Details

Time bar (total: 15.1s)

analyze1.3s (8.4%)

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
12.5%87.4%0.1%5
18.7%81.1%0.1%6
21.8%71.8%6.4%7
31.2%62.4%6.4%8
35.9%55.4%8.7%9
37.8%48.8%13.4%10
42.7%42.3%15%11
47.7%34.2%18.1%12
49.1%30.4%20.5%13
51.9%25.8%22.3%14
Compiler

Compiled 21 to 15 computations (28.6% saved)

sample92.0ms (0.6%)

Algorithm
intervals
Results
23.0ms35×body2048valid
22.0ms175×body128valid
11.0ms14×body4096valid
9.0ms14×body1024valid
4.0ms11×body512valid
2.0ms19×body128nan
2.0msbody256valid
1.0msbody128invalid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify296.0ms (2%)

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

prune7.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
32.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
33.0b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
33.0b
(/.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)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
0.8b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.9b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
23.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

rewrite61.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
10×fma-def_binary64
10×add-cube-cbrt_binary64
10×add-log-exp_binary64
Counts
4 → 90
Calls

4 calls:

22.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
16.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
7.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
6.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

series391.0ms (2.6%)

Counts
4 → 96
Calls

4 calls:

154.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
98.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
79.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
59.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify259.0ms (1.7%)

Algorithm
egg-herbie
Rules
701×fma-neg_binary64
334×cancel-sign-sub-inv_binary64
215×distribute-rgt-neg-in_binary64
159×associate-*r*_binary64
150×distribute-rgt-neg-out_binary64
Counts
186 → 346
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02434208
16953858
225123724
346943704
450313704

prune384.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3379346
Fresh101
Picked011
Done000
Total33810348
Error
6.9b
Counts
348 → 10
Alt Table
StatusErrorProgram
35.6b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
47.1b
(-.f64 (/.f64 c b) (/.f64 b a))
33.0b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
32.3b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
42.0b
(neg.f64 (/.f64 c b))
56.3b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
45.3b
(/.f64 (-.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
44.0b
(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)) (*.f64 (*.f64 2 a) (+.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (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))))))))
33.0b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
46.8b
(/.f64 (neg.f64 b) a)
Compiler

Compiled 5741 to 3347 computations (41.7% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
0.2b
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
2.8b
(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)))
14.6b
(sqrt.f64 (*.f64 c (*.f64 a -4)))

rewrite44.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity_binary64
26×add-sqr-sqrt_binary64
18×add-cube-cbrt_binary64
15×exp-sum_binary64
15×log-prod_binary64
Counts
4 → 100
Calls

4 calls:

13.0ms
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
6.0ms
(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)))
6.0ms
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
5.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))

series1.8s (12.1%)

Counts
4 → 36
Calls

4 calls:

985.0ms
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (*.f64 2 a))
569.0ms
(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)))
243.0ms
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
32.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))

simplify261.0ms (1.7%)

Algorithm
egg-herbie
Rules
768×fma-def_binary64
423×cancel-sign-sub-inv_binary64
338×fma-neg_binary64
223×times-frac_binary64
170×associate-/r*_binary64
Counts
136 → 257
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03244496
17753894
230843576
349673576
449743576

prune422.0ms (2.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New2534257
Fresh088
Picked101
Done011
Total25413267
Error
4.4b
Counts
267 → 13
Alt Table
StatusErrorProgram
44.0b
(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) 3)) (*.f64 (*.f64 2 a) (+.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (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))))))))
45.1b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))) b) b))) (*.f64 2 a))
35.6b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
47.1b
(-.f64 (/.f64 c b) (/.f64 b a))
33.0b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
42.0b
(neg.f64 (/.f64 c b))
56.3b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
49.0b
(/.f64 (exp.f64 (log.f64 (*.f64 -2 b))) (*.f64 2 a))
45.3b
(/.f64 (-.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 (*.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
46.4b
(/.f64 (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 c a) -2) b) (/.f64 b (/.f64 (*.f64 -4 (*.f64 c a)) b))) -1/4 (/.f64 (*.f64 (*.f64 c a) -2) b)) (*.f64 2 a))
33.0b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
46.8b
(/.f64 (neg.f64 b) a)
33.5b
(/.f64 (pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))))) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)))) (*.f64 2 a))
Compiler

Compiled 7612 to 5112 computations (32.8% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
0.8b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.9b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
23.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

rewrite36.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
53×times-frac_binary64
37×*-un-lft-identity_binary64
22×add-exp-log_binary64
21×add-sqr-sqrt_binary64
21×add-cube-cbrt_binary64
Counts
1 → 74
Calls

1 calls:

23.0ms
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

series153.0ms (1%)

Counts
1 → 20
Calls

1 calls:

152.0ms
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

simplify210.0ms (1.4%)

Algorithm
egg-herbie
Rules
665×associate-/l*_binary64
599×div-sub_binary64
349×fma-def_binary64
295×fma-neg_binary64
265×associate-/r/_binary64
Counts
94 → 184
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01643247
14392847
215172670
345952670
461782670

prune406.0ms (2.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New4303433
Fresh2911
Picked011
Done101
Total43313446
Error
4.4b
Counts
446 → 13
Alt Table
StatusErrorProgram
46.4b
(/.f64 (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 c a) -2) b) (/.f64 b (/.f64 (*.f64 -4 (*.f64 c a)) b))) -1/4 (/.f64 (*.f64 (*.f64 c a) -2) b)) (*.f64 2 a))
33.0b
(*.f64 (/.f64 1/2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
35.6b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
47.1b
(-.f64 (/.f64 c b) (/.f64 b a))
34.3b
(*.f64 (*.f64 (*.f64 4 (*.f64 c a)) (/.f64 1/2 a)) (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
46.8b
(/.f64 (neg.f64 b) a)
56.3b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
49.0b
(/.f64 (exp.f64 (log.f64 (*.f64 -2 b))) (*.f64 2 a))
45.1b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))) b) b))) (*.f64 2 a))
33.0b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
35.7b
(/.f64 1 (/.f64 (*.f64 2 a) (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))))
33.5b
(/.f64 (pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))))) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)))) (*.f64 2 a))
42.0b
(neg.f64 (/.f64 c b))
Compiler

Compiled 7970 to 4906 computations (38.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (/.f64 1/2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))
0.8b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
0.9b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
23.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

rewrite27.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
13×associate-*l*_binary64
13×*-un-lft-identity_binary64
10×times-frac_binary64
add-cube-cbrt_binary64
Counts
1 → 42
Calls

1 calls:

21.0ms
(*.f64 (/.f64 1/2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

series142.0ms (0.9%)

Counts
1 → 20
Calls

1 calls:

141.0ms
(*.f64 (/.f64 1/2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))))

simplify136.0ms (0.9%)

Algorithm
egg-herbie
Rules
660×times-frac_binary64
540×fma-def_binary64
412×distribute-rgt-in_binary64
330×fma-neg_binary64
154×distribute-rgt-neg-out_binary64
Counts
62 → 120
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01571930
15401695
217841607
349361607
450741607

prune355.0ms (2.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New6162618
Fresh2911
Picked101
Done011
Total61912631
Error
4.4b
Counts
631 → 12
Alt Table
StatusErrorProgram
34.3b
(*.f64 (*.f64 (*.f64 4 (*.f64 c a)) (/.f64 1/2 a)) (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
46.8b
(/.f64 (neg.f64 b) a)
30.3b
(/.f64 (*.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)) a)
33.5b
(/.f64 (pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b))))) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)))) (*.f64 2 a))
56.3b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
49.0b
(/.f64 (exp.f64 (log.f64 (*.f64 -2 b))) (*.f64 2 a))
45.1b
(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))) b) b))) (*.f64 2 a))
46.4b
(/.f64 (fma.f64 (/.f64 (/.f64 (*.f64 (*.f64 c a) -2) b) (/.f64 b (/.f64 (*.f64 -4 (*.f64 c a)) b))) -1/4 (/.f64 (*.f64 (*.f64 c a) -2) b)) (*.f64 2 a))
33.0b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
35.7b
(*.f64 (/.f64 1/2 a) (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))))
47.1b
(-.f64 (/.f64 c b) (/.f64 b a))
42.0b
(neg.f64 (/.f64 c b))
Compiler

Compiled 6222 to 3653 computations (41.3% saved)

regimes4.9s (32.1%)

Accuracy

Total 7.3b remaining (69.8%)

Threshold costs 0b (0%)

Compiler

Compiled 20139 to 14473 computations (28.1% saved)

bsearch124.0ms (0.8%)

Steps
ItersRangePoint
8
6.144593741441501e-98
1.4640050268977364e-94
4.7492894376772045e-95
9
-1.009631966683708e+100
-1.380297336827828e+95
-4.558931914031214e+98
Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02552
13850
24950
35550
45750
55750

end2.0ms (0%)

Compiler

Compiled 37 to 22 computations (40.5% saved)

sample3.3s (21.5%)

Algorithm
intervals
Results
720.0ms1114×body2048valid
679.0ms5160×body128valid
356.0ms718×body1024valid
311.0ms407×body4096valid
151.0ms406×body512valid
87.0ms725×body128nan
49.0ms359×body128invalid
49.0ms195×body256valid
Compiler

Compiled 296 to 206 computations (30.4% saved)

Profiling

Loading profile data...