Details

Time bar (total: 7.9s)

analyze1.8s (23.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
3.9%95.8%0.3%11
7.4%92.3%0.3%12
8.8%90.9%0.3%13
10.2%89.5%0.3%14
Compiler

Compiled 24 to 16 computations (33.3% saved)

sample1.4s (17.9%)

Results
1.3s8256×body128valid
51.0ms263×body128invalid
Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
16×fma-def_binary64
+-commutative_binary64
*-commutative_binary64
associate-/l*_binary64
associate-/r/_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01625
12925
24121
35121
46121
56521
66421

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
12.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
15.7b
(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
16.3b
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
Compiler

Compiled 126 to 78 computations (38.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 1 (fma.f64 b (/.f64 y t) a))
2.4b
(fma.f64 y (/.f64 z t) x)
3.2b
(fma.f64 b (/.f64 y t) a)
11.7b
(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

series258.0ms (3.3%)

Counts
4 → 216
Calls

4 calls:

216.0ms
(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
14.0ms
(fma.f64 y (/.f64 z t) x)
14.0ms
(+.f64 1 (fma.f64 b (/.f64 y t) a))
13.0ms
(fma.f64 b (/.f64 y t) a)

rewrite10.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity_binary64
14×add-sqr-sqrt_binary64
14×add-cube-cbrt_binary64
12×times-frac_binary64
add-cbrt-cube_binary64
Counts
4 → 73
Calls

4 calls:

3.0ms
(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
2.0ms
(+.f64 1 (fma.f64 b (/.f64 y t) a))
0.0ms
(fma.f64 b (/.f64 y t) a)
0.0ms
(fma.f64 y (/.f64 z t) x)

simplify135.0ms (1.7%)

Algorithm
egg-herbie
Rules
741×times-frac_binary64
527×associate-/l*_binary64
403×associate-/r*_binary64
235×fma-def_binary64
208×associate-*l*_binary64
Counts
289 → 158
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04409932
113799371
250369371

prune236.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1499158
Fresh011
Picked101
Done000
Total15010160
Error
0.0b
Counts
160 → 10
Alt Table
StatusErrorProgram
15.7b
(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 (fma.f64 b (/.f64 y t) 1) a))
15.0b
(+.f64 (/.f64 (*.f64 y z) (*.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
16.0b
(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
16.3b
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
16.5b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (cbrt.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a))))) (cbrt.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
15.1b
(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
50.4b
(-.f64 (fma.f64 2 (/.f64 (*.f64 a (*.f64 z (*.f64 t t))) (*.f64 (*.f64 y y) (pow.f64 b 3))) (+.f64 (fma.f64 (*.f64 (/.f64 t y) (/.f64 t y)) (/.f64 z (pow.f64 b 3)) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 (*.f64 a (*.f64 a (*.f64 z (*.f64 t t)))) (*.f64 (*.f64 y y) (pow.f64 b 3)))))) (fma.f64 (/.f64 t y) (/.f64 z (*.f64 b b)) (fma.f64 (*.f64 (/.f64 t y) (/.f64 t y)) (/.f64 x (*.f64 b b)) (fma.f64 (/.f64 a y) (/.f64 (*.f64 z t) (*.f64 b b)) (/.f64 (*.f64 a (*.f64 x (*.f64 t t))) (*.f64 y (*.f64 y (*.f64 b b))))))))
43.2b
(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (*.f64 b b)) (/.f64 (*.f64 a (*.f64 z t)) (*.f64 y (*.f64 b b)))))
43.9b
(-.f64 (+.f64 (/.f64 z b) (/.f64 (*.f64 t x) (*.f64 y b))) (+.f64 (/.f64 (*.f64 t z) (*.f64 y (pow.f64 b 2))) (/.f64 (*.f64 a (*.f64 t z)) (*.f64 y (pow.f64 b 2)))))
45.0b
(/.f64 z b)
Compiler

Compiled 8876 to 3999 computations (54.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.5b
(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
4.9b
(/.f64 (*.f64 y b) t)
5.5b
(*.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t)
12.4b
(/.f64 (*.f64 y z) (*.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series265.0ms (3.4%)

Counts
4 → 152
Calls

4 calls:

124.0ms
(/.f64 (*.f64 y z) (*.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
112.0ms
(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
17.0ms
(*.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t)
12.0ms
(/.f64 (*.f64 y b) t)

rewrite30.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity_binary64
25×add-cbrt-cube_binary64
25×add-exp-log_binary64
20×add-sqr-sqrt_binary64
19×times-frac_binary64
Counts
4 → 111
Calls

4 calls:

8.0ms
(*.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t)
7.0ms
(/.f64 (*.f64 y z) (*.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
6.0ms
(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
3.0ms
(/.f64 (*.f64 y b) t)

simplify185.0ms (2.3%)

Algorithm
egg-herbie
Rules
687×associate-/l*_binary64
522×associate-/r*_binary64
472×fma-def_binary64
298×associate-*l*_binary64
156×associate-*l/_binary64
Counts
263 → 241
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
043010630
113689571
249359243
352549243

prune315.0ms (4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2645269
Fresh459
Picked101
Done000
Total26910279
Error
0.0b
Counts
279 → 10
Alt Table
StatusErrorProgram
43.9b
(-.f64 (+.f64 (/.f64 z b) (/.f64 (*.f64 t x) (*.f64 y b))) (+.f64 (/.f64 (*.f64 t z) (*.f64 y (pow.f64 b 2))) (/.f64 (*.f64 a (*.f64 t z)) (*.f64 y (pow.f64 b 2)))))
12.6b
(+.f64 (/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
16.0b
(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
16.3b
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
12.8b
(+.f64 (/.f64 y (/.f64 (*.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
15.0b
(+.f64 (*.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))) (/.f64 z t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
26.2b
(+.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 y z) (*.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))) (sqrt.f64 (/.f64 (*.f64 y z) (*.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t)))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
50.4b
(-.f64 (fma.f64 2 (/.f64 (*.f64 a (*.f64 z (*.f64 t t))) (*.f64 (*.f64 y y) (pow.f64 b 3))) (+.f64 (fma.f64 (*.f64 (/.f64 t y) (/.f64 t y)) (/.f64 z (pow.f64 b 3)) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 (*.f64 a (*.f64 a (*.f64 z (*.f64 t t)))) (*.f64 (*.f64 y y) (pow.f64 b 3)))))) (fma.f64 (/.f64 t y) (/.f64 z (*.f64 b b)) (fma.f64 (*.f64 (/.f64 t y) (/.f64 t y)) (/.f64 x (*.f64 b b)) (fma.f64 (/.f64 a y) (/.f64 (*.f64 z t) (*.f64 b b)) (/.f64 (*.f64 a (*.f64 x (*.f64 t t))) (*.f64 y (*.f64 y (*.f64 b b))))))))
43.2b
(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (*.f64 b b)) (/.f64 (*.f64 a (*.f64 z t)) (*.f64 y (*.f64 b b)))))
28.7b
(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
Compiler

Compiled 12159 to 4662 computations (61.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 a (/.f64 (*.f64 y b) t))
4.5b
(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
4.9b
(/.f64 (*.f64 y b) t)
12.4b
(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))

series130.0ms (1.6%)

Counts
2 → 72
Calls

2 calls:

115.0ms
(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))
15.0ms
(+.f64 a (/.f64 (*.f64 y b) t))

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
2 → 40
Calls

2 calls:

3.0ms
(+.f64 a (/.f64 (*.f64 y b) t))
3.0ms
(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))

simplify105.0ms (1.3%)

Algorithm
egg-herbie
Rules
490×cancel-sign-sub-inv_binary64
484×times-frac_binary64
340×associate-/l*_binary64
241×associate-/r*_binary64
219×fma-neg_binary64
Counts
112 → 102
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02524598
17874250
239264208
353314208

prune344.0ms (4.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2142216
Fresh279
Picked101
Done000
Total2179226
Error
0.0b
Counts
226 → 9
Alt Table
StatusErrorProgram
16.0b
(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
16.3b
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
15.0b
(+.f64 (*.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))) (/.f64 z t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
25.3b
(+.f64 (*.f64 (sqrt.f64 (/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))) (sqrt.f64 (/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t))))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
50.4b
(-.f64 (fma.f64 2 (/.f64 (*.f64 a (*.f64 z (*.f64 t t))) (*.f64 (*.f64 y y) (pow.f64 b 3))) (+.f64 (fma.f64 (*.f64 (/.f64 t y) (/.f64 t y)) (/.f64 z (pow.f64 b 3)) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 (*.f64 a (*.f64 a (*.f64 z (*.f64 t t)))) (*.f64 (*.f64 y y) (pow.f64 b 3)))))) (fma.f64 (/.f64 t y) (/.f64 z (*.f64 b b)) (fma.f64 (*.f64 (/.f64 t y) (/.f64 t y)) (/.f64 x (*.f64 b b)) (fma.f64 (/.f64 a y) (/.f64 (*.f64 z t) (*.f64 b b)) (/.f64 (*.f64 a (*.f64 x (*.f64 t t))) (*.f64 y (*.f64 y (*.f64 b b))))))))
43.2b
(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (*.f64 b b)) (/.f64 (*.f64 a (*.f64 z t)) (*.f64 y (*.f64 b b)))))
43.9b
(-.f64 (+.f64 (/.f64 z b) (/.f64 (*.f64 t x) (*.f64 y b))) (+.f64 (/.f64 (*.f64 t z) (*.f64 y (pow.f64 b 2))) (/.f64 (*.f64 a (*.f64 t z)) (*.f64 y (pow.f64 b 2)))))
28.7b
(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
10.6b
(+.f64 (/.f64 y (/.f64 (fma.f64 y b (fma.f64 a t t)) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
Compiler

Compiled 9471 to 3308 computations (65.1% saved)

localize38.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.5b
(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
4.9b
(/.f64 (*.f64 y b) t)
5.2b
(/.f64 (fma.f64 y b (fma.f64 a t t)) z)
7.1b
(/.f64 y (/.f64 (fma.f64 y b (fma.f64 a t t)) z))

series216.0ms (2.7%)

Counts
2 → 120
Calls

2 calls:

182.0ms
(/.f64 y (/.f64 (fma.f64 y b (fma.f64 a t t)) z))
33.0ms
(/.f64 (fma.f64 y b (fma.f64 a t t)) z)

rewrite18.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
84×times-frac_binary64
52×*-un-lft-identity_binary64
52×add-sqr-sqrt_binary64
52×add-cube-cbrt_binary64
16×associate-/r*_binary64
Counts
2 → 101
Calls

2 calls:

4.0ms
(/.f64 y (/.f64 (fma.f64 y b (fma.f64 a t t)) z))
2.0ms
(/.f64 (fma.f64 y b (fma.f64 a t t)) z)

simplify237.0ms (3%)

Algorithm
egg-herbie
Rules
478×times-frac_binary64
346×associate-/l*_binary64
253×associate-/r*_binary64
237×fma-neg_binary64
198×unswap-sqr_binary64
Counts
221 → 237
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03457620
19347228
243057177
349927177
449957177

prune353.0ms (4.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3492351
Fresh268
Picked101
Done000
Total3528360
Error
0.0b
Counts
360 → 8
Alt Table
StatusErrorProgram
16.0b
(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
16.3b
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
10.9b
(+.f64 (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (fma.f64 y b (fma.f64 t a t)) (*.f64 z (cbrt.f64 y)))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
50.4b
(-.f64 (fma.f64 2 (/.f64 (*.f64 a (*.f64 z (*.f64 t t))) (*.f64 (*.f64 y y) (pow.f64 b 3))) (+.f64 (fma.f64 (*.f64 (/.f64 t y) (/.f64 t y)) (/.f64 z (pow.f64 b 3)) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 (*.f64 a (*.f64 a (*.f64 z (*.f64 t t)))) (*.f64 (*.f64 y y) (pow.f64 b 3)))))) (fma.f64 (/.f64 t y) (/.f64 z (*.f64 b b)) (fma.f64 (*.f64 (/.f64 t y) (/.f64 t y)) (/.f64 x (*.f64 b b)) (fma.f64 (/.f64 a y) (/.f64 (*.f64 z t) (*.f64 b b)) (/.f64 (*.f64 a (*.f64 x (*.f64 t t))) (*.f64 y (*.f64 y (*.f64 b b))))))))
43.2b
(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (*.f64 b b)) (/.f64 (*.f64 a (*.f64 z t)) (*.f64 y (*.f64 b b)))))
43.9b
(-.f64 (+.f64 (/.f64 z b) (/.f64 (*.f64 t x) (*.f64 y b))) (+.f64 (/.f64 (*.f64 t z) (*.f64 y (pow.f64 b 2))) (/.f64 (*.f64 a (*.f64 t z)) (*.f64 y (pow.f64 b 2)))))
28.7b
(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
10.9b
(+.f64 (/.f64 y (/.f64 (+.f64 (*.f64 y b) (+.f64 t (*.f64 a t))) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
Compiler

Compiled 14039 to 4110 computations (70.7% saved)

regimes1.5s (18.7%)

Accuracy

Total 8.3b remaining (96.4%)

Threshold costs 0b (0%)

Counts
126 → 4
Compiler

Compiled 30103 to 17346 computations (42.4% saved)

bsearch77.0ms (1%)

Steps
ItersRangePoint
8
1.3938806967303927e+270
1.0988210929937358e+274
5.257518677882633e+271
9
1.4574859568117804e+123
2.4297222063334165e+131
8.803249001269132e+124
8
-6.6454693031015914e+72
-3.805095483585008e+68
-5.847993058855016e+71
Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0.1%)

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
047139
161139
265139
367139
468139
567139

end172.0ms (2.2%)

Compiler

Compiled 527 to 267 computations (49.3% saved)

Profiling

Loading profile data...