Details

Time bar (total: 52.3s)

analyze2.6s (4.9%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
15.6%84.3%0.1%8
15.6%84.3%0.1%9
15.6%84.3%0.1%10
30.4%69.4%0.1%11
30.4%69.4%0.1%12
30.4%69.4%0.1%13
39.6%60.3%0.1%14
Compiler

Compiled 25 to 23 computations (8% saved)

sample144.0ms (0.3%)

Algorithm
1×intervals
Results
65.0ms60×body1024valid
30.0ms146×body128valid
24.0ms32×body512valid
9.0ms18×body256valid
Compiler

Compiled 49 to 48 computations (2% saved)

simplify334.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (173.0ms)

IterNodesCost
0487137
1487137

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 17.9b

Counts
2 → 1
Compiler

Compiled 48 to 44 computations (8.3% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.3b
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
7.7b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.2b
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite57.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
28×add-exp-log_binary64_457
20×pow1_binary64_480
18×add-cbrt-cube_binary64_455
15×*-un-lft-identity_binary64_419
12×prod-exp_binary64_468 add-sqr-sqrt_binary64_441
11×add-cube-cbrt_binary64_454
10×associate-*r*_binary64_359
9×pow-prod-down_binary64_490 cbrt-unprod_binary64_452
8×sqrt-prod_binary64_435
7×unpow-prod-down_binary64_498
4×sqrt-div_binary64_436 add-log-exp_binary64_458 pow-exp_binary64_487
3×times-frac_binary64_425 pow-unpow_binary64_496 div-exp_binary64_470
2×flip3-+_binary64_422 distribute-lft-out_binary64_370 associate-*r/_binary64_361 *-commutative_binary64_350 associate-*l*_binary64_360 flip-+_binary64_393
1×pow1/2_binary64_499 div-inv_binary64_416 sqr-pow_binary64_391 pow-to-exp_binary64_488 pow-pow_binary64_491 sqrt-pow1_binary64_437 unpow2_binary64_484 rem-sqrt-square_binary64_432
Counts
4 → 86
Calls

4 calls:

18.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
14.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))

series647.0ms (1.2%)

Counts
4 → 12
Calls

4 calls:

272.0ms
(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
188.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
148.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
39.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify65.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
052572394

prune774.0ms (1.5%)

Pruning

34 alts after pruning (33 fresh and 1 done)

PrunedKeptTotal
New653398
Fresh000
Picked011
Done000
Total653499

Merged error: 13.6b

Counts
99 → 34
Compiler

Compiled 4076 to 3351 computations (17.8% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.3b
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
7.7b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (pow.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/2))
9.2b
(pow.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/2)

rewrite49.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
44×add-exp-log_binary64_457
24×prod-exp_binary64_468
18×add-cbrt-cube_binary64_455
16×*-un-lft-identity_binary64_419
15×unpow-prod-down_binary64_498
12×add-cube-cbrt_binary64_454 add-sqr-sqrt_binary64_441
11×associate-*r*_binary64_359 pow1_binary64_480
9×cbrt-unprod_binary64_452
8×pow-exp_binary64_487
6×pow-unpow_binary64_496
5×pow-to-exp_binary64_488
4×add-log-exp_binary64_458
3×pow-prod-down_binary64_490 times-frac_binary64_425 sqr-pow_binary64_391 div-exp_binary64_470
2×distribute-lft-out_binary64_370 *-commutative_binary64_350 associate-*l*_binary64_360 pow-pow_binary64_491
1×div-inv_binary64_416 unpow1/2_binary64_483 unpow2_binary64_484
Counts
4 → 91
Calls

4 calls:

16.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (pow.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/2))
9.0ms
(pow.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/2)
7.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
5.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))

series812.0ms (1.6%)

Counts
4 → 12
Calls

4 calls:

390.0ms
(pow.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/2)
211.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (pow.f64 (+.f64 1 (pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/2))
131.0ms
(pow.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
80.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify184.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (138.0ms)

IterNodesCost
049642571
149642571

prune1.2s (2.4%)

Pruning

52 alts after pruning (50 fresh and 2 done)

PrunedKeptTotal
New8122103
Fresh42832
Picked011
Done011
Total8552137

Merged error: 13.6b

Counts
137 → 52
Compiler

Compiled 4871 to 4056 computations (16.7% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.3b
(*.f64 (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
7.7b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (pow.f64 (+.f64 1 (*.f64 (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))) 1/2))
9.2b
(pow.f64 (+.f64 1 (*.f64 (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))) 1/2)

rewrite41.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
36×add-exp-log_binary64_457
22×prod-exp_binary64_468
20×add-cbrt-cube_binary64_455
17×pow1_binary64_480
15×add-sqr-sqrt_binary64_441
13×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 associate-*r*_binary64_359
10×cbrt-unprod_binary64_452
6×unpow-prod-down_binary64_498
5×associate-*l*_binary64_360
4×pow-prod-down_binary64_490 add-log-exp_binary64_458 pow-exp_binary64_487 pow-to-exp_binary64_488
3×*-commutative_binary64_350 swap-sqr_binary64_386 pow-unpow_binary64_496
2×sqr-pow_binary64_391
1×unswap-sqr_binary64_387 sqr-abs_binary64_434 pow-plus_binary64_482 pow-pow_binary64_491 unpow1/2_binary64_483 pow-sqr_binary64_392 pow-prod-up_binary64_489 pow2_binary64_500
Counts
4 → 90
Calls

4 calls:

12.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (pow.f64 (+.f64 1 (*.f64 (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))) 1/2))
8.0ms
(pow.f64 (+.f64 1 (*.f64 (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))) 1/2)
5.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
4.0ms
(*.f64 (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))

series546.0ms (1%)

Counts
4 → 12
Calls

4 calls:

260.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (pow.f64 (+.f64 1 (*.f64 (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))) 1/2))
204.0ms
(pow.f64 (+.f64 1 (*.f64 (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))) 1/2)
41.0ms
(*.f64 (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))) (fabs.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2))))))
40.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify114.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049442785
149442785

prune1.8s (3.4%)

Pruning

75 alts after pruning (72 fresh and 3 done)

PrunedKeptTotal
New7428102
Fresh54449
Picked011
Done022
Total7975154

Merged error: 13.6b

Counts
154 → 75
Compiler

Compiled 6564 to 5497 computations (16.3% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.3b
(*.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))
7.7b
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (pow.f64 (+.f64 1 (*.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))) 1/2))
9.2b
(pow.f64 (+.f64 1 (*.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))) 1/2)

rewrite76.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
114×add-exp-log_binary64_457
98×add-cbrt-cube_binary64_455
61×prod-exp_binary64_468
49×cbrt-unprod_binary64_452
24×div-exp_binary64_470 cbrt-undiv_binary64_453
19×add-sqr-sqrt_binary64_441
17×*-un-lft-identity_binary64_419 add-cube-cbrt_binary64_454 associate-*r*_binary64_359 pow1_binary64_480
12×times-frac_binary64_425
9×associate-*l*_binary64_360
7×swap-sqr_binary64_386
6×unpow-prod-down_binary64_498
4×pow-prod-down_binary64_490 add-log-exp_binary64_458 div-inv_binary64_416 pow-exp_binary64_487 pow-to-exp_binary64_488
3×*-commutative_binary64_350 pow-unpow_binary64_496
2×sqr-pow_binary64_391
1×associate-*l/_binary64_362 unswap-sqr_binary64_387 frac-times_binary64_429 associate-*r/_binary64_361 pow-plus_binary64_482 pow-pow_binary64_491 unpow1/2_binary64_483 pow-sqr_binary64_392 pow-prod-up_binary64_489 pow2_binary64_500
Counts
4 → 134
Calls

4 calls:

19.0ms
(*.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))
12.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (pow.f64 (+.f64 1 (*.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))) 1/2))
5.0ms
(pow.f64 (+.f64 1 (*.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))) 1/2)
5.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))

series802.0ms (1.5%)

Counts
4 → 12
Calls

4 calls:

388.0ms
(pow.f64 (+.f64 1 (*.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))) 1/2)
212.0ms
(*.f64 (*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))) (pow.f64 (+.f64 1 (*.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))) 1/2))
142.0ms
(*.f64 (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) (/.f64 U (*.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))))
59.0ms
(*.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify171.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 0 (114.0ms)

IterNodesCost
049963543
149963543

prune2.3s (4.5%)

Pruning

99 alts after pruning (95 fresh and 4 done)

PrunedKeptTotal
New12125146
Fresh17071
Picked011
Done033
Total12299221

Merged error: 13.6b

Counts
221 → 99
Compiler

Compiled 4780 to 3769 computations (21.2% saved)

regimes6.8s (13%)

Compiler

Compiled 52087 to 45916 computations (11.8% saved)

bsearch16.1s (30.9%)

Compiler

Compiled 24 to 22 computations (8.3% saved)

simplify13.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
053167
153167

end0.0ms (0%)

sample16.5s (31.5%)

Algorithm
1×intervals
Results
1.6s1935×body1024valid
755.0ms4533×body128valid
554.0ms987×body512valid
211.0ms542×body256valid
4.0ms3×body2048valid
Compiler

Compiled 8816 to 7762 computations (12% saved)

Pareto

0

Profiling

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