Details

Time bar (total: 10.9s)

analyze1.8s (16.5%)

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)

sample1.5s (13.9%)

Results
1.4s8256×body128valid
43.0ms277×body128invalid
Compiler

Compiled 71 to 47 computations (33.8% saved)

simplify8.0ms (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%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
13.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
18.5b
(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
18.2b
(/.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 x (/.f64 (*.f64 y z) t))
3.7b
(/.f64 (*.f64 y z) t)
5.1b
(/.f64 (*.f64 y b) t)
13.5b
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

series276.0ms (2.5%)

Counts
4 → 120
Calls

4 calls:

232.0ms
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
16.0ms
(/.f64 (*.f64 y b) t)
15.0ms
(+.f64 x (/.f64 (*.f64 y z) t))
13.0ms
(/.f64 (*.f64 y z) t)

rewrite28.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
59×*-un-lft-identity_binary64
26×times-frac_binary64
22×distribute-lft-out_binary64
20×add-sqr-sqrt_binary64
20×add-cube-cbrt_binary64
Counts
4 → 112
Calls

4 calls:

11.0ms
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
3.0ms
(+.f64 x (/.f64 (*.f64 y z) t))
3.0ms
(/.f64 (*.f64 y b) t)
3.0ms
(/.f64 (*.f64 y z) t)

simplify158.0ms (1.4%)

Algorithm
egg-herbie
Rules
897×times-frac_binary64
656×associate-/l*_binary64
274×fma-def_binary64
148×+-commutative_binary64
118×distribute-rgt-in_binary64
Counts
232 → 201
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
052110152
116269540
250479540

prune249.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1929201
Fresh011
Picked101
Done000
Total19310203
Error
0.0b
Counts
203 → 10
Alt Table
StatusErrorProgram
32.8b
(-.f64 (+.f64 (/.f64 x (+.f64 1 a)) (/.f64 (*.f64 y z) (*.f64 (+.f64 1 a) t))) (/.f64 (*.f64 y (*.f64 b x)) (*.f64 (pow.f64 (+.f64 1 a) 2) t)))
18.5b
(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
41.3b
(-.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)))))
42.9b
(-.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)))))
43.0b
(/.f64 z b)
32.7b
(/.f64 (+.f64 x (*.f64 (sqrt.f64 (/.f64 (*.f64 y z) t)) (sqrt.f64 (/.f64 (*.f64 y z) t)))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
18.0b
(fma.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)))))
16.8b
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))
20.4b
(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
39.9b
(-.f64 (fma.f64 (/.f64 y t) (/.f64 z (+.f64 1 (/.f64 (*.f64 y b) t))) (/.f64 x (+.f64 1 (/.f64 (*.f64 y b) t)))) (fma.f64 (/.f64 a t) (/.f64 (*.f64 y z) (pow.f64 (+.f64 1 (/.f64 (*.f64 y b) t)) 2)) (/.f64 (*.f64 a x) (pow.f64 (+.f64 1 (/.f64 (*.f64 y b) t)) 2))))
Compiler

Compiled 10287 to 4431 computations (56.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 t)
2.9b
(*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))
3.7b
(/.f64 (*.f64 y z) t)
13.5b
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))

series323.0ms (3%)

Counts
3 → 120
Calls

3 calls:

242.0ms
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))
45.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))
35.0ms
(cbrt.f64 t)

rewrite33.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt_binary64
40×times-frac_binary64
36×*-un-lft-identity_binary64
28×add-cube-cbrt_binary64
26×add-exp-log_binary64
Counts
3 → 117
Calls

3 calls:

12.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))
9.0ms
(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))
1.0ms
(cbrt.f64 t)

simplify164.0ms (1.5%)

Algorithm
egg-herbie
Rules
914×times-frac_binary64
680×associate-/l*_binary64
295×fma-def_binary64
151×+-commutative_binary64
144×*-commutative_binary64
Counts
237 → 250
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
058211367
118159780
252579780

prune335.0ms (3.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3092311
Fresh279
Picked101
Done000
Total3129321
Error
0.0b
Counts
321 → 9
Alt Table
StatusErrorProgram
32.8b
(-.f64 (+.f64 (/.f64 x (+.f64 1 a)) (/.f64 (*.f64 y z) (*.f64 (+.f64 1 a) t))) (/.f64 (*.f64 y (*.f64 b x)) (*.f64 (pow.f64 (+.f64 1 a) 2) t)))
18.5b
(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
41.3b
(-.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)))))
42.9b
(-.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)))))
43.0b
(/.f64 z b)
32.7b
(/.f64 (+.f64 x (*.f64 (sqrt.f64 (/.f64 (*.f64 y z) t)) (sqrt.f64 (/.f64 (*.f64 y z) t)))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
18.0b
(fma.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)))))
32.8b
(*.f64 (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (-.f64 (pow.f64 (+.f64 1 a) 2) (*.f64 (/.f64 (*.f64 y b) t) (/.f64 (*.f64 y b) t)))) (-.f64 (+.f64 a 1) (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))
18.2b
(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))
Compiler

Compiled 14774 to 5532 computations (62.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
2.7b
(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
4.6b
(/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
5.1b
(/.f64 (*.f64 y b) t)
10.4b
(fma.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)))))

series521.0ms (4.8%)

Counts
3 → 168
Calls

3 calls:

318.0ms
(fma.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)))))
123.0ms
(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
79.0ms
(/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
63×*-un-lft-identity_binary64
30×times-frac_binary64
24×distribute-lft-out_binary64
23×add-sqr-sqrt_binary64
23×add-cube-cbrt_binary64
Counts
3 → 88
Calls

3 calls:

8.0ms
(/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
7.0ms
(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
0.0ms
(fma.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)))))

simplify220.0ms (2%)

Algorithm
egg-herbie
Rules
678×associate-/l*_binary64
534×associate-/r*_binary64
291×fma-def_binary64
174×+-commutative_binary64
163×associate-*l/_binary64
Counts
256 → 200
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
055616369
1178715540
2511315540

prune331.0ms (3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2524256
Fresh268
Picked011
Done000
Total25411265
Error
0.0b
Counts
265 → 11
Alt Table
StatusErrorProgram
42.0b
(cbrt.f64 (pow.f64 (fma.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))))) 3))
39.2b
(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
32.8b
(-.f64 (+.f64 (/.f64 x (+.f64 1 a)) (/.f64 (*.f64 y z) (*.f64 (+.f64 1 a) t))) (/.f64 (*.f64 y (*.f64 b x)) (*.f64 (pow.f64 (+.f64 1 a) 2) t)))
18.5b
(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
18.0b
(fma.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)))))
35.1b
(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))) (/.f64 z t) (-.f64 (/.f64 x (+.f64 1 (/.f64 (*.f64 y b) t))) (/.f64 (*.f64 a x) (pow.f64 (+.f64 1 (/.f64 (*.f64 y b) t)) 2))))
18.2b
(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))
29.2b
(fma.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))) 3)) (/.f64 z t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
41.3b
(-.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)))))
43.0b
(/.f64 z b)
32.7b
(/.f64 (+.f64 x (*.f64 (sqrt.f64 (/.f64 (*.f64 y z) t)) (sqrt.f64 (/.f64 (*.f64 y z) t)))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
Compiler

Compiled 14617 to 6341 computations (56.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 t)
2.9b
(*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))
7.3b
(/.f64 y (/.f64 t z))
13.5b
(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))

series250.0ms (2.3%)

Counts
2 → 108
Calls

2 calls:

235.0ms
(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))
14.0ms
(/.f64 y (/.f64 t z))

rewrite34.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
87×times-frac_binary64
61×*-un-lft-identity_binary64
53×add-sqr-sqrt_binary64
53×add-cube-cbrt_binary64
16×associate-/r*_binary64
Counts
2 → 115
Calls

2 calls:

20.0ms
(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))
4.0ms
(/.f64 y (/.f64 t z))

simplify206.0ms (1.9%)

Algorithm
egg-herbie
Rules
854×times-frac_binary64
638×associate-/l*_binary64
295×fma-def_binary64
204×associate-/r/_binary64
159×associate-/l/_binary64
Counts
223 → 242
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
060211121
117909810
252829810

prune587.0ms (5.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New3921393
Fresh099
Picked011
Done011
Total39212404
Error
0.0b
Counts
404 → 12
Alt Table
StatusErrorProgram
42.0b
(cbrt.f64 (pow.f64 (fma.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))))) 3))
39.2b
(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
32.8b
(-.f64 (+.f64 (/.f64 x (+.f64 1 a)) (/.f64 (*.f64 y z) (*.f64 (+.f64 1 a) t))) (/.f64 (*.f64 y (*.f64 b x)) (*.f64 (pow.f64 (+.f64 1 a) 2) t)))
18.5b
(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
18.0b
(fma.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)))))
35.1b
(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))) (/.f64 z t) (-.f64 (/.f64 x (+.f64 1 (/.f64 (*.f64 y b) t))) (/.f64 (*.f64 a x) (pow.f64 (+.f64 1 (/.f64 (*.f64 y b) t)) 2))))
18.2b
(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))
29.2b
(fma.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))) 3)) (/.f64 z t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
41.3b
(-.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)))))
43.0b
(/.f64 z b)
32.7b
(/.f64 (+.f64 x (*.f64 (sqrt.f64 (/.f64 (*.f64 y z) t)) (sqrt.f64 (/.f64 (*.f64 y z) t)))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
38.6b
(/.f64 (+.f64 x (*.f64 (/.f64 (sqrt.f64 y) (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (sqrt.f64 y) (/.f64 t (cbrt.f64 z))))) (+.f64 (+.f64 a 1) (*.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))
Compiler

Compiled 17289 to 6100 computations (64.7% saved)

regimes3.5s (32.3%)

Accuracy

Total 7.4b remaining (96.9%)

Threshold costs 0b (0%)

Counts
169 → 5
Compiler

Compiled 39388 to 24454 computations (37.9% saved)

bsearch8.0ms (0.1%)

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify19.0ms (0.2%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
054247
181245
2106245
3135245
4157245
5168245
6173245
7174245
8172245

end227.0ms (2.1%)

Compiler

Compiled 711 to 347 computations (51.2% saved)

Profiling

Loading profile data...