Details

Time bar (total: 8.6s)

analyze1.4s (16.6%)

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
0%99.9%0.1%5
0%99.9%0.1%6
0%95.2%4.8%7
0%94.4%5.6%8
0%91.7%8.3%9
0%88.7%11.3%10
0%86.1%13.9%11
0%83.6%16.4%12
0%81.8%18.2%13
0%79.8%20.2%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.9s (33%)

Results
722.0ms1157×body2048valid
679.0ms5364×body128valid
288.0ms738×body1024valid
280.0ms386×body8192exit
259.0ms444×body4096valid
123.0ms956×body128invalid
108.0ms345×body512valid
45.0ms208×body256valid
Compiler

Compiled 33 to 21 computations (36.4% saved)

simplify86.0ms (1%)

Algorithm
egg-herbie
Rules
808×fma-neg_binary64
379×associate-/l*_binary64
361×div-sub_binary64
341×fma-def_binary64
224×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01120
12318
23918
36918
410718
517818
627918
738218
854718
958718
1085518
11124718
12111718
13103518
14104318
15105118
16107718
17109318
18112918
19113118
20114318
21105018

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
34.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
34.5b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
Compiler

Compiled 58 to 30 computations (48.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
1.4b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
1.9b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
21.9b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

series499.0ms (5.8%)

Counts
4 → 96
Calls

4 calls:

293.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
116.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
79.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
11.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

rewrite32.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt_binary64
41×*-un-lft-identity_binary64
31×add-cube-cbrt_binary64
20×sqrt-prod_binary64
19×prod-diff_binary64
Counts
4 → 120
Calls

4 calls:

10.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
7.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
4.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
3.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

simplify301.0ms (3.5%)

Algorithm
egg-herbie
Rules
682×fma-neg_binary64
364×cancel-sign-sub-inv_binary64
248×distribute-rgt-neg-in_binary64
220×distribute-lft-neg-in_binary64
172×distribute-rgt-in_binary64
Counts
216 → 237
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02725492
16834712
224844515
345214514
449154514
549904514
650004514
749994514
849324514

prune159.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New22413237
Fresh000
Picked101
Done000
Total22513238
Error
6.6b
Counts
238 → 13
Alt Table
StatusErrorProgram
34.9b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) (/.f64 a (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))
38.0b
(*.f64 -1/2 (/.f64 c b_2))
34.5b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
42.5b
(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) 3) (pow.f64 b_2 3)) (+.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (+.f64 (*.f64 b_2 b_2) (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))) a)
49.1b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
42.5b
(fma.f64 -1/2 (/.f64 c b_2) (*.f64 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
51.5b
(exp.f64 (-.f64 (log.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (log.f64 a)))
41.3b
(/.f64 (cbrt.f64 (pow.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) 3)) a)
48.9b
(/.f64 (*.f64 -2 b_2) a)
32.7b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (cbrt.f64 a)))
40.9b
(expm1.f64 (log1p.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
56.1b
(/.f64 (-.f64 b_2 b_2) a)
34.5b
(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))
Compiler

Compiled 6067 to 1768 computations (70.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(*.f64 (cbrt.f64 a) (cbrt.f64 a))
0.6b
(cbrt.f64 a)
1.2b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
15.2b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series282.0ms (3.3%)

Counts
4 → 36
Calls

4 calls:

176.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
42.0ms
(cbrt.f64 a)
42.0ms
(*.f64 (cbrt.f64 a) (cbrt.f64 a))
21.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt_binary64
24×*-un-lft-identity_binary64
22×add-cube-cbrt_binary64
19×cbrt-prod_binary64
12×pow1_binary64
Counts
4 → 103
Calls

4 calls:

5.0ms
(*.f64 (cbrt.f64 a) (cbrt.f64 a))
3.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
2.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))
1.0ms
(cbrt.f64 a)

simplify102.0ms (1.2%)

Algorithm
egg-herbie
Rules
821×fma-def_binary64
559×associate-/l*_binary64
418×associate-/r*_binary64
233×fma-neg_binary64
200×cancel-sign-sub-inv_binary64
Counts
139 → 153
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01932143
13801657
212671554
343181545
449691545
548791545

prune108.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1872189
Fresh4812
Picked011
Done000
Total19111202
Error
0.3b
Counts
202 → 11
Alt Table
StatusErrorProgram
34.9b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) (/.f64 a (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))
38.0b
(*.f64 -1/2 (/.f64 c b_2))
34.5b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
42.5b
(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) 3) (pow.f64 b_2 3)) (+.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (+.f64 (*.f64 b_2 b_2) (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))) a)
49.1b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
42.5b
(fma.f64 -1/2 (/.f64 c b_2) (*.f64 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
46.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) (cbrt.f64 a)))
45.2b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) (cbrt.f64 a)))
32.7b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (cbrt.f64 a)))
40.9b
(expm1.f64 (log1p.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
34.5b
(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))
Compiler

Compiled 5673 to 1714 computations (69.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
1.4b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
1.9b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
21.9b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

series84.0ms (1%)

Counts
1 → 20
Calls

1 calls:

84.0ms
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64
13×associate-*r*_binary64
12×*-un-lft-identity_binary64
11×times-frac_binary64
10×add-exp-log_binary64
Counts
1 → 45
Calls

1 calls:

16.0ms
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

simplify92.0ms (1.1%)

Algorithm
egg-herbie
Rules
461×times-frac_binary64
381×associate-*l*_binary64
320×associate-/l*_binary64
257×associate-/r*_binary64
248×fma-neg_binary64
Counts
65 → 91
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01421800
13721651
212041581
347351581
449851581
549511581

prune146.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2412243
Fresh369
Picked011
Done101
Total2459254
Error
0.3b
Counts
254 → 9
Alt Table
StatusErrorProgram
34.5b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
42.5b
(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) 3) (pow.f64 b_2 3)) (+.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (+.f64 (*.f64 b_2 b_2) (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))) a)
49.1b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
42.7b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 c a (*.f64 b_2 b_2))) a) (+.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
42.5b
(fma.f64 -1/2 (/.f64 c b_2) (*.f64 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
38.0b
(*.f64 -1/2 (/.f64 c b_2))
32.2b
(pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 1)
46.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) (cbrt.f64 a)))
45.2b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) (cbrt.f64 a)))
Compiler

Compiled 6355 to 2216 computations (65.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
0.1b
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
1.2b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
15.2b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series355.0ms (4.1%)

Counts
2 → 26
Calls

2 calls:

229.0ms
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
125.0ms
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

rewrite9.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
15×times-frac_binary64
12×add-cube-cbrt_binary64
associate-/l*_binary64
Counts
2 → 50
Calls

2 calls:

5.0ms
(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
0.0ms
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

simplify85.0ms (1%)

Algorithm
egg-herbie
Rules
665×fma-def_binary64
616×associate-/l*_binary64
532×associate-/r*_binary64
196×associate-*l/_binary64
194×fma-neg_binary64
Counts
76 → 99
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01742173
14532043
213421943
346061941
449981941

prune124.0ms (1.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1732175
Fresh077
Picked011
Done011
Total17311184
Error
0.1b
Counts
184 → 11
Alt Table
StatusErrorProgram
44.9b
(pow.f64 (/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) a) 1)
34.5b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
42.5b
(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) 3) (pow.f64 b_2 3)) (+.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (+.f64 (*.f64 b_2 b_2) (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))) a)
46.6b
(pow.f64 (/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) a) 1)
32.2b
(pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a) 1)
49.1b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
42.7b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 c a (*.f64 b_2 b_2))) a) (+.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))
42.5b
(fma.f64 -1/2 (/.f64 c b_2) (*.f64 (/.f64 (*.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
38.0b
(*.f64 -1/2 (/.f64 c b_2))
46.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) (cbrt.f64 a)))
45.2b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) (cbrt.f64 a)))
Compiler

Compiled 4701 to 1705 computations (63.7% saved)

regimes1.6s (18.1%)

Accuracy

Total 9.4b remaining (98.6%)

Threshold costs 0b (0%)

Counts
138 → 3
Compiler

Compiled 13292 to 7122 computations (46.4% saved)

bsearch83.0ms (1%)

Steps
ItersRangePoint
8
9.825083045698206e-99
2.2274204836273953e-94
1.7908910694223973e-96
9
-3.5867331195417755e+161
-2.4253433369542276e+152
-9.131732657146973e+152
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: 1 (0.0ms)

IterNodesCost
02548
13946
25246
36346
47146
57546
67646
77546

end158.0ms (1.8%)

Compiler

Compiled 301 to 176 computations (41.5% saved)

Profiling

Loading profile data...