Details

Time bar (total: 8.8s)

analyze366.0ms (4.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
0%0%100%2
0%0%100%3
0%0%100%4
0%0%100%5
0%0%100%6
0%0%100%7
0%0%100%8
0%0%100%9
0%0%100%10
0%0%100%11
0%0%100%12
0%0%100%13
0%0%100%14
Compiler

Compiled 43 to 31 computations (27.9% saved)

sample1.6s (17.7%)

Results
1.2s7930×body128valid
123.0ms847×body128invalid
117.0ms326×body256valid
Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify261.0ms (3%)

Algorithm
egg-herbie
Rules
1743×fma-neg_binary64
1393×fma-def_binary64
800×div-sub_binary64
619×times-frac_binary64
473×associate-/r/_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13322
26722
313822
420422
533822
655822
792422
8138822
9160422
10237522
11274222
12253322
13262122
14317122
15331322
16387322
17367922
18402922
19431722
20448522
21456122
22480522
23479322
24479722
25479722
26494822

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
27.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
27.3b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
27.3b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
Compiler

Compiled 111 to 74 computations (33.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
0.3b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.3b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
27.2b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)

series125.0ms (1.4%)

Counts
4 → 96
Calls

4 calls:

54.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
34.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
27.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
9.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

rewrite23.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt_binary64
32×*-un-lft-identity_binary64
28×add-cube-cbrt_binary64
18×prod-diff_binary64
17×sqrt-prod_binary64
Counts
4 → 109
Calls

4 calls:

10.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
4.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
1.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
0.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

simplify188.0ms (2.1%)

Algorithm
egg-herbie
Rules
527×fma-neg_binary64
338×distribute-rgt-in_binary64
273×cancel-sign-sub-inv_binary64
155×associate-*l*_binary64
153×associate-*r*_binary64
Counts
205 → 226
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02675424
16734468
225244293
345504293
449914293
549944293
648844293

prune143.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2215226
Fresh101
Picked101
Done000
Total2235228
Error
0.1b
Counts
228 → 5
Alt Table
StatusErrorProgram
6.0b
(neg.f64 (fma.f64 2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3))))))
6.2b
(*.f64 (neg.f64 (+.f64 (*.f64 2 (/.f64 (*.f64 c a) b)) (+.f64 (*.f64 2 (/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (*.f64 10 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (*.f64 4 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/2 a))
27.3b
(*.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (*.f64 (cbrt.f64 (/.f64 1/2 a)) (cbrt.f64 (/.f64 1/2 a)))) (cbrt.f64 (/.f64 1/2 a)))
27.2b
(/.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) 1/2) a)
0.4b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
Compiler

Compiled 6227 to 3638 computations (41.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
0.3b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.3b
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
0.3b
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

series167.0ms (1.9%)

Counts
3 → 64
Calls

3 calls:

131.0ms
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
32.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
3.0ms
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

rewrite30.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
17×add-cbrt-cube_binary64
17×add-exp-log_binary64
15×add-cube-cbrt_binary64
Counts
3 → 92
Calls

3 calls:

12.0ms
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
8.0ms
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))
3.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)

simplify402.0ms (4.6%)

Algorithm
egg-herbie
Rules
616×fma-neg_binary64
248×associate-*l*_binary64
225×associate-/l*_binary64
220×associate-*r*_binary64
176×div-sub_binary64
Counts
156 → 196
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02503787
17083244
231323157
346133157
449323157

prune244.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2087215
Fresh224
Picked101
Done000
Total2119220
Error
0b
Counts
220 → 9
Alt Table
StatusErrorProgram
6.0b
(neg.f64 (fma.f64 2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3))))))
0.5b
(*.f64 (/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) 1) (/.f64 (/.f64 1/2 a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))
0.6b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (/.f64 (+.f64 (pow.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) 3) (pow.f64 b 3)) (+.f64 (*.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (-.f64 (*.f64 b b) (*.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))))
0.7b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))))
0.4b
(/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))
0.6b
(/.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 c (*.f64 a -4)) 3) (pow.f64 0 3)) 1/2) (*.f64 (+.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (-.f64 (*.f64 0 0) (*.f64 (*.f64 c (*.f64 a -4)) 0))) a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
27.2b
(/.f64 (*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) 1/2) a)
0.5b
(/.f64 (*.f64 (-.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (*.f64 0 0)) (/.f64 1/2 a)) (*.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (-.f64 (*.f64 c (*.f64 a -4)) 0)))
0.6b
(/.f64 (*.f64 (*.f64 c (*.f64 (*.f64 a -4) (sqrt.f64 (/.f64 1/2 a)))) (sqrt.f64 (/.f64 1/2 a))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
Compiler

Compiled 7496 to 4732 computations (36.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.3b
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
0.3b
(/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
0.3b
(/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))

series186.0ms (2.1%)

Counts
2 → 40
Calls

2 calls:

134.0ms
(/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))
52.0ms
(/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

rewrite100.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
620×times-frac_binary64
409×*-un-lft-identity_binary64
277×add-sqr-sqrt_binary64
277×add-cube-cbrt_binary64
70×associate-/r*_binary64
Counts
2 → 340
Calls

2 calls:

24.0ms
(/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))
7.0ms
(/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

simplify360.0ms (4.1%)

Algorithm
egg-herbie
Rules
624×associate-/r/_binary64
461×associate-/l*_binary64
403×associate-*l/_binary64
403×associate-/l/_binary64
355×fma-neg_binary64
Counts
380 → 558
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
057319325
1141318727
2497018727
3531418727

prune741.0ms (8.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New6243627
Fresh538
Picked011
Done000
Total6297636
Error
0b
Counts
636 → 7
Alt Table
StatusErrorProgram
6.0b
(neg.f64 (fma.f64 2 (/.f64 (*.f64 (*.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b 3))))))
0.6b
(/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (sqrt.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b) (/.f64 1/2 a)))
0.4b
(/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))
0.6b
(/.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 c (*.f64 a -4)) 3) (pow.f64 0 3)) 1/2) (*.f64 (+.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (-.f64 (*.f64 0 0) (*.f64 (*.f64 c (*.f64 a -4)) 0))) a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
0.6b
(/.f64 (/.f64 c (/.f64 (sqrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1/2 a))) (*.f64 a -4))) (sqrt.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))))
0.5b
(/.f64 (*.f64 (/.f64 c (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (*.f64 a -4))) 1/2) a)
0.6b
(/.f64 (*.f64 (*.f64 c (*.f64 (*.f64 a -4) (sqrt.f64 (/.f64 1/2 a)))) (sqrt.f64 (/.f64 1/2 a))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
Compiler

Compiled 27275 to 16995 computations (37.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 c (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (*.f64 a -4)))
0.3b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.3b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
0.3b
(/.f64 (*.f64 (/.f64 c (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (*.f64 a -4))) 1/2) a)

series332.0ms (3.8%)

Counts
3 → 60
Calls

3 calls:

161.0ms
(/.f64 c (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (*.f64 a -4)))
137.0ms
(/.f64 (*.f64 (/.f64 c (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (*.f64 a -4))) 1/2) a)
34.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))

rewrite31.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
43×times-frac_binary64
33×*-un-lft-identity_binary64
32×add-cbrt-cube_binary64
32×add-exp-log_binary64
23×add-sqr-sqrt_binary64
Counts
3 → 101
Calls

3 calls:

10.0ms
(/.f64 (*.f64 (/.f64 c (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (*.f64 a -4))) 1/2) a)
8.0ms
(/.f64 c (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (*.f64 a -4)))
3.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))

simplify145.0ms (1.7%)

Algorithm
egg-herbie
Rules
809×fma-def_binary64
237×times-frac_binary64
226×associate-/l*_binary64
224×cancel-sign-sub-inv_binary64
206×fma-neg_binary64
Counts
161 → 233
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03135878
18785185
233544922
346944922
449564922

prune251.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2502252
Fresh235
Picked011
Done011
Total2527259
Error
0b
Counts
259 → 7
Alt Table
StatusErrorProgram
6.0b
(-.f64 (*.f64 (/.f64 (*.f64 (pow.f64 c 3) (*.f64 a a)) (pow.f64 b 5)) -2) (fma.f64 5 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
0.4b
(/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)))
0.3b
(/.f64 (*.f64 c 1/2) (*.f64 a (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (*.f64 a -4))))
0.6b
(/.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (sqrt.f64 (cbrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) b) (/.f64 1/2 a)))
0.6b
(/.f64 (/.f64 (*.f64 (+.f64 (pow.f64 (*.f64 c (*.f64 a -4)) 3) (pow.f64 0 3)) 1/2) (*.f64 (+.f64 (*.f64 (*.f64 c (*.f64 a -4)) (*.f64 c (*.f64 a -4))) (-.f64 (*.f64 0 0) (*.f64 (*.f64 c (*.f64 a -4)) 0))) a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
0.6b
(/.f64 (/.f64 c (/.f64 (sqrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1/2 a))) (*.f64 a -4))) (sqrt.f64 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))))
0.5b
(/.f64 (*.f64 (/.f64 c (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (*.f64 a -4))) 1/2) a)
Compiler

Compiled 8101 to 4897 computations (39.6% saved)

regimes2.9s (33.2%)

Accuracy

Total 0.2b remaining (88.2%)

Threshold costs 0.2b (88.2%)

Counts
479 → 1
Compiler

Compiled 71012 to 48226 computations (32.1% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01631
12131
22131

end154.0ms (1.8%)

Compiler

Compiled 307 to 207 computations (32.6% saved)

Profiling

Loading profile data...