Details

Time bar (total: 15.0s)

analyze1.1s (7.6%)

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)

sample104.0ms (0.7%)

Algorithm
intervals
Results
24.0ms36×body2048valid
22.0ms168×body128valid
14.0ms23×body1024valid
10.0ms12×body4096valid
7.0ms11×body512valid
4.0msbody256valid
3.0ms20×body128nan
2.0ms12×body128invalid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify182.0ms (1.2%)

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

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
33.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
33.9b
(*.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)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
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))))
22.1b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series229.0ms (1.5%)

Counts
3 → 60
Calls

3 calls:

109.0ms
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
62.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
57.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

rewrite29.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity_binary64
15×add-sqr-sqrt_binary64
14×add-cube-cbrt_binary64
12×times-frac_binary64
distribute-lft-out_binary64
Counts
3 → 67
Calls

3 calls:

14.0ms
(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)
6.0ms
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
2.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

simplify132.0ms (0.9%)

Algorithm
egg-herbie
Rules
820×times-frac_binary64
539×associate-/l*_binary64
458×fma-def_binary64
246×fma-neg_binary64
189×cancel-sign-sub-inv_binary64
Counts
127 → 169
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01883311
15103170
215343008
348403008
449543008

prune153.0ms (1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New15811169
Fresh000
Picked101
Done000
Total15911170
Error
5.3b
Counts
170 → 11
Alt Table
StatusErrorProgram
32.9b
(*.f64 -1/2 (*.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a)))
41.5b
(*.f64 -1/2 (/.f64 (/.f64 (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) 3)) (+.f64 (*.f64 b b) (-.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 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))) a))
40.5b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
34.4b
(*.f64 -1/2 (*.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (cbrt.f64 a))))
48.2b
(*.f64 -1/2 (/.f64 (*.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
45.6b
(*.f64 -1/2 (/.f64 (/.f64 (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a))
44.1b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
44.3b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
32.8b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))))
57.3b
(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
49.6b
(*.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) a) 3)))
Compiler

Compiled 4894 to 2954 computations (39.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))
0.2b
(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
0.4b
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))
12.8b
(sqrt.f64 (*.f64 a (*.f64 c -4)))

series1.1s (7.5%)

Counts
4 → 42
Calls

4 calls:

687.0ms
(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))
264.0ms
(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
155.0ms
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))
26.0ms
(sqrt.f64 (*.f64 a (*.f64 c -4)))

rewrite45.0ms (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:

8.0ms
(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
5.0ms
(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))
3.0ms
(sqrt.f64 (*.f64 a (*.f64 c -4)))
3.0ms
(+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))

simplify274.0ms (1.8%)

Algorithm
egg-herbie
Rules
500×associate-*l/_binary64
496×fma-def_binary64
478×fma-neg_binary64
422×associate-/r/_binary64
308×cancel-sign-sub-inv_binary64
Counts
206 → 291
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02616330
16445816
221635690
349385684
451875684

prune453.0ms (3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2883291
Fresh2810
Picked011
Done000
Total29012302
Error
3.2b
Counts
302 → 12
Alt Table
StatusErrorProgram
40.5b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2))))
41.5b
(*.f64 -1/2 (/.f64 (/.f64 (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) 3)) (+.f64 (*.f64 b b) (-.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 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))) a))
40.5b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
34.4b
(*.f64 -1/2 (*.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (cbrt.f64 a))))
48.2b
(*.f64 -1/2 (/.f64 (*.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
44.8b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (*.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
49.6b
(*.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) a) 3)))
45.6b
(*.f64 -1/2 (/.f64 (/.f64 (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a))
44.1b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
44.3b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
40.9b
(*.f64 -1/2 (/.f64 1 (*.f64 (/.f64 b (*.f64 -4 c)) -2)))
32.8b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))))
Compiler

Compiled 9250 to 6099 computations (34.1% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(*.f64 (cbrt.f64 a) (cbrt.f64 a))
0.6b
(cbrt.f64 a)
0.9b
(+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))
22.1b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series132.0ms (0.9%)

Counts
2 → 24
Calls

2 calls:

66.0ms
(*.f64 (cbrt.f64 a) (cbrt.f64 a))
65.0ms
(cbrt.f64 a)

rewrite14.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt_binary64
19×cbrt-prod_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
pow1_binary64
Counts
2 → 55
Calls

2 calls:

9.0ms
(*.f64 (cbrt.f64 a) (cbrt.f64 a))
1.0ms
(cbrt.f64 a)

simplify96.0ms (0.6%)

Algorithm
egg-herbie
Rules
577×distribute-rgt-in_binary64
561×log-prod_binary64
538×distribute-lft-in_binary64
525×unswap-sqr_binary64
384×fma-def_binary64
Counts
79 → 74
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
058610
198554
2296516
3769502
41799410
54642410
64805410

prune399.0ms (2.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New2940294
Fresh01010
Picked011
Done011
Total29412306
Error
3.2b
Counts
306 → 12
Alt Table
StatusErrorProgram
40.5b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2))))
41.5b
(*.f64 -1/2 (/.f64 (/.f64 (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) 3)) (+.f64 (*.f64 b b) (-.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 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))) a))
40.5b
(*.f64 -1/2 (*.f64 2 (/.f64 c b)))
34.4b
(*.f64 -1/2 (*.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (cbrt.f64 a))))
48.2b
(*.f64 -1/2 (/.f64 (*.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
44.8b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (*.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
49.6b
(*.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) a) 3)))
45.6b
(*.f64 -1/2 (/.f64 (/.f64 (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a))
44.1b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
44.3b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
40.9b
(*.f64 -1/2 (/.f64 1 (*.f64 (/.f64 b (*.f64 -4 c)) -2)))
32.8b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))))
Compiler

Compiled 13350 to 6936 computations (48% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (/.f64 b (*.f64 -4 c)) -2)
0.0b
(fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2))
0.0b
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2))))
1.1b
(/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2)))

series162.0ms (1.1%)

Counts
4 → 132
Calls

4 calls:

62.0ms
(/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2)))
51.0ms
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2))))
33.0ms
(fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2))
15.0ms
(*.f64 (/.f64 b (*.f64 -4 c)) -2)

rewrite46.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt_binary64
26×add-exp-log_binary64
24×*-un-lft-identity_binary64
23×times-frac_binary64
23×add-cube-cbrt_binary64
Counts
4 → 110
Calls

4 calls:

16.0ms
(*.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2))))
11.0ms
(*.f64 (/.f64 b (*.f64 -4 c)) -2)
5.0ms
(/.f64 1 (fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2)))
1.0ms
(fma.f64 -1/2 (/.f64 a b) (*.f64 (/.f64 b (*.f64 -4 c)) -2))

simplify209.0ms (1.4%)

Algorithm
egg-herbie
Rules
818×associate-/l*_binary64
726×associate-/r*_binary64
336×fma-def_binary64
155×associate-/l/_binary64
129×associate-/r/_binary64
Counts
242 → 205
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02085438
15134689
217304448
352794448

prune280.0ms (1.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New2023205
Fresh279
Picked101
Done022
Total20512217
Error
3.2b
Counts
217 → 12
Alt Table
StatusErrorProgram
44.3b
(*.f64 -1/2 (*.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
40.9b
(*.f64 -1/2 (/.f64 1 (*.f64 1/2 (/.f64 b c))))
34.4b
(*.f64 -1/2 (*.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (cbrt.f64 a))))
48.2b
(*.f64 -1/2 (/.f64 (*.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
44.8b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (*.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
49.6b
(*.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))) a) 3)))
45.6b
(*.f64 -1/2 (/.f64 (/.f64 (-.f64 (*.f64 b b) (fma.f64 a (*.f64 c -4) (*.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a))
44.1b
(*.f64 -1/2 (/.f64 (+.f64 b b) a))
41.5b
(*.f64 -1/2 (/.f64 (/.f64 (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) 3)) (+.f64 (*.f64 b b) (-.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 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))) a))
40.5b
(neg.f64 (/.f64 c b))
32.8b
(*.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))))
57.0b
(*.f64 -1/2 (log.f64 (exp.f64 (/.f64 2 (-.f64 (/.f64 b c) (/.f64 a b))))))
Compiler

Compiled 5213 to 3390 computations (35% saved)

regimes6.6s (44.3%)

Accuracy

Total 7.2b remaining (72.5%)

Threshold costs 0b (0%)

Counts
225 → 3
Compiler

Compiled 28608 to 19226 computations (32.8% saved)

bsearch60.0ms (0.4%)

Steps
ItersRangePoint
6
1.248413451690913e+92
1.9559568678196597e+93
7.08885791477575e+92
7
-1.6035107811692475e-69
-1.150435523968392e-71
-1.640926511843023e-70
Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03060
14260
24860
35260
45560
55660
65560

end1.0ms (0%)

Compiler

Compiled 44 to 29 computations (34.1% saved)

sample3.0s (20%)

Algorithm
intervals
Results
650.0ms1126×body2048valid
603.0ms5201×body128valid
364.0ms748×body1024valid
267.0ms380×body4096valid
114.0ms352×body512valid
74.0ms686×body128nan
42.0ms383×body128invalid
42.0ms193×body256valid
Compiler

Compiled 338 to 224 computations (33.7% saved)

Profiling

Loading profile data...