Details

Time bar (total: 2.5min)

analyze1.5s (1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
1.7%98%0.3%13
2.5%97.2%0.3%14
Compiler

Compiled 22 to 20 computations (9.1% saved)

sample42.0ms (0%)

Algorithm
1×intervals
Results
14.0ms256×body128valid
8.0ms153×body128invalid
Compiler

Compiled 43 to 45 computations (-4.7% saved)

simplify272.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (107.0ms)

IterNodesCost
0517731

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1
Compiler

Compiled 42 to 38 computations (9.5% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (-.f64 t 1) a)
0.0b
(-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))
0.0b
(*.f64 (-.f64 (+.f64 y t) 2) b)
0.0b
(+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))

rewrite56.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
28×associate-*l/_binary64_366
23×flip3--_binary64_427 flip--_binary64_398
18×add-sqr-sqrt_binary64_445 add-log-exp_binary64_462
16×*-un-lft-identity_binary64_423
13×associate-*l*_binary64_364
12×frac-add_binary64_431 frac-sub_binary64_432
8×add-cube-cbrt_binary64_458 pow1_binary64_484 add-exp-log_binary64_461 add-cbrt-cube_binary64_459
6×diff-log_binary64_515 associate-*r*_binary64_363
4×associate--l+_binary64_360 sub-neg_binary64_416 associate-+l+_binary64_356 cancel-sign-sub-inv_binary64_389
3×distribute-lft-out--_binary64_375 difference-of-squares_binary64_392 sum-log_binary64_514
2×pow-prod-down_binary64_494 prod-exp_binary64_472 *-commutative_binary64_354 unswap-sqr_binary64_391 cbrt-unprod_binary64_456
1×flip-+_binary64_397 associate-+l-_binary64_358 associate--l-_binary64_361 +-commutative_binary64_353 distribute-lft-out_binary64_374 flip3-+_binary64_426 difference-of-sqr-1_binary64_393
Counts
4 → 97
Calls

4 calls:

16.0ms
(+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))
10.0ms
(*.f64 (-.f64 (+.f64 y t) 2) b)
9.0ms
(-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))
8.0ms
(*.f64 (-.f64 t 1) a)

series547.0ms (0.4%)

Counts
4 → 12
Calls

4 calls:

317.0ms
(+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))
147.0ms
(-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))
48.0ms
(*.f64 (-.f64 (+.f64 y t) 2) b)
36.0ms
(*.f64 (-.f64 t 1) a)

simplify81.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
051824023

prune209.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1063109
Fresh000
Picked101
Done000
Total1073110

Merged error: 0.0b

Counts
110 → 3
Compiler

Compiled 4936 to 3050 computations (38.2% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (+.f64 (*.f64 (-.f64 y 1) z) (*.f64 (-.f64 t 1) a)))
0.0b
(*.f64 (-.f64 t 1) a)
0.0b
(*.f64 (-.f64 (+.f64 y t) 2) b)
0.0b
(+.f64 x (-.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (+.f64 (*.f64 (-.f64 y 1) z) (*.f64 (-.f64 t 1) a))))

rewrite71.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
32×associate-*l/_binary64_366
20×*-un-lft-identity_binary64_423 add-sqr-sqrt_binary64_445
18×add-log-exp_binary64_462
17×flip3--_binary64_427 flip--_binary64_398
13×associate-*l*_binary64_364
12×frac-sub_binary64_432
10×add-cube-cbrt_binary64_458
8×frac-add_binary64_431 pow1_binary64_484 add-exp-log_binary64_461 add-cbrt-cube_binary64_459
6×cancel-sign-sub-inv_binary64_389 associate-*r*_binary64_363
5×sum-log_binary64_514
4×associate-+r+_binary64_355 diff-log_binary64_515
3×flip-+_binary64_397 distribute-lft-out--_binary64_375 flip3-+_binary64_426 difference-of-squares_binary64_392
2×pow-prod-down_binary64_494 sub-neg_binary64_416 prod-exp_binary64_472 distribute-lft-out_binary64_374 *-commutative_binary64_354 unswap-sqr_binary64_391 cbrt-unprod_binary64_456
1×associate--r+_binary64_359 +-commutative_binary64_353 associate-+r-_binary64_357 difference-of-sqr-1_binary64_393
Counts
4 → 94
Calls

4 calls:

20.0ms
(+.f64 x (-.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (+.f64 (*.f64 (-.f64 y 1) z) (*.f64 (-.f64 t 1) a))))
19.0ms
(-.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (+.f64 (*.f64 (-.f64 y 1) z) (*.f64 (-.f64 t 1) a)))
10.0ms
(*.f64 (-.f64 (+.f64 y t) 2) b)
8.0ms
(*.f64 (-.f64 t 1) a)

series617.0ms (0.4%)

Counts
4 → 12
Calls

4 calls:

327.0ms
(+.f64 x (-.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (+.f64 (*.f64 (-.f64 y 1) z) (*.f64 (-.f64 t 1) a))))
207.0ms
(-.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (+.f64 (*.f64 (-.f64 y 1) z) (*.f64 (-.f64 t 1) a)))
48.0ms
(*.f64 (-.f64 (+.f64 y t) 2) b)
35.0ms
(*.f64 (-.f64 t 1) a)

simplify79.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049443446
149443446

prune174.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1060106
Fresh022
Picked011
Done000
Total1063109

Merged error: 0.0b

Counts
109 → 3
Compiler

Compiled 4221 to 2563 computations (39.3% saved)

localize25.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)))
0.2b
(*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b))
9.6b
(-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b)))
41.8b
(/.f64 (-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b))) (-.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b)))

rewrite898.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
2432×associate-*l/_binary64_366
1791×flip3--_binary64_427 flip--_binary64_398
1740×frac-sub_binary64_432
1000×frac-times_binary64_433
386×associate-/l/_binary64_370
296×associate-*r/_binary64_365
50×pow1_binary64_484
20×add-exp-log_binary64_461 add-cbrt-cube_binary64_459
19×add-sqr-sqrt_binary64_445
18×pow-prod-down_binary64_494
17×*-un-lft-identity_binary64_423 add-cube-cbrt_binary64_458
16×associate--l+_binary64_360
14×associate-/r/_binary64_369
12×times-frac_binary64_429
9×sub-neg_binary64_416 cancel-sign-sub-inv_binary64_389 prod-exp_binary64_472 cbrt-unprod_binary64_456
8×distribute-rgt-in_binary64_373 distribute-lft-in_binary64_372
6×add-log-exp_binary64_462
5×pow-sqr_binary64_396 pow-prod-up_binary64_493 difference-of-squares_binary64_392
4×associate-*l*_binary64_364 swap-sqr_binary64_390 associate-*r*_binary64_363 associate-/l*_binary64_368
3×pow-plus_binary64_486 associate-/r*_binary64_367
2×*-commutative_binary64_354 pow2_binary64_504
1×diff-log_binary64_515 div-sub_binary64_428 clear-num_binary64_422 frac-2neg_binary64_434 div-inv_binary64_420 unswap-sqr_binary64_391 cbrt-undiv_binary64_457 div-exp_binary64_474
Counts
4 → 960
Calls

4 calls:

107.0ms
(/.f64 (-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b))) (-.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b)))
53.0ms
(-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b)))
24.0ms
(*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b))
20.0ms
(*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)))

series9.7s (6.5%)

Counts
4 → 12
Calls

4 calls:

5.6s
(/.f64 (-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b))) (-.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b)))
3.4s
(-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b)))
685.0ms
(*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)))
77.0ms
(*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b))

simplify1.4s (0.9%)

Algorithm
1×egg-herbie
Counts
972 → 972
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
05071169752

prune28.7s (19.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New9711972
Fresh011
Picked101
Done011
Total9723975

Merged error: 0.0b

Counts
975 → 3
Compiler

Compiled 192490 to 111312 computations (42.2% saved)

localize40.0ms (0%)

Local error

Found 4 expressions with local error:

9.6b
(-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b)))
9.6b
(-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b)))
30.0b
(sqrt.f64 (-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b))))
30.0b
(sqrt.f64 (-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b))))

rewrite2.1s (1.4%)

Algorithm
1×rewrite-expression-head
Rules
4672×associate-*l/_binary64_366
3396×flip3--_binary64_427 flip--_binary64_398
3328×frac-sub_binary64_432
1920×frac-times_binary64_433
772×sqrt-div_binary64_440
576×associate-*r/_binary64_365
24×associate--l+_binary64_360
10×sub-neg_binary64_416 cancel-sign-sub-inv_binary64_389
8×distribute-rgt-in_binary64_373 distribute-lft-in_binary64_372 sqrt-prod_binary64_439 add-sqr-sqrt_binary64_445 add-log-exp_binary64_462
6×*-un-lft-identity_binary64_423 add-cube-cbrt_binary64_458 pow1_binary64_484
4×add-exp-log_binary64_461 difference-of-squares_binary64_392 add-cbrt-cube_binary64_459
2×diff-log_binary64_515 rem-sqrt-square_binary64_436 pow1/2_binary64_503 sqrt-pow1_binary64_441
Counts
4 → 1610
Calls

4 calls:

79.0ms
(sqrt.f64 (-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b))))
78.0ms
(sqrt.f64 (-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b))))
57.0ms
(-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b)))
53.0ms
(-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b)))

series1.7min (67.3%)

Counts
4 → 12
Calls

4 calls:

47.2s
(sqrt.f64 (-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b))))
46.9s
(sqrt.f64 (-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b))))
3.5s
(-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b)))
3.4s
(-.f64 (*.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a))) (*.f64 (*.f64 (-.f64 (+.f64 y t) 2) b) (*.f64 (-.f64 (+.f64 y t) 2) b)))

simplify2.5s (1.7%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (88.0ms)

IterNodesCost
05108445370

Profiling

Loading profile data...