Details

Time bar (total: 9.9s)

analyze1.6s (16%)

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
0%99.9%0.1%6
0%93.6%6.4%7
0%93.6%6.4%8
0%91.3%8.7%9
0%86.6%13.4%10
0%85%15%11
0%82.3%17.7%12
0%79.9%20.1%13
0%78.8%21.2%14
Compiler

Compiled 21 to 15 computations (28.6% saved)

sample3.2s (32.4%)

Results
1.0s1147×body2048valid
753.0ms5346×body128valid
345.0ms771×body1024valid
309.0ms372×body8192exit
273.0ms413×body4096valid
133.0ms384×body512valid
120.0ms892×body128invalid
48.0ms195×body256valid
Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify141.0ms (1.4%)

Algorithm
egg-herbie
Rules
2079×fma-neg_binary64
1006×fma-def_binary64
919×div-sub_binary64
626×distribute-rgt-in_binary64
435×cancel-sign-sub-inv_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01526
13824
29524
322722
435722
561422
6110322
7137322
8163622
9233022
10318722
11288022
12282722
13289622
14292222
15379722
16482422
17524022

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
31.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
31.1b
(*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a))
Compiler

Compiled 71 to 46 computations (35.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.1b
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
0.9b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
19.3b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series180.0ms (1.8%)

Counts
4 → 96
Calls

4 calls:

73.0ms
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
52.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
44.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
10.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity_binary64
16×add-sqr-sqrt_binary64
15×add-cube-cbrt_binary64
12×times-frac_binary64
add-cbrt-cube_binary64
Counts
4 → 77
Calls

4 calls:

5.0ms
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
4.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 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))

simplify87.0ms (0.9%)

Algorithm
egg-herbie
Rules
834×times-frac_binary64
539×associate-/l*_binary64
468×fma-def_binary64
198×cancel-sign-sub-inv_binary64
125×associate-/r/_binary64
Counts
173 → 193
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01973876
15213658
215783494
350113494

prune165.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New18013193
Fresh000
Picked101
Done000
Total18113194
Error
3.8b
Counts
194 → 13
Alt Table
StatusErrorProgram
29.9b
(*.f64 -1/2 (*.f64 (*.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))) (/.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) a)))
32.0b
(*.f64 -1/2 (/.f64 (+.f64 b (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))))) (sqrt.f64 (cbrt.f64 (fma.f64 b b (*.f64 c (*.f64 a -4))))))) a))
45.5b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
29.4b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))))
31.7b
(*.f64 -1/2 (*.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)) (cbrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a))) (cbrt.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a))))
35.1b
(*.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))) a))
56.7b
(*.f64 -1/2 (/.f64 (+.f64 b (-.f64 (*.f64 2 (/.f64 (*.f64 c a) b)) b)) a))
45.4b
(*.f64 -1/2 (*.f64 2 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
43.0b
(*.f64 -1/2 (/.f64 (/.f64 (-.f64 (*.f64 b b) (fma.f64 b b (*.f64 c (*.f64 a -4)))) (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) a))
40.7b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
45.7b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
44.2b
(*.f64 -1/2 (/.f64 (-.f64 (*.f64 b b) (*.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (*.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))
31.1b
(*.f64 -1/2 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a)))
Compiler

Compiled 5457 to 3305 computations (39.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))
0.1b
(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))))
0.6b
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))
11.9b
(sqrt.f64 (*.f64 c (*.f64 a -4)))

series797.0ms (8.1%)

Counts
4 → 42
Calls

4 calls:

386.0ms
(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))
214.0ms
(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))))
175.0ms
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))
21.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))

rewrite31.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
114×times-frac_binary64
99×*-un-lft-identity_binary64
65×add-sqr-sqrt_binary64
65×add-cube-cbrt_binary64
22×associate-/r*_binary64
Counts
4 → 164
Calls

4 calls:

6.0ms
(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))))
4.0ms
(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))
3.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))
2.0ms
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))

simplify167.0ms (1.7%)

Algorithm
egg-herbie
Rules
504×fma-neg_binary64
501×fma-def_binary64
444×associate-/r/_binary64
326×cancel-sign-sub-inv_binary64
212×associate-/l/_binary64
Counts
206 → 291
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02626330
16475816
222205699
345415689
449335689

prune240.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2883291
Fresh6612
Picked011
Done000
Total29410304
Error
0.5b
Counts
304 → 10
Alt Table
StatusErrorProgram
45.5b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
47.8b
(*.f64 -1/2 (/.f64 1 (*.f64 (/.f64 (sqrt.f64 a) (*.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))))) (/.f64 (sqrt.f64 a) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))))))
43.0b
(*.f64 -1/2 (/.f64 (/.f64 (-.f64 (*.f64 b b) (fma.f64 b b (*.f64 c (*.f64 a -4)))) (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) a))
40.7b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
45.7b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
43.6b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))))))))
44.2b
(*.f64 -1/2 (/.f64 (-.f64 (*.f64 b b) (*.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (*.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))
31.1b
(*.f64 -1/2 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a)))
29.4b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))))
40.4b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b)))))
Compiler

Compiled 9162 to 6056 computations (33.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.2b
(*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a))
0.9b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
19.3b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series81.0ms (0.8%)

Counts
1 → 20
Calls

1 calls:

81.0ms
(*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt_binary64
13×associate-*r*_binary64
12×*-un-lft-identity_binary64
11×times-frac_binary64
10×add-exp-log_binary64
Counts
1 → 43
Calls

1 calls:

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

simplify73.0ms (0.7%)

Algorithm
egg-herbie
Rules
460×times-frac_binary64
408×associate-*l*_binary64
317×unswap-sqr_binary64
311×associate-/l*_binary64
305×fma-def_binary64
Counts
63 → 91
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01311718
13701571
211781497
344451497
452761497

prune150.0ms (1.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2070207
Fresh088
Picked011
Done011
Total20710217
Error
0.5b
Counts
217 → 10
Alt Table
StatusErrorProgram
45.5b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
47.8b
(*.f64 -1/2 (/.f64 1 (*.f64 (/.f64 (sqrt.f64 a) (*.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))))) (/.f64 (sqrt.f64 a) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))))))
43.0b
(*.f64 -1/2 (/.f64 (/.f64 (-.f64 (*.f64 b b) (fma.f64 b b (*.f64 c (*.f64 a -4)))) (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) a))
40.7b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
45.7b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
43.6b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))))))))
44.2b
(*.f64 -1/2 (/.f64 (-.f64 (*.f64 b b) (*.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (*.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))
31.1b
(*.f64 -1/2 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a)))
29.4b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))))
40.4b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b)))))
Compiler

Compiled 5830 to 3672 computations (37% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b)))
0.0b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b)))))
0.2b
(/.f64 -2 (/.f64 (*.f64 -4 c) b))
1.3b
(/.f64 1 (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b))))

series88.0ms (0.9%)

Counts
4 → 132
Calls

4 calls:

33.0ms
(/.f64 1 (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b))))
31.0ms
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b)))))
16.0ms
(fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b)))
8.0ms
(/.f64 -2 (/.f64 (*.f64 -4 c) b))

rewrite23.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
53×times-frac_binary64
43×add-sqr-sqrt_binary64
37×*-un-lft-identity_binary64
36×add-cube-cbrt_binary64
26×add-exp-log_binary64
Counts
4 → 131
Calls

4 calls:

5.0ms
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b)))))
4.0ms
(/.f64 -2 (/.f64 (*.f64 -4 c) b))
4.0ms
(/.f64 1 (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b))))
0.0ms
(fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b)))

simplify123.0ms (1.2%)

Algorithm
egg-herbie
Rules
748×associate-/l*_binary64
662×associate-/r*_binary64
346×fma-def_binary64
318×associate-/r/_binary64
201×associate-/l/_binary64
Counts
263 → 245
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02545544
15895144
218514903
352924903

prune178.0ms (1.8%)

Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New2414245
Fresh167
Picked011
Done022
Total24213255
Error
0.5b
Counts
255 → 13
Alt Table
StatusErrorProgram
45.5b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
47.8b
(*.f64 -1/2 (/.f64 1 (*.f64 (/.f64 (sqrt.f64 a) (*.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))))) (/.f64 (sqrt.f64 a) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))))))
31.1b
(*.f64 -1/2 (*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a)))
51.6b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (exp.f64 (log.f64 (*.f64 1/2 (/.f64 b c)))))))
51.3b
(exp.f64 (log.f64 (/.f64 -1 (-.f64 (/.f64 b c) (/.f64 a b)))))
43.0b
(*.f64 -1/2 (/.f64 (/.f64 (-.f64 (*.f64 b b) (fma.f64 b b (*.f64 c (*.f64 a -4)))) (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))) a))
45.7b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
43.6b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))))))))
44.2b
(*.f64 -1/2 (/.f64 (-.f64 (*.f64 b b) (*.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (*.f64 a (-.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))))
29.4b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4))))))))
40.4b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (/.f64 -2 (/.f64 (*.f64 -4 c) b)))))
40.7b
(neg.f64 (/.f64 c b))
40.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 -1 (-.f64 (/.f64 b c) (/.f64 a b)))) (cbrt.f64 (/.f64 -1 (-.f64 (/.f64 b c) (/.f64 a b))))) (cbrt.f64 (/.f64 -1 (-.f64 (/.f64 b c) (/.f64 a b)))))
Compiler

Compiled 6209 to 4071 computations (34.4% saved)

regimes2.2s (22.5%)

Accuracy

Total 7.3b remaining (72.9%)

Threshold costs 0b (0%)

Counts
179 → 3
Compiler

Compiled 17432 to 12170 computations (30.2% saved)

bsearch86.0ms (0.9%)

Steps
ItersRangePoint
9
1.5715138568678295e+86
4.064402674512648e+91
2.717407992462613e+91
7
-8.90430219568148e-63
-1.0462680099667602e-64
-4.125134219839089e-63
Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02856
13656
23656

end185.0ms (1.9%)

Compiler

Compiled 379 to 253 computations (33.2% saved)

Profiling

Loading profile data...