_binary64_441
17×div-exp_binary64_470 cbrt-undiv_binary64_453
14×associate-/l*_binary64_364
13×prod-exp_binary64_468 cbrt-unprod_binary64_452
12×add-cube-cbrt_binary64_454
10×difference-of-squares_binary64_388 add-log-exp_binary64_458 distribute-lft-out--_binary64_371
8×sqrt-prod_binary64_435 associate-/r*_binary64_363
7×cancel-sign-sub-inv_binary64_385
6×associate-/r/_binary64_365
5×distribute-rgt-neg-in_binary64_377 flip3--_binary64_423 flip--_binary64_394
4×div-inv_binary64_416 pow1_binary64_480
3×diff-log_binary64_511
2×clear-num_binary64_418 sub-neg_binary64_412 frac-2neg_binary64_430
1×associate--l-_binary64_357 neg-log_binary64_512 associate-/l/_binary64_366 neg-sub0_binary64_414
Counts
4 → 122
Calls

8 calls:

25.0ms
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
16.0ms
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
11.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series894.0ms (0.4%)

Counts
4 → 72
Calls

4 calls:

302.0ms
(/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
257.0ms
(/.f64 (/.f64 (*.f64 (*.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 2 a))
176.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
159.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
Compiler

Compiled 2487 to 2008 computations (19.3% saved)

simplify166.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 0 (110.0ms)

IterNodesCost
049475531
149475531

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
000

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(/.f64 (*.f64 a c) b)
0.1b
(/.f64 (-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b) (*.f64 a 2))
0.1b
(+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))
0.0b
(+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))))
0.2b
(/.f64 (*.f64 a c) b)
0.4b
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
0.4b
(*.f64 (*.f64 a a) (*.f64 c c))
26.0b
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b)

rewrite59.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
70×add-exp-log_binary64_457
39×add-cbrt-cube_binary64_455
33×prod-exp_binary64_468
32×pow1_binary64_480
17×cbrt-unprod_binary64_452 div-exp_binary64_470
15×*-un-lft-identity_binary64_419 times-frac_binary64_425 add-sqr-sqrt_binary64_441 associate-/r*_binary64_363
14×pow-prod-down_binary64_490
13×add-cube-cbrt_binary64_454
9×add-log-exp_binary64_458
7×cbrt-undiv_binary64_453
6×unpow-prod-down_binary64_498 cube-prod_binary64_447
5×pow-exp_binary64_487 pow-to-exp_binary64_488
4×pow-plus_binary64_482 pow-prod-up_binary64_489
3×cancel-sign-sub-inv_binary64_385
2×clear-num_binary64_418 unpow3_binary64_485 cube-mult_binary64_449 div-inv_binary64_416 sqr-pow_binary64_391 frac-2neg_binary64_430 diff-log_binary64_511 pow-sqr_binary64_392 pow2_binary64_500 associate-/l*_binary64_364
1×associate--l+_binary64_356 sub-neg_binary64_412 difference-of-squares_binary64_388 associate-*r*_binary64_359 unswap-sqr_binary64_387 sum-log_binary64_510 flip3--_binary64_423 distribute-lft-out--_binary64_371 *-commutative_binary64_350 associate-*l*_binary64_360 flip--_binary64_394
Counts
4 → 123
Calls

8 calls:

15.0ms
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
10.0ms
(*.f64 (*.f64 a a) (*.f64 c c))
8.0ms
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b)
5.0ms
(/.f64 (*.f64 a c) b)
0.0ms
(+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3)))))

series938.0ms (0.4%)

Counts
4 → 42
Calls

4 calls:

503.0ms
(-.f64 (+.f64 b (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))))) b)
236.0ms
(/.f64 (*.f64 (*.f64 a a) (*.f64 c c)) (pow.f64 b 3))
117.0ms
(/.f64 (*.f64 a c) b)
82.0ms
(*.f64 (*.f64 a a) (*.f64 c c))
Compiler

Compiled 1893 to 1488 computations (21.4% saved)

simplify77.0ms (0%)

Algorithm
1×egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
054462567

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.6b
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
0.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))) (*.f64 2 a))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.6b
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
0.7b
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)
26.0b
(+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))))

rewrite42.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
14×*-un-lft-identity_binary64_419
12×cbrt-prod_binary64_450
10×add-log-exp_binary64_458 add-cube-cbrt_binary64_454 add-sqr-sqrt_binary64_441
6×unpow-prod-down_binary64_498 cube-prod_binary64_447
5×add-cbrt-cube_binary64_455 add-exp-log_binary64_457 pow1_binary64_480
4×cube-div_binary64_448
3×flip3--_binary64_423 pow-unpow_binary64_496 flip--_binary64_394
2×cbrt-div_binary64_451 unpow3_binary64_485 cube-mult_binary64_449 sqr-pow_binary64_391 sum-log_binary64_510 distribute-lft-out_binary64_370
1×flip3-+_binary64_422 pow1/3_binary64_501 sub-neg_binary64_412 rem-cube-cbrt_binary64_442 associate-+l-_binary64_354 distribute-rgt-neg-in_binary64_377 pow-exp_binary64_487 rem-cbrt-cube_binary64_443 pow-to-exp_binary64_488 flip-+_binary64_393 pow-pow_binary64_491 diff-log_binary64_511 cancel-sign-sub-inv_binary64_385 neg-log_binary64_512 +-commutative_binary64_349 neg-sub0_binary64_414
Counts
4 → 75
Calls

8 calls:

17.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))))
6.0ms
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
6.0ms
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)))

series757.0ms (0.4%)

Counts
4 → 80
Calls

4 calls:

220.0ms
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3)
181.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
181.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))))
174.0ms
(cbrt.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3))
Compiler

Compiled 2418 to 2116 computations (12.5% saved)

simplify101.0ms (0%)

Algorithm
1×egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
049913105
149913105

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.1b
(sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
0.0b
(-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))
0.3b
(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
0.3b
(*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.7b
(pow.f64 (*.f64 (*.f64 4 a) c) 3)
31.6b
(-.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) b)

rewrite94.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
57×add-sqr-sqrt_binary64_441
32×*-un-lft-identity_binary64_419
31×times-frac_binary64_425
27×difference-of-squares_binary64_388
22×add-cube-cbrt_binary64_454
21×sqr-pow_binary64_391
17×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
15×pow1_binary64_480
10×associate-/l*_binary64_364
9×unpow-prod-down_binary64_498
6×pow-prod-down_binary64_490 add-log-exp_binary64_458 prod-exp_binary64_468 cbrt-unprod_binary64_452
5×distribute-lft-out--_binary64_371
3×rem-cube-cbrt_binary64_442 associate-*r*_binary64_359 pow-exp_binary64_487 pow-pow_binary64_491 pow-unpow_binary64_496 cancel-sign-sub-inv_binary64_385 associate-/r*_binary64_363
2×flip3-+_binary64_422 flip3--_binary64_423 associate-*r/_binary64_361 associate-/r/_binary64_365 flip-+_binary64_393 flip--_binary64_394 sqrt-prod_binary64_435 associate-/l/_binary64_366
1×clear-num_binary64_418 sub-neg_binary64_412 distribute-rgt-in_binary64_369 unpow3_binary64_485 cube-mult_binary64_449 div-inv_binary64_416 pow-to-exp_binary64_488 distribute-lft-in_binary64_368 *-commutative_binary64_350 cube-prod_binary64_447 associate-*l*_binary64_360 frac-2neg_binary64_430 diff-log_binary64_511 div-exp_binary64_470 cbrt-undiv_binary64_453 div-sub_binary64_424
Counts
4 → 125
Calls

8 calls:

31.0ms
(-.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) b)
18.0ms
(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
10.0ms
(*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
6.0ms
(pow.f64 (*.f64 (*.f64 4 a) c) 3)
0.0ms
(-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3))

series1.6s (0.7%)

Counts
4 → 60
Calls

4 calls:

784.0ms
(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
328.0ms
(*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
316.0ms
(-.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (*.f64 (*.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (*.f64 4 (*.f64 (*.f64 a c) (+.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) b)
122.0ms
(pow.f64 (*.f64 (*.f64 4 a) c) 3)
Compiler

Compiled 2503 to 2069 computations (17.3% saved)

simplify140.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
052077280

prune10.9s (5.1%)

Pruning

259 alts after pruning (253 fresh and 6 done)

PrunedKeptTotal
New517182699
Fresh97180
Picked000
Done167
Total527259786
Error
0.0b
Counts
786 → 259
Compiler

Compiled 22327 to 14380 computations (35.6% saved)

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
0.1b
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
0.1b
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
0.2b
(*.f64 (*.f64 a 2) (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) a))
0.3b
(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) a)

rewrite127.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
330×times-frac_binary64_425
249×*-un-lft-identity_binary64_419 add-sqr-sqrt_binary64_441
149×add-cube-cbrt_binary64_454
85×associate-*r*_binary64_359
50×difference-of-squares_binary64_388 distribute-lft-out--_binary64_371
32×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
30×associate-/l*_binary64_364
25×distribute-rgt-neg-in_binary64_377 sqrt-prod_binary64_435
16×associate-/r/_binary64_365
10×div-inv_binary64_416 associate-/r*_binary64_363 div-exp_binary64_470 cbrt-undiv_binary64_453
9×prod-exp_binary64_468 cbrt-unprod_binary64_452 flip3--_binary64_423 flip--_binary64_394 pow1_binary64_480
6×add-log-exp_binary64_458
3×pow-prod-down_binary64_490
2×clear-num_binary64_418 frac-2neg_binary64_430
1×sub-neg_binary64_412 associate-*r/_binary64_361 *-commutative_binary64_350 associate-*l*_binary64_360 diff-log_binary64_511 cancel-sign-sub-inv_binary64_385 associate-/l/_binary64_366
Counts
4 → 292
Calls

8 calls:

36.0ms
(*.f64 (*.f64 a 2) (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) a))
20.0ms
(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) a)
12.0ms
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))

series954.0ms (0.4%)

Counts
4 → 72
Calls

4 calls:

283.0ms
(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) a)
255.0ms
(*.f64 (*.f64 a 2) (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))) a))
244.0ms
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
172.0ms
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
Compiler

Compiled 2432 to 1921 computations (21% saved)

simplify185.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
364 → 364
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
0498212804
1498212804

localize6.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
000

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(/.f64 (-.f64 (sqrt.f64 (log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b) (*.f64 a 2))
0.0b
(sqrt.f64 (log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.1b
(exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
8.1b
(-.f64 (sqrt.f64 (log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)
10.2b
(log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))

rewrite38.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64_441
11×add-log-exp_binary64_458
10×*-un-lft-identity_binary64_419
8×add-cube-cbrt_binary64_454
6×exp-prod_binary64_471 cancel-sign-sub-inv_binary64_385
5×log-prod_binary64_505 pow1_binary64_480
4×sub-neg_binary64_412 log-pow_binary64_508 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 exp-sum_binary64_465
3×diff-log_binary64_511
2×difference-of-squares_binary64_388 exp-diff_binary64_467 flip3--_binary64_423 flip--_binary64_394 rem-exp-log_binary64_459
1×rem-log-exp_binary64_460 distribute-lft-out--_binary64_371 sqrt-prod_binary64_435 log-div_binary64_506
Counts
4 → 62
Calls

8 calls:

10.0ms
(-.f64 (sqrt.f64 (log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)
6.0ms
(exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
6.0ms
(log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.0ms
(sqrt.f64 (log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

series1.2s (0.5%)

Counts
4 → 66
Calls

4 calls:

465.0ms
(log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
425.0ms
(-.f64 (sqrt.f64 (log.f64 (exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) b)
175.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
118.0ms
(exp.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 2016 to 1786 computations (11.4% saved)

simplify111.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (82.0ms)

IterNodesCost
049402313
149402313

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2))))) (*.f64 2 a))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.1b
(sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2))))
0.3b
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)
0.5b
(*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2))
0.6b
(cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)))
26.5b
(+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)))))

rewrite60.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
26×add-sqr-sqrt_binary64_441
21×unpow-prod-down_binary64_498
18×*-un-lft-identity_binary64_419
17×add-exp-log_binary64_457
14×add-cube-cbrt_binary64_454
11×sqr-pow_binary64_391
9×unswap-sqr_binary64_387 prod-exp_binary64_468
8×add-log-exp_binary64_458
7×associate-*r*_binary64_359 pow-exp_binary64_487 pow-to-exp_binary64_488 swap-sqr_binary64_386 associate-*l*_binary64_360
6×add-cbrt-cube_binary64_455
5×pow1_binary64_480
3×pow-unpow_binary64_496
2×sum-log_binary64_510 distribute-lft-out_binary64_370
1×flip3-+_binary64_422 pow-prod-down_binary64_490 pow1/3_binary64_501 associate-+l-_binary64_354 distribute-rgt-neg-in_binary64_377 cbrt-unprod_binary64_452 cbrt-prod_binary64_450 *-commutative_binary64_350 flip-+_binary64_393 pow-pow_binary64_491 pow-sqr_binary64_392 neg-log_binary64_512 pow-prod-up_binary64_489 +-commutative_binary64_349 pow2_binary64_500 neg-sub0_binary64_414
Counts
4 → 93
Calls

8 calls:

21.0ms
(*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2))
11.0ms
(cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)))
8.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)))))
6.0ms
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)
0.0ms
(sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2))))

series816.0ms (0.4%)

Counts
4 → 80
Calls

4 calls:

230.0ms
(*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2))
220.0ms
(pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)
184.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)))))
181.0ms
(cbrt.f64 (*.f64 (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2) (pow.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) 3/2)))
Compiler

Compiled 2891 to 2444 computations (15.5% saved)

simplify114.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
050544093

localize39.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a c) (*.f64 a c)) (pow.f64 b 3)))
0.1b
(+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a c) (*.f64 a c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4))
0.0b
(+.f64 (+.f64 (*.f64 -2 (+.f64 (/.f64 (*.f64 a c) b) (/.f64 (*.f64 (*.f64 a c) (*.f64 a c)) (pow.f64 b 3)))) (*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4)) (*.f64 (/.f64 (*.f64 (pow.f64 a 4) (pow.f64 c 4)) (pow.f64 b 7)) -10))
0.0b
(*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4)
0.4b
(/.f64 (*.f64 (*.f64 a c) (*.f64 a c)) (pow.f64 b 3))
0.4b
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
0.5b
(*.f64 (*.f64 a c) (*.f64 a c))
0.7b
(pow.f64 (*.f64 a c) 3)

rewrite76.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
88×add-exp-log_binary64_457
68×times-frac_binary64_425
46×pow1_binary64_480
42×unpow-prod-down_binary64_498
39×add-cbrt-cube_binary64_455
37×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 add-sqr-sqrt_binary64_441
36×prod-exp_binary64_468
27×div-exp_binary64_470
20×sqr-pow_binary64_391
19×associate-/r*_binary64_363
18×pow-prod-down_binary64_490
17×cbrt-unprod_binary64_452 pow-exp_binary64_487
15×cube-prod_binary64_447
13×pow-to-exp_binary64_488
11×unpow3_binary64_485 cube-mult_binary64_449
9×associate-/l*_binary64_364
6×cbrt-undiv_binary64_453
4×add-log-exp_binary64_458 pow-sqr_binary64_392 pow-prod-up_binary64_489
3×pow-unpow_binary64_496
2×clear-num_binary64_418 div-inv_binary64_416 rem-cube-cbrt_binary64_442 pow-plus_binary64_482 frac-2neg_binary64_430 pow-pow_binary64_491
1×associate-*r*_binary64_359 *-commutative_binary64_350 swap-sqr_binary64_386 associate-*l*_binary64_360 pow2_binary64_500
Counts
4 → 205
Calls

8 calls:

13.0ms
(/.f64 (*.f64 (*.f64 a c) (*.f64 a c)) (pow.f64 b 3))
8.0ms
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
8.0ms
(*.f64 (*.f64 a c) (*.f64 a c))
5.0ms
(pow.f64 (*.f64 a c) 3)
0.0ms
(*.f64 (/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5)) -4)

series771.0ms (0.4%)

Counts
4 → 30
Calls

4 calls:

339.0ms
(/.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 b 5))
240.0ms
(/.f64 (*.f64 (*.f64 a c) (*.f64 a c)) (pow.f64 b 3))
97.0ms
(pow.f64 (*.f64 a c) 3)
94.0ms
(*.f64 (*.f64 a c) (*.f64 a c))
Compiler

Compiled 3000 to 2250 computations (25% saved)

simplify122.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
051323471

prune28.8s (13.3%)

Pruning

469 alts after pruning (460 fresh and 9 done)

PrunedKeptTotal
New670230900
Fresh18230248
Picked000
Done2911
Total6904691159
Error
0b
Counts
1159 → 469
Compiler

Compiled 36851 to 23298 computations (36.8% saved)

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
0.1b
(sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
0.0b
(-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a))))
0.2b
(*.f64 (*.f64 a 2) (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a))
0.3b
(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a)
0.5b
(*.f64 (*.f64 c a) (*.f64 c a))
0.5b
(/.f64 (-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))

rewrite181.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
378×times-frac_binary64_425
305×add-sqr-sqrt_binary64_441
242×*-un-lft-identity_binary64_419
158×add-cube-cbrt_binary64_454
95×associate-*r*_binary64_359
63×difference-of-squares_binary64_388
48×pow1_binary64_480
44×add-cbrt-cube_binary64_455 add-exp-log_binary64_457
42×distribute-lft-out--_binary64_371 sqrt-prod_binary64_435
33×associate-/l*_binary64_364
21×distribute-rgt-neg-in_binary64_377
20×pow-prod-down_binary64_490
17×prod-exp_binary64_468 cbrt-unprod_binary64_452
16×associate-/r/_binary64_365
10×div-inv_binary64_416 div-exp_binary64_470 cbrt-undiv_binary64_453
8×flip3--_binary64_423 flip--_binary64_394
6×associate-/r*_binary64_363
4×add-log-exp_binary64_458 pow-sqr_binary64_392 pow-prod-up_binary64_489
3×associate-/l/_binary64_366
2×clear-num_binary64_418 pow-plus_binary64_482 *-commutative_binary64_350 associate-*l*_binary64_360 frac-2neg_binary64_430
1×flip3-+_binary64_422 associate-*r/_binary64_361 swap-sqr_binary64_386 flip-+_binary64_393 pow2_binary64_500 div-sub_binary64_424
Counts
4 → 322
Calls

8 calls:

48.0ms
(*.f64 (*.f64 a 2) (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a))
36.0ms
(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a)
13.0ms
(/.f64 (-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
8.0ms
(*.f64 (*.f64 c a) (*.f64 c a))
0.0ms
(-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a))))

series1.3s (0.6%)

Counts
4 → 60
Calls

4 calls:

480.0ms
(/.f64 (-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
369.0ms
(/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a)
328.0ms
(*.f64 (*.f64 a 2) (/.f64 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (*.f64 16 (*.f64 (*.f64 c a) (*.f64 c a)))) (+.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))) a))
85.0ms
(*.f64 (*.f64 c a) (*.f64 c a))
Compiler

Compiled 2165 to 1715 computations (20.8% saved)

simplify280.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
382 → 382
Iterations

Useful iterations: 0 (119.0ms)

IterNodesCost
0496519971
1496519971

localize6.0ms (0%)

rewrite0.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms (0%)

Counts
0 → 0

simplify9.0ms (0%)

Algorithm
1×egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
000

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(/.f64 a (/.f64 (sqrt.f64 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
0.1b
(-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))
0.1b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
0.2b
(/.f64 a (/.f64 (sqrt.f64 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
0.2b
(*.f64 (*.f64 a 2) (/.f64 (/.f64 (sqrt.f64 c) 1) (/.f64 a (/.f64 (sqrt.f64 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))))
0.3b
(/.f64 (sqrt.f64 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
0.3b
(/.f64 (/.f64 (sqrt.f64 c) 1) (/.f64 a (/.f64 (sqrt.f64 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))))

rewrite3.7s (1.7%)

Algorithm
1×rewrite-expression-head
Rules
24442×times-frac_binary64_425
12452×*-un-lft-identity_binary64_419 add-sqr-sqrt_binary64_441
9088×add-cube-cbrt_binary64_454
6475×sqrt-prod_binary64_435
3283×associate-*r*_binary64_359
1682×difference-of-squares_binary64_388 distribute-lft-out--_binary64_371
841×distribute-rgt-neg-in_binary64_377
487×div-inv_binary64_416
328×associate-/r/_binary64_365
204×associate-/r*_binary64_363
140×flip3--_binary64_423 flip--_binary64_394
133×add-exp-log_binary64_457
97×add-cbrt-cube_binary64_455
76×div-exp_binary64_470
49×cbrt-undiv_binary64_453
31×associate-/l*_binary64_364
30×prod-exp_binary64_468
21×cbrt-unprod_binary64_452
9×1-exp_binary64_463 pow1_binary64_480
4×add-log-exp_binary64_458
3×pow-prod-down_binary64_490 clear-num_binary64_418 frac-2neg_binary64_430
1×associate-*r/_binary64_361 *-commutative_binary64_350 associate-*l*_binary64_360 associate-/l/_binary64_366
Counts
4 → 1000
Calls

8 calls:

709.0ms
(*.f64 (*.f64 a 2) (/.f64 (/.f64 (sqrt.f64 c) 1) (/.f64 a (/.f64 (sqrt.f64 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))))
135.0ms
(/.f64 (/.f64 (sqrt.f64 c) 1) (/.f64 a (/.f64 (sqrt.f64 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))))
23.0ms
(/.f64 a (/.f64 (sqrt.f64 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
14.0ms
(/.f64 (sqrt.f64 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))

series1.2s (0.5%)

Counts
4 → 66
Calls

4 calls:

312.0ms
(/.f64 (/.f64 (sqrt.f64 c) 1) (/.f64 a (/.f64 (sqrt.f64 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))))
299.0ms
(/.f64 (sqrt.f64 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
285.0ms
(/.f64 a (/.f64 (sqrt.f64 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))
266.0ms
(*.f64 (*.f64 a 2) (/.f64 (/.f64 (sqrt.f64 c) 1) (/.f64 a (/.f64 (sqrt.f64 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))))))
Compiler

Compiled 2899 to 2265 computations (21.9% saved)

simplify716.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
1066 → 1066
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
0512082634

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
0.1b
(/.f64 (-.f64 (sqrt.f64 (log.f64 (exp.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) b) (*.f64 a 2))
0.0b
(sqrt.f64 (log.f64 (exp.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))
0.1b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.2b
(*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
8.1b
(-.f64 (sqrt.f64 (log.f64 (exp.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) b)
10.2b
(log.f64 (exp.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

rewrite53.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
32×add-sqr-sqrt_binary64_441
20×pow1_binary64_480
19×sqrt-prod_binary64_435
16×*-un-lft-identity_binary64_419
14×add-cube-cbrt_binary64_454
12×sqrt-div_binary64_436
9×add-log-exp_binary64_458
8×pow1/2_binary64_499 flip3--_binary64_423 swap-sqr_binary64_386 sqrt-pow1_binary64_437 flip--_binary64_394
6×associate-*r*_binary64_359 associate-*l*_binary64_360 add-cbrt-cube_binary64_455 add-exp-log_binary64_457
5×pow-prod-up_binary64_489
4×unswap-sqr_binary64_387 frac-times_binary64_429 cancel-sign-sub-inv_binary64_385
3×pow-prod-down_binary64_490 log-prod_binary64_505 log-pow_binary64_508 pow-sqr_binary64_392
2×associate-*l/_binary64_362 sub-neg_binary64_412 difference-of-squares_binary64_388 associate-*r/_binary64_361 diff-log_binary64_511 rem-sqrt-square_binary64_432
1×sqrt-unprod_binary64_439 rem-square-sqrt_binary64_431 rem-log-exp_binary64_460 exp-to-pow_binary64_481 sqr-abs_binary64_434 prod-exp_binary64_468 cbrt-unprod_binary64_452 exp-prod_binary64_471 distribute-lft-out--_binary64_371 pow-plus_binary64_482 *-commutative_binary64_350 pow2_binary64_500
Counts
4 → 101
Calls

8 calls:

16.0ms
(*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
7.0ms
(-.f64 (sqrt.f64 (log.f64 (exp.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) b)
5.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
2.0ms
(log.f64 (exp.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
0.0ms
(sqrt.f64 (log.f64 (exp.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))))

series1.3s (0.6%)

Counts
4 → 66
Calls

4 calls:

490.0ms
(log.f64 (exp.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
463.0ms
(-.f64 (sqrt.f64 (log.f64 (exp.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))) b)
194.0ms
(*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
188.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
Compiler

Compiled 2176 to 1885 computations (13.4% saved)

simplify121.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 0 (81.0ms)

IterNodesCost
048972982
148972982

localize34.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(-.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))) 3))
0.1b
(*.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a)))))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
0.1b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))
0.6b
(cbrt.f64 a)
0.6b
(cbrt.f64 a)
0.6b
(cbrt.f64 a)
26.1b
(-.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))) (*.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))

rewrite25.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
9×add-log-exp_binary64_458 cbrt-prod_binary64_450
8×add-sqr-sqrt_binary64_441
7×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454
5×flip3--_binary64_423 flip--_binary64_394
4×sqrt-div_binary64_436 associate-*r/_binary64_361 add-cbrt-cube_binary64_455 add-exp-log_binary64_457 pow1_binary64_480 frac-sub_binary64_428
3×pow1/3_binary64_501 diff-log_binary64_511
2×associate--l+_binary64_356 sub-neg_binary64_412 cancel-sign-sub-inv_binary64_385
1×distribute-rgt-out--_binary64_373 associate--l-_binary64_357
Counts
4 → 54
Calls

8 calls:

11.0ms
(-.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))) (*.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
1.0ms
(cbrt.f64 a)
1.0ms
(cbrt.f64 a)
1.0ms
(cbrt.f64 a)
0.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))

series567.0ms (0.3%)

Counts
4 → 27
Calls

4 calls:

268.0ms
(-.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))) (*.f64 b (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 c (*.f64 4 a))))))
101.0ms
(cbrt.f64 a)
99.0ms
(cbrt.f64 a)
99.0ms
(cbrt.f64 a)
Compiler

Compiled 2427 to 1625 computations (33% saved)

simplify138.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 0 (111.0ms)

IterNodesCost
050041848

prune1.2min (32.2%)

Pruning

838 alts after pruning (825 fresh and 13 done)

PrunedKeptTotal
New12914051696
Fresh35420455
Picked000
Done11314
Total13278382165
Error
0b
Counts
2165 → 838
Compiler

Compiled 36941 to 17426 computations (52.8% saved)

simplify1.9s (0.9%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0641499460

regimes24.7s (11.5%)

Compiler

Compiled 254444 to 167576 computations (34.1% saved)

bsearch0.0ms (0%)

regimes530.0ms (0.2%)

Compiler

Compiled 4413 to 3684 computations (16.5% saved)

bsearch0.0ms (0%)

regimes160.0ms (0.1%)

Compiler

Compiled 1131 to 969 computations (14.3% saved)

bsearch0.0ms (0%)

regimes97.0ms (0%)

Compiler

Compiled 498 to 504 computations (-1.2% saved)

bsearch0.0ms (0%)

regimes28.0ms (0%)

Accuracy

Total 0.2b remaining (100%)

Threshold costs 0.2b (100%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch5.0ms (0%)

Compiler

Compiled 59 to 51 computations (13.6% saved)

simplify6.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
014188
114188

end0.0ms (0%)

sample55.8s (25.9%)

Algorithm
1×intervals
Results
405.0ms3791×body256valid
291.0ms8832×pre128true
222.0ms1434×body512valid
154.0ms2775×body128valid
42.0ms832×body128nan
Compiler

Compiled 63726 to 41990 computations (34.1% saved)

Pareto

0.8673567854140873

Profiling

Loading profile data...