Details

Time bar (total: 2.4s)

analyze5.0ms (0.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
25%25%50%4
37.5%12.5%50%5
43.7%6.2%50%6
46.9%3.1%50%7
48.4%1.6%50%8
49.2%0.8%50%9
49.6%0.4%50%10
49.8%0.2%50%11
49.9%0.1%50%12
49.9%0%50.1%13
49.9%0%50.1%14
Compiler

Compiled 21 to 17 computations (19% saved)

sample20.0ms (0.8%)

Algorithm
1×intervals
Results
12.0ms256×body128valid
Compiler

Compiled 41 to 34 computations (17.1% saved)

simplify286.0ms (11.7%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (182.0ms)

IterNodesCost
0484328
1484328

prune7.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 2
Compiler

Compiled 56 to 44 computations (21.4% saved)

localize10.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.0b
(*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
0.0b
(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))
0.0b
(sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))
0.0b
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
0.0b
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
0.0b
(*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
0.0b
(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))
0.1b
(*.f64 (*.f64 v v) 6)

rewrite49.0ms (2%)

Algorithm
1×rewrite-expression-head
Rules
25×add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
22×associate-*r/_binary64_1384
18×flip3--_binary64_1446 sqrt-div_binary64_1459 flip--_binary64_1417
17×add-sqr-sqrt_binary64_1464
16×pow1_binary64_1503
12×frac-times_binary64_1452 *-un-lft-identity_binary64_1442
11×add-cube-cbrt_binary64_1477
10×associate-*r*_binary64_1382 cbrt-unprod_binary64_1475 prod-exp_binary64_1491
9×associate-*l*_binary64_1383
8×associate-/r/_binary64_1388
7×pow-prod-down_binary64_1513
6×associate-*l/_binary64_1385
4×add-log-exp_binary64_1481 sqrt-prod_binary64_1458
3×cbrt-undiv_binary64_1476 times-frac_binary64_1448 associate-/l*_binary64_1387 *-commutative_binary64_1373 div-exp_binary64_1493 unswap-sqr_binary64_1410
2×difference-of-squares_binary64_1411
1×associate-/r*_binary64_1386 div-inv_binary64_1439 clear-num_binary64_1441 frac-2neg_binary64_1453
Counts
4 → 108
Calls

8 calls:

11.0ms
(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))
10.0ms
(*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
10.0ms
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
6.0ms
(*.f64 (*.f64 v v) 6)
0.0ms
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))

series263.0ms (10.8%)

Counts
4 → 21
Calls

4 calls:

107.0ms
(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))
68.0ms
(*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
59.0ms
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
29.0ms
(*.f64 (*.f64 v v) 6)
Compiler

Compiled 822 to 732 computations (10.9% saved)

simplify87.0ms (3.5%)

Algorithm
1×egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
050773412

prune188.0ms (7.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1272129
Fresh101
Picked101
Done000
Total1292131
Error
0b
Counts
131 → 2
Compiler

Compiled 3497 to 2352 computations (32.7% saved)

localize13.0ms (0.5%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (*.f64 v v) 6)
0.0b
(/.f64 4/3 (*.f64 (sqrt.f64 PI.f64) (*.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))) (sqrt.f64 PI.f64))))
0.0b
(sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))
0.0b
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
0.1b
(*.f64 (*.f64 v v) 6)
1.0b
(*.f64 (sqrt.f64 PI.f64) (*.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))) (sqrt.f64 PI.f64)))
1.0b
(sqrt.f64 PI.f64)
1.0b
(sqrt.f64 PI.f64)

rewrite32.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Rules
20×pow1_binary64_1503
18×add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
12×add-sqr-sqrt_binary64_1464
10×associate-*r/_binary64_1384 associate-*l/_binary64_1385
9×cbrt-unprod_binary64_1475 pow-prod-down_binary64_1513 sqrt-prod_binary64_1458 prod-exp_binary64_1491 add-cube-cbrt_binary64_1477 *-un-lft-identity_binary64_1442
7×associate-*l*_binary64_1383
6×flip3--_binary64_1446 sqrt-div_binary64_1459 flip--_binary64_1417
4×associate-*r*_binary64_1382 add-log-exp_binary64_1481 frac-times_binary64_1452
2×sqrt-pow1_binary64_1460 rem-sqrt-square_binary64_1455 *-commutative_binary64_1373 pow1/2_binary64_1522
1×unswap-sqr_binary64_1410
Counts
4 → 77
Calls

8 calls:

15.0ms
(*.f64 (sqrt.f64 PI.f64) (*.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))) (sqrt.f64 PI.f64)))
6.0ms
(*.f64 (*.f64 v v) 6)
1.0ms
(sqrt.f64 PI.f64)
1.0ms
(sqrt.f64 PI.f64)
0.0ms
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))

series94.0ms (3.8%)

Counts
4 → 9
Calls

4 calls:

70.0ms
(*.f64 (sqrt.f64 PI.f64) (*.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))) (sqrt.f64 PI.f64)))
23.0ms
(*.f64 (*.f64 v v) 6)
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 360 to 306 computations (15% saved)

simplify42.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
052571475

prune100.0ms (4.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New86086
Fresh011
Picked011
Done000
Total86288
Error
0b
Counts
88 → 2
Compiler

Compiled 2279 to 1372 computations (39.8% saved)

localize11.0ms (0.5%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (*.f64 v v) 6)
0.0b
(/.f64 (/.f64 4/3 PI.f64) (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))))
0.0b
(sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))
0.0b
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
0.0b
(sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))
0.0b
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
0.1b
(*.f64 (*.f64 v v) 6)
1.0b
(/.f64 4/3 PI.f64)

rewrite31.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Rules
24×add-sqr-sqrt_binary64_1464
18×*-un-lft-identity_binary64_1442
17×add-cube-cbrt_binary64_1477
13×add-cbrt-cube_binary64_1478 add-exp-log_binary64_1480
12×pow1_binary64_1503
9×associate-*r*_binary64_1382 times-frac_binary64_1448
8×sqrt-div_binary64_1459
7×flip3--_binary64_1446 flip--_binary64_1417 sqrt-prod_binary64_1458
6×associate-*l*_binary64_1383
4×cbrt-unprod_binary64_1475 pow-prod-down_binary64_1513 add-log-exp_binary64_1481 frac-times_binary64_1452 prod-exp_binary64_1491
3×associate-/r*_binary64_1386 associate-/l*_binary64_1387 unswap-sqr_binary64_1410
2×associate-*r/_binary64_1384 *-commutative_binary64_1373 difference-of-squares_binary64_1411 associate-*l/_binary64_1385
1×sqrt-pow1_binary64_1460 cbrt-undiv_binary64_1476 rem-sqrt-square_binary64_1455 div-inv_binary64_1439 clear-num_binary64_1441 frac-2neg_binary64_1453 pow1/2_binary64_1522 div-exp_binary64_1493
Counts
4 → 93
Calls

8 calls:

9.0ms
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
6.0ms
(*.f64 (*.f64 v v) 6)
3.0ms
(/.f64 4/3 PI.f64)
3.0ms
(sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))
0.0ms
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))

series116.0ms (4.7%)

Counts
4 → 15
Calls

4 calls:

57.0ms
(*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))
35.0ms
(sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6)))
23.0ms
(*.f64 (*.f64 v v) 6)
0.0ms
(/.f64 4/3 PI.f64)
Compiler

Compiled 485 to 441 computations (9.1% saved)

simplify114.0ms (4.7%)

Algorithm
1×egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 0 (89.0ms)

IterNodesCost
049201875
149201875

prune130.0ms (5.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1080108
Fresh000
Picked011
Done011
Total1082110
Error
0b
Counts
110 → 2
Compiler

Compiled 2619 to 1740 computations (33.6% saved)

simplify6.0ms (0.2%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0120267
1120267

regimes39.0ms (1.6%)

Compiler

Compiled 354 to 286 computations (19.2% saved)

bsearch0.0ms (0%)

regimes22.0ms (0.9%)

Compiler

Compiled 98 to 88 computations (10.2% saved)

bsearch0.0ms (0%)

regimes8.0ms (0.3%)

Compiler

Compiled 11 to 15 computations (-36.4% saved)

bsearch0.0ms (0%)

regimes7.0ms (0.3%)

Accuracy

Total 0.0b remaining (95.7%)

Threshold costs 0.0b (95.7%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch3.0ms (0.1%)

Compiler

Compiled 45 to 39 computations (13.3% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05570
15570

end0.0ms (0%)

sample758.0ms (31%)

Algorithm
1×intervals
Results
397.0ms8000×body128valid
0.0ms2×body128nan
Compiler

Compiled 239 to 197 computations (17.6% saved)

Pareto

0.10621945563723857

Profiling

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