Details

Time bar (total: 7.8s)

analyze4.0ms (0.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%100%0%3
75%25%0%4
87.5%12.5%0%5
93.7%6.2%0%6
96.8%3.1%0%7
98.4%1.6%0%8
99.2%0.8%0%9
99.6%0.4%0%10
99.8%0.2%0%11
99.9%0.1%0%12
99.9%0%0%13
99.9%0%0%14
Compiler

Compiled 14 to 11 computations (21.4% saved)

sample27.0ms (0.3%)

Algorithm
intervals
Results
8.0ms65×body1024valid
5.0ms148×body128valid
4.0ms12×body256valid
2.0ms27×body512valid
1.0msbody2048valid
Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify172.0ms (2.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
068119
168119

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
27.0b
Counts
2 → 1
Compiler

Compiled 26 to 20 computations (23.1% saved)

localize7.0ms (0.1%)

Local error

Found 6 expressions with local error:

2.4b
(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
0.0b
(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b
(/.f64 x (+.f64 x 1))
0.0b
(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b
(/.f64 x (+.f64 x 1))
2.4b
(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite73.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
148×*-un-lft-identity_binary64_3488
88×times-frac_binary64_3494
85×add-sqr-sqrt_binary64_3510
37×add-cube-cbrt_binary64_3523
34×cancel-sign-sub-inv_binary64_3454
27×distribute-lft-out_binary64_3439
22×difference-of-squares_binary64_3457 distribute-lft-out--_binary64_3440
11×associate-/r*_binary64_3432
difference-of-sqr-1_binary64_3458
add-cbrt-cube_binary64_3524 add-exp-log_binary64_3526 associate-/l*_binary64_3433
associate-/r/_binary64_3434
add-log-exp_binary64_3527
flip3--_binary64_3492 flip--_binary64_3463 pow1_binary64_3549 div-inv_binary64_3485
clear-num_binary64_3487 associate-/l/_binary64_3435 flip-+_binary64_3462 flip3-+_binary64_3491 frac-2neg_binary64_3499 div-exp_binary64_3539 cbrt-undiv_binary64_3522
diff-log_binary64_3580 frac-sub_binary64_3497 sub-neg_binary64_3481
Counts
3 → 147
Calls

6 calls:

45.0ms
(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms
(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms
(/.f64 x (+.f64 x 1))
0.0ms
(/.f64 x (+.f64 x 1))
0.0ms
(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series124.0ms (1.6%)

Counts
3 → 32
Calls

3 calls:

64.0ms
(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
32.0ms
(/.f64 (+.f64 x 1) (-.f64 x 1))
28.0ms
(/.f64 x (+.f64 x 1))
Compiler

Compiled 524 to 451 computations (13.9% saved)

simplify84.0ms (1.1%)

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
055723013

prune491.0ms (6.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1727179
Fresh000
Picked101
Done000
Total1737180
Error
0.0b
Counts
180 → 7
Compiler

Compiled 3446 to 2436 computations (29.3% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b
(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b
(/.f64 x (+.f64 x 1))
0.0b
(/.f64 x (+.f64 x 1))
0.0b
(/.f64 x (+.f64 x 1))
0.0b
(/.f64 (-.f64 (*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
0.0b
(*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0b
(*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.4b
(-.f64 (*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))

rewrite214.0ms (2.7%)

Algorithm
rewrite-expression-head
Rules
636×*-un-lft-identity_binary64_3488
384×times-frac_binary64_3494
246×add-sqr-sqrt_binary64_3510
161×distribute-lft-out_binary64_3439
118×add-cube-cbrt_binary64_3523
96×swap-sqr_binary64_3455
66×difference-of-squares_binary64_3457
52×distribute-lft-out--_binary64_3440 associate-*l*_binary64_3429 associate-*r*_binary64_3428
32×difference-of-sqr-1_binary64_3458
30×add-cbrt-cube_binary64_3524 add-exp-log_binary64_3526
19×associate-/r/_binary64_3434
18×frac-sub_binary64_3497 pow1_binary64_3549
14×associate-*l/_binary64_3431 frac-times_binary64_3498 associate-*r/_binary64_3430
12×associate-/r*_binary64_3432
11×associate-/l/_binary64_3435
div-exp_binary64_3539 cbrt-undiv_binary64_3522 div-inv_binary64_3485
unswap-sqr_binary64_3456 cbrt-unprod_binary64_3521 prod-exp_binary64_3537
flip3--_binary64_3492 add-log-exp_binary64_3527 flip--_binary64_3463
flip-+_binary64_3462 flip3-+_binary64_3491
associate-/l*_binary64_3433
pow-prod-up_binary64_3558 pow2_binary64_3569 pow-prod-down_binary64_3559 pow-plus_binary64_3551 *-commutative_binary64_3419 pow-sqr_binary64_3461
clear-num_binary64_3487 frac-add_binary64_3496 diff-log_binary64_3580 cancel-sign-sub-inv_binary64_3454 frac-2neg_binary64_3499 div-sub_binary64_3493 sub-neg_binary64_3481
Counts
4 → 369
Calls

8 calls:

60.0ms
(/.f64 (-.f64 (*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
42.0ms
(*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
19.0ms
(*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
14.0ms
(-.f64 (*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
0.0ms
(/.f64 x (+.f64 x 1))

series298.0ms (3.8%)

Counts
4 → 43
Calls

4 calls:

121.0ms
(/.f64 (-.f64 (*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))) (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
86.0ms
(-.f64 (*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1))) (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
50.0ms
(*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
41.0ms
(*.f64 (/.f64 x (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
Compiler

Compiled 1382 to 1109 computations (19.8% saved)

simplify176.0ms (2.2%)

Algorithm
egg-herbie
Counts
412 → 412
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0497213488
1497213488

prune1.6s (20.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4093412
Fresh246
Picked011
Done000
Total4118419
Error
0.0b
Counts
419 → 8
Compiler

Compiled 19366 to 14015 computations (27.6% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
0.1b
(/.f64 (-.f64 x 1) (cbrt.f64 (+.f64 x 1)))
0.0b
(/.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (/.f64 (-.f64 x 1) (cbrt.f64 (+.f64 x 1))))
0.0b
(/.f64 x (+.f64 x 1))
0.3b
(cbrt.f64 (+.f64 x 1))
0.3b
(cbrt.f64 (+.f64 x 1))
0.3b
(cbrt.f64 (+.f64 x 1))
18.7b
(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (/.f64 (-.f64 x 1) (cbrt.f64 (+.f64 x 1)))))

rewrite95.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
118×times-frac_binary64_3494
82×add-sqr-sqrt_binary64_3510
73×*-un-lft-identity_binary64_3488
60×cancel-sign-sub-inv_binary64_3454
42×cbrt-prod_binary64_3519
30×add-cube-cbrt_binary64_3523
22×difference-of-squares_binary64_3457
10×distribute-lft-out_binary64_3439
distribute-lft-out--_binary64_3440 cbrt-div_binary64_3520
difference-of-sqr-1_binary64_3458
add-log-exp_binary64_3527
add-cbrt-cube_binary64_3524 add-exp-log_binary64_3526 flip-+_binary64_3462 flip3-+_binary64_3491 pow1_binary64_3549
associate-/r/_binary64_3434 pow1/3_binary64_3570
div-inv_binary64_3485
flip3--_binary64_3492 diff-log_binary64_3580 flip--_binary64_3463 frac-sub_binary64_3497 sub-neg_binary64_3481
Counts
4 → 123
Calls

8 calls:

69.0ms
(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (/.f64 (-.f64 x 1) (cbrt.f64 (+.f64 x 1)))))
3.0ms
(cbrt.f64 (+.f64 x 1))
3.0ms
(cbrt.f64 (+.f64 x 1))
3.0ms
(cbrt.f64 (+.f64 x 1))
0.0ms
(/.f64 x (+.f64 x 1))

series218.0ms (2.8%)

Counts
4 → 35
Calls

4 calls:

70.0ms
(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (/.f64 (-.f64 x 1) (cbrt.f64 (+.f64 x 1)))))
51.0ms
(cbrt.f64 (+.f64 x 1))
50.0ms
(cbrt.f64 (+.f64 x 1))
47.0ms
(cbrt.f64 (+.f64 x 1))
Compiler

Compiled 1175 to 981 computations (16.5% saved)

simplify98.0ms (1.2%)

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
050764388

prune274.0ms (3.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1580158
Fresh066
Picked011
Done011
Total1588166
Error
0.0b
Counts
166 → 8
Compiler

Compiled 4853 to 3645 computations (24.9% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

4.4b
(/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))
0.0b
(/.f64 x (+.f64 x 1))
0.0b
(+.f64 (+.f64 x 1) (*.f64 x x))
0.0b
(+.f64 -1 (pow.f64 x 3))
0.0b
(/.f64 x (+.f64 x 1))
4.4b
(/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))
8.2b
(+.f64 (/.f64 x (+.f64 x 1)) (*.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (+.f64 x 1) (*.f64 x x))))
16.5b
(*.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (+.f64 x 1) (*.f64 x x)))

rewrite72.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity_binary64_3488
58×add-sqr-sqrt_binary64_3510
53×times-frac_binary64_3494
35×add-cube-cbrt_binary64_3523
26×associate-*l*_binary64_3429
15×distribute-lft-out_binary64_3439
13×add-cbrt-cube_binary64_3524 add-exp-log_binary64_3526
difference-of-squares_binary64_3457 distribute-lft-out--_binary64_3440
associate-/r*_binary64_3432 flip-+_binary64_3462 flip3-+_binary64_3491 associate-/l*_binary64_3433
associate-/r/_binary64_3434 add-log-exp_binary64_3527 pow1_binary64_3549
frac-add_binary64_3496
frac-times_binary64_3498 associate-*r/_binary64_3430
associate-*r*_binary64_3428 div-exp_binary64_3539 cbrt-undiv_binary64_3522 div-inv_binary64_3485
distribute-lft-in_binary64_3437 associate-*l/_binary64_3431 clear-num_binary64_3487 distribute-rgt-in_binary64_3438 unswap-sqr_binary64_3456 associate-/l/_binary64_3435 cbrt-unprod_binary64_3521 associate-+r+_binary64_3420 frac-2neg_binary64_3499 prod-exp_binary64_3537
flip3--_binary64_3492 +-commutative_binary64_3418 pow-prod-down_binary64_3559 flip--_binary64_3463 *-commutative_binary64_3419 sum-log_binary64_3579 div-sub_binary64_3493
Counts
4 → 148
Calls

8 calls:

22.0ms
(*.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (+.f64 x 1) (*.f64 x x)))
14.0ms
(+.f64 (/.f64 x (+.f64 x 1)) (*.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (+.f64 x 1) (*.f64 x x))))
14.0ms
(/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))
5.0ms
(/.f64 x (+.f64 x 1))
0.0ms
(+.f64 -1 (pow.f64 x 3))

series220.0ms (2.8%)

Counts
4 → 42
Calls

4 calls:

91.0ms
(+.f64 (/.f64 x (+.f64 x 1)) (*.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (+.f64 x 1) (*.f64 x x))))
47.0ms
(/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3)))
47.0ms
(*.f64 (/.f64 (-.f64 -1 x) (+.f64 -1 (pow.f64 x 3))) (+.f64 (+.f64 x 1) (*.f64 x x)))
33.0ms
(/.f64 x (+.f64 x 1))
Compiler

Compiled 920 to 747 computations (18.8% saved)

simplify96.0ms (1.2%)

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
050094453

prune327.0ms (4.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1891190
Fresh145
Picked101
Done022
Total1917198
Error
0.0b
Counts
198 → 7
Compiler

Compiled 5689 to 3885 computations (31.7% saved)

simplify30.0ms (0.4%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (9.0ms)

IterNodesCost
06761715
16761715

regimes242.0ms (3.1%)

Compiler

Compiled 2453 to 1880 computations (23.4% saved)

bsearch48.0ms (0.6%)

Steps
ItersRangePoint
8
44.79751205509612
87417.7786515175
1977.3153917547227
8
-315734.20136470115
-73.04333385933747
-10487.592747220726
Compiler

Compiled 1 to 1 computations (0% saved)

regimes138.0ms (1.8%)

Compiler

Compiled 1132 to 879 computations (22.3% saved)

bsearch38.0ms (0.5%)

Steps
ItersRangePoint
8
44.79751205509612
87417.7786515175
13635.28794537155
8
-315734.20136470115
-73.04333385933747
-10487.592747220726
Compiler

Compiled 1 to 1 computations (0% saved)

regimes81.0ms (1%)

Compiler

Compiled 482 to 382 computations (20.7% saved)

bsearch30.0ms (0.4%)

Steps
ItersRangePoint
9
87417.7786515175
7196754274351.372
540498.6414826551
6
-4900916.382688271
-387457.089668734
-515943.379764342
Compiler

Compiled 1 to 1 computations (0% saved)

regimes71.0ms (0.9%)

Compiler

Compiled 354 to 288 computations (18.6% saved)

bsearch28.0ms (0.4%)

Steps
ItersRangePoint
9
87417.7786515175
7196754274351.372
303456.6825641965
6
-4900916.382688271
-387457.089668734
-515943.379764342
Compiler

Compiled 1 to 1 computations (0% saved)

regimes69.0ms (0.9%)

Compiler

Compiled 316 to 260 computations (17.7% saved)

bsearch28.0ms (0.4%)

Steps
ItersRangePoint
9
87417.7786515175
7196754274351.372
303456.6825641965
6
-4900916.382688271
-387457.089668734
-515943.379764342
Compiler

Compiled 1 to 1 computations (0% saved)

regimes57.0ms (0.7%)

Compiler

Compiled 180 to 156 computations (13.3% saved)

bsearch27.0ms (0.3%)

Steps
ItersRangePoint
9
87417.7786515175
7196754274351.372
384257.84897965455
6
-4900916.382688271
-387457.089668734
-515943.379764342
Compiler

Compiled 1 to 1 computations (0% saved)

regimes26.0ms (0.3%)

Compiler

Compiled 29 to 29 computations (0% saved)

bsearch32.0ms (0.4%)

Steps
ItersRangePoint
9
2.307904188735251e-08
16.74594831582501
0.992455561826402
9
-3.221532685900676
-5.458083995085865e-08
-1.0247328982238428
Compiler

Compiled 1 to 1 computations (0% saved)

regimes22.0ms (0.3%)

Compiler

Compiled 20 to 22 computations (-10% saved)

bsearch30.0ms (0.4%)

Steps
ItersRangePoint
9
2.307904188735251e-08
16.74594831582501
0.992455561826402
9
-3.221532685900676
-5.458083995085865e-08
-1.0247328982238428
Compiler

Compiled 1 to 1 computations (0% saved)

regimes20.0ms (0.3%)

Compiler

Compiled 13 to 16 computations (-23.1% saved)

bsearch30.0ms (0.4%)

Steps
ItersRangePoint
9
2.307904188735251e-08
16.74594831582501
0.992455561826402
9
-3.221532685900676
-5.458083995085865e-08
-1.0247328982238428
Compiler

Compiled 1 to 1 computations (0% saved)

regimes19.0ms (0.2%)

Compiler

Compiled 8 to 11 computations (-37.5% saved)

bsearch28.0ms (0.4%)

Steps
ItersRangePoint
9
2.307904188735251e-08
16.74594831582501
0.992455561826402
9
-3.221532685900676
-5.458083995085865e-08
-1.0247328982238428
Compiler

Compiled 1 to 1 computations (0% saved)

regimes7.0ms (0.1%)

Accuracy

Total 0.0b remaining (64.5%)

Threshold costs 0.0b (64.5%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch18.0ms (0.2%)

Compiler

Compiled 437 to 313 computations (28.4% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0190570
1190570

end0.0ms (0%)

sample2.0s (25.3%)

Algorithm
intervals
Results
241.0ms1967×body1024valid
144.0ms4369×body128valid
88.0ms952×body512valid
35.0ms218×body2048valid
32.0ms494×body256valid
Compiler

Compiled 1531 to 1162 computations (24.1% saved)

Pareto

0.9643828073693332

Profiling

Loading profile data...