Details

Time bar (total: 9.3s)

analyze756.0ms (8.1%)

Algorithm
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
12.5%87.4%0.1%6
20.3%73.3%6.4%7
27.3%66.3%6.4%8
38.2%53%8.7%9
46%40.6%13.4%10
49.9%35.1%15%11
54.9%26.9%18.1%12
57.4%22%20.6%13
59.7%18%22.4%14
Compiler

Compiled 42 to 27 computations (35.7% saved)

sample2.4s (25.5%)

Results
2.0s8256×body128valid
186.0ms1038×body128invalid
Compiler

Compiled 125 to 80 computations (36% saved)

simplify129.0ms (1.4%)

Algorithm
egg-herbie
Rules
1002×fma-def_binary64
782×fma-neg_binary64
748×distribute-rgt-in_binary64
560×div-sub_binary64
469×associate-/l*_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02258
14452
29452
321150
434150
559450
6108250
7170250
8206650
9287050
10349550
11350150
12350350
13419650
14424950
15488150

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
21.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
22.1b
(if (>=.f64 b 0) (*.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))
22.0b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)))
Compiler

Compiled 231 to 143 computations (38.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.7b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
24.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series152.0ms (1.6%)

Counts
4 → 96
Calls

4 calls:

49.0ms
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
49.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
42.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
12.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

rewrite117.0ms (1.3%)

Algorithm
batch-egg-rewrite
Rules
368×egg-rr
Counts
4 → 368
Calls

2 calls:

101.0ms
((sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01368
129656
2358456
3533156
000
100

simplify89.0ms (1%)

Algorithm
egg-herbie
Rules
458×times-frac_binary64
447×unswap-sqr_binary64
295×fma-def_binary64
283×associate-*r*_binary64
278×associate-/l*_binary64
Counts
464 → 426
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0902213
12932123
29182035
344072035
452582035

prune929.0ms (10%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New6534657
Fresh011
Picked101
Done000
Total6545659
Error
7.7b
Counts
659 → 5
Alt Table
StatusErrorProgram
23.4b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)))
22.1b
(if (>=.f64 b 0) (*.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))
22.0b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (*.f64 (*.f64 a -4) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (*.f64 b b)))) (*.f64 2 a)))
22.0b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (*.f64 -1 b)) (*.f64 2 a)))
22.0b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (*.f64 a c) (*.f64 b b)) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)))
Compiler

Compiled 34763 to 18954 computations (45.5% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.7b
(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (*.f64 (*.f64 a -4) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (*.f64 b b))))
24.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
24.7b
(sqrt.f64 (fma.f64 (*.f64 (*.f64 a -4) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (*.f64 b b)))
Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series301.0ms (3.2%)

Counts
2 → 56
Calls

2 calls:

154.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (*.f64 (*.f64 a -4) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (*.f64 b b))))
147.0ms
(sqrt.f64 (fma.f64 (*.f64 (*.f64 a -4) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (*.f64 b b)))

rewrite91.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
91×egg-rr
Counts
2 → 91
Calls

2 calls:

88.0ms
((sqrt.f64 (fma.f64 (*.f64 (*.f64 a -4) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (*.f64 b b))) (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (*.f64 (*.f64 a -4) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (*.f64 b b)))))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01551
131333
2331527
3498027
4483327
000
100

simplify62.0ms (0.7%)

Algorithm
egg-herbie
Rules
447×unswap-sqr_binary64
444×times-frac_binary64
280×associate-*r*_binary64
278×associate-/l*_binary64
270×fma-def_binary64
Counts
147 → 139
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0841368
12701305
28441235
341771235
450091235

prune556.0ms (6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3673370
Fresh044
Picked011
Done000
Total3678375
Error
5.5b
Counts
375 → 8
Alt Table
StatusErrorProgram
22.0b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (*.f64 -1 b)) (*.f64 2 a)))
25.5b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (hypot.f64 b (*.f64 (*.f64 (cbrt.f64 c) (sqrt.f64 (*.f64 a -4))) (pow.f64 c 1/6)))) (*.f64 2 a)))
23.4b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)))
22.1b
(if (>=.f64 b 0) (*.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))
22.0b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (*.f64 (*.f64 a -4) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (*.f64 b b)))) (*.f64 2 a)))
22.1b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (*.f64 (*.f64 a -4) c)))))) (*.f64 2 a)))
21.3b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 (*.f64 a -4) c)))) 3)) (*.f64 2 a)))
22.0b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (*.f64 a c) (*.f64 b b)) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)))
Compiler

Compiled 20078 to 11248 computations (44% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
6.8b
(+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 (*.f64 a -4) c)))) 3))
15.0b
(sqrt.f64 (*.f64 (*.f64 a -4) c))
24.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series161.0ms (1.7%)

Counts
2 → 12
Calls

2 calls:

138.0ms
(+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 (*.f64 a -4) c)))) 3))
22.0ms
(sqrt.f64 (*.f64 (*.f64 a -4) c))

rewrite62.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
97×egg-rr
Counts
2 → 97
Calls

2 calls:

60.0ms
((sqrt.f64 (*.f64 (*.f64 a -4) c)) (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (sqrt.f64 (*.f64 (*.f64 a -4) c)))) 3)))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01426
128224
2305624
3533124
000
100

simplify38.0ms (0.4%)

Algorithm
egg-herbie
Rules
601×fma-def_binary64
594×cancel-sign-sub-inv_binary64
435×fma-neg_binary64
349×distribute-rgt-neg-in_binary64
290×distribute-neg-frac_binary64
Counts
109 → 119
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
060445
1172406
2482379
32339371
45016371

prune730.0ms (7.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New3482350
Fresh246
Picked101
Done011
Total3517358
Error
4.0b
Counts
358 → 7
Alt Table
StatusErrorProgram
23.4b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) b)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)))
22.1b
(if (>=.f64 b 0) (*.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))
25.2b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 a -4)) (sqrt.f64 c)))) 3)) (*.f64 2 a)))
29.2b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (*.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 -4 c))))) 3)) (*.f64 2 a)))
22.0b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (*.f64 (*.f64 a -4) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (*.f64 b b)))) (*.f64 2 a)))
22.0b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (*.f64 -1 b)) (*.f64 2 a)))
22.0b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (*.f64 a c) (*.f64 b b)) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)))
Compiler

Compiled 18285 to 11060 computations (39.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.2b
(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
24.7b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
Compiler

Compiled 1536 to 1280 computations (16.7% saved)

series255.0ms (2.7%)

Counts
1 → 20
Calls

1 calls:

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

rewrite70.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
45×egg-rr
Counts
1 → 45
Calls

2 calls:

69.0ms
((/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01526
133822
2420522
3488822
000
100

simplify48.0ms (0.5%)

Algorithm
egg-herbie
Rules
907×fma-neg_binary64
473×times-frac_binary64
442×unswap-sqr_binary64
288×associate-/l*_binary64
232×associate-/r*_binary64
Counts
65 → 68
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
067659
1218639
2682598
33651597
45374597

prune563.0ms (6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4112413
Fresh145
Picked101
Done011
Total4137420
Error
3.9b
Counts
420 → 7
Alt Table
StatusErrorProgram
22.0b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (*.f64 (*.f64 a -4) (pow.f64 (cbrt.f64 c) 2)) (cbrt.f64 c) (*.f64 b b)))) (*.f64 2 a)))
23.4b
(if (>=.f64 b 0) (*.f64 -1 (/.f64 c b)) (/.f64 (+.f64 (neg.f64 b) (*.f64 -1 b)) (*.f64 2 a)))
40.7b
(if (>=.f64 b 0) (*.f64 (/.f64 (*.f64 2 c) (-.f64 (*.f64 b b) (fma.f64 b b (*.f64 -4 (*.f64 c a))))) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 -4 (*.f64 c a)))))) (/.f64 (+.f64 (neg.f64 b) (*.f64 -1 b)) (*.f64 2 a)))
22.1b
(if (>=.f64 b 0) (*.f64 c (/.f64 -2 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))) (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))
25.2b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 a -4)) (sqrt.f64 c)))) 3)) (*.f64 2 a)))
29.2b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (hypot.f64 b (*.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 -4 c))))) 3)) (*.f64 2 a)))
22.0b
(if (>=.f64 b 0) (/.f64 (*.f64 2 c) (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 -4 (*.f64 a c) (*.f64 b b)) 1/4) 2))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a)))
Compiler

Compiled 18799 to 10641 computations (43.4% saved)

regimes1.5s (15.7%)

Accuracy

Total 3.9b remaining (58.7%)

Threshold costs 0b (0%)

Counts
121 → 5
Compiler

Compiled 18026 to 12194 computations (32.4% saved)

bsearch6.0ms (0.1%)

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify15.0ms (0.2%)

Algorithm
egg-herbie
Rules
17×*-commutative_binary64
16×+-commutative_binary64
13×sub-neg_binary64
10×neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
055498
174482
298482
3118482
4132482
5138482
6139482
7138482

end255.0ms (2.7%)

Compiler

Compiled 919 to 568 computations (38.2% saved)

Profiling

Loading profile data...