Details

Time bar (total: 12.7s)

analyze3.5s (27.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
9.4%90.4%0.2%11
9.4%90.4%0.2%12
10.1%89.6%0.2%13
20.8%78.9%0.2%14
Compiler

Compiled 19 to 14 computations (26.3% saved)

sample92.0ms (0.7%)

Algorithm
intervals
Results
28.0ms256×body128valid
8.0ms82×body128invalid
Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify224.0ms (1.8%)

Algorithm
egg-herbie
Rules
2966×fma-def_binary64
757×fma-neg_binary64
541×cancel-sign-sub-inv_binary64
473×associate-/l/_binary64
472×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01419
13117
210317
331817
479417
5152617
6205417
7228117
8297517
9354017
10395417
11415817
12409717
13410817
14411817
15446217
16453117
17453617
18453617
19647417

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
8.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
8.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
8.3b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
Compiler

Compiled 100 to 69 computations (31% saved)

localize18.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.5b
(fma.f64 -9 (*.f64 z t) (*.f64 x y))
7.8b
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))

series96.0ms (0.8%)

Counts
2 → 108
Calls

2 calls:

75.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
20.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

rewrite14.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt_binary64
13×associate-*r*_binary64
10×times-frac_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
Counts
2 → 44
Calls

2 calls:

9.0ms
(*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))
1.0ms
(fma.f64 -9 (*.f64 z t) (*.f64 x y))

simplify189.0ms (1.5%)

Algorithm
egg-herbie
Rules
937×fma-def_binary64
487×associate-*l*_binary64
418×associate-*r*_binary64
225×associate-*r/_binary64
211×associate-*l/_binary64
Counts
152 → 88
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01082547
12482243
28122243
332062242
449372242
550192242

prune178.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New761288
Fresh011
Picked101
Done000
Total771390
Error
7.8b
Counts
90 → 13
Alt Table
StatusErrorProgram
35.1b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a) 3))
8.7b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
29.5b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
29.5b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
9.0b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (cbrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)))) (*.f64 (cbrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (/.f64 1/2 a)))
9.0b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1/2 (cbrt.f64 a)))
8.2b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
36.1b
(*.f64 (sqrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (*.f64 (sqrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (/.f64 1/2 a)))
35.5b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
34.3b
(*.f64 (sqrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))) (sqrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))))
9.1b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))) (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a)))) (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))))
8.2b
(/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a)
Compiler

Compiled 2282 to 1250 computations (45.2% saved)

localize19.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(*.f64 1/2 (*.f64 y x))
0.5b
(fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x)))
7.8b
(/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a)

series105.0ms (0.8%)

Counts
3 → 108
Calls

3 calls:

69.0ms
(/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a)
27.0ms
(fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x)))
9.0ms
(*.f64 1/2 (*.f64 y x))

rewrite17.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
Counts
3 → 59
Calls

3 calls:

7.0ms
(*.f64 1/2 (*.f64 y x))
5.0ms
(/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a)
1.0ms
(fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x)))

simplify147.0ms (1.2%)

Algorithm
egg-herbie
Rules
455×associate-*l*_binary64
428×distribute-rgt-in_binary64
425×distribute-lft-in_binary64
423×fma-def_binary64
320×associate-*r*_binary64
Counts
167 → 77
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01142934
12342627
26112624
318562624
449452624

prune173.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New75277
Fresh11112
Picked101
Done000
Total771390
Error
7.8b
Counts
90 → 13
Alt Table
StatusErrorProgram
35.1b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a) 3))
8.7b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
8.2b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.3b
(/.f64 1 (/.f64 a (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x)))))
29.5b
(*.f64 (*.f64 y x) (/.f64 1/2 a))
29.5b
(*.f64 1/2 (/.f64 (*.f64 y x) a))
9.0b
(*.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 1/2 (cbrt.f64 a)))
8.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
36.1b
(*.f64 (sqrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (*.f64 (sqrt.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y))) (/.f64 1/2 a)))
35.5b
(*.f64 (*.f64 -9 (*.f64 t z)) (/.f64 1/2 a))
34.3b
(*.f64 (sqrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))) (sqrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))))
9.1b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))) (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a)))) (cbrt.f64 (*.f64 (fma.f64 -9 (*.f64 z t) (*.f64 x y)) (/.f64 1/2 a))))
8.7b
(/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 1/2) (*.f64 y x)))) a)
Compiler

Compiled 2049 to 1120 computations (45.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
0.2b
(*.f64 9/2 (/.f64 (*.f64 t z) a))
4.9b
(/.f64 (*.f64 y x) a)
8.1b
(/.f64 (*.f64 t z) a)

series166.0ms (1.3%)

Counts
4 → 24
Calls

4 calls:

82.0ms
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
30.0ms
(*.f64 9/2 (/.f64 (*.f64 t z) a))
27.0ms
(/.f64 (*.f64 t z) a)
27.0ms
(/.f64 (*.f64 y x) a)

rewrite44.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
23×add-cbrt-cube_binary64
23×add-exp-log_binary64
13×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
Counts
4 → 93
Calls

4 calls:

12.0ms
(*.f64 9/2 (/.f64 (*.f64 t z) a))
9.0ms
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.0ms
(/.f64 (*.f64 y x) a)
7.0ms
(/.f64 (*.f64 t z) a)

simplify116.0ms (0.9%)

Algorithm
egg-herbie
Rules
676×times-frac_binary64
581×fma-def_binary64
359×*-commutative_binary64
335×associate-/l/_binary64
254×associate-/r*_binary64
Counts
117 → 134
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01681744
14231541
215231530
341621530
449411530

prune252.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1259134
Fresh9312
Picked101
Done000
Total13512147
Error
0.7b
Counts
147 → 12
Alt Table
StatusErrorProgram
35.1b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a) 3))
8.7b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
8.2b
(+.f64 (/.f64 (fma.f64 -9/2 (*.f64 t z) (*.f64 1/2 (*.f64 y x))) a) 0)
6.2b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 t (/.f64 z a))))
8.1b
(-.f64 (*.f64 1/2 (*.f64 y (/.f64 x a))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
9.0b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 x (cbrt.f64 a)))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
6.6b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 (*.f64 z (/.f64 t (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (cbrt.f64 a))))
6.1b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 t (/.f64 a z))))
6.2b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 t 9/2) (/.f64 z a)))
33.9b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 (/.f64 t (sqrt.f64 a)) (/.f64 z (sqrt.f64 a)))))
8.0b
(-.f64 (*.f64 1/2 (/.f64 y (/.f64 a x))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
Compiler

Compiled 3316 to 1470 computations (55.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 t (/.f64 a z))))
0.2b
(*.f64 9/2 (/.f64 t (/.f64 a z)))
4.2b
(/.f64 t (/.f64 a z))
4.9b
(/.f64 (*.f64 y x) a)

series127.0ms (1%)

Counts
3 → 132
Calls

3 calls:

74.0ms
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 t (/.f64 a z))))
28.0ms
(*.f64 9/2 (/.f64 t (/.f64 a z)))
24.0ms
(/.f64 t (/.f64 a z))

rewrite64.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
144×times-frac_binary64
90×add-sqr-sqrt_binary64
81×*-un-lft-identity_binary64
81×add-cube-cbrt_binary64
44×associate-*r*_binary64
Counts
3 → 157
Calls

3 calls:

21.0ms
(*.f64 9/2 (/.f64 t (/.f64 a z)))
9.0ms
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (/.f64 t (/.f64 a z))))
8.0ms
(/.f64 t (/.f64 a z))

simplify239.0ms (1.9%)

Algorithm
egg-herbie
Rules
635×associate-/l*_binary64
617×fma-def_binary64
601×associate-/r/_binary64
441×times-frac_binary64
162×*-commutative_binary64
Counts
289 → 257
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02704402
16384164
221154148
346044148
449424148

prune505.0ms (4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2832285
Fresh3811
Picked101
Done000
Total28710297
Error
0.0b
Counts
297 → 10
Alt Table
StatusErrorProgram
35.1b
(cbrt.f64 (pow.f64 (/.f64 (fma.f64 (*.f64 t z) -9/2 (*.f64 1/2 (*.f64 y x))) a) 3))
8.7b
(*.f64 (*.f64 (fma.f64 y x (*.f64 (*.f64 t z) -9)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) a))
8.2b
(+.f64 (/.f64 (fma.f64 -9/2 (*.f64 t z) (*.f64 1/2 (*.f64 y x))) a) 0)
6.2b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 t (/.f64 z a))))
8.1b
(-.f64 (*.f64 1/2 (*.f64 y (/.f64 x a))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
6.1b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 9/2 (*.f64 (/.f64 t a) z)))
9.0b
(-.f64 (*.f64 1/2 (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 x (cbrt.f64 a)))) (*.f64 9/2 (/.f64 (*.f64 t z) a)))
8.5b
(/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))
5.0b
(-.f64 (*.f64 1/2 (/.f64 y (/.f64 a x))) (*.f64 9/2 (/.f64 t (/.f64 a z))))
6.2b
(-.f64 (*.f64 1/2 (/.f64 (*.f64 y x) a)) (*.f64 (*.f64 t 9/2) (/.f64 z a)))
Compiler

Compiled 6790 to 2462 computations (63.7% saved)

regimes3.7s (28.9%)

Accuracy

Total 1.2b remaining (97.4%)

Threshold costs 0b (0%)

Counts
102 → 3
Compiler

Compiled 27520 to 18684 computations (32.1% saved)

bsearch8.0ms (0.1%)

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
12×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
distribute-rgt-neg-in_binary64
neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03079
15079
27379
38679
49579
59879
69679

end75.0ms (0.6%)

Remove

(sort z t)

Compiler

Compiled 406 to 259 computations (36.2% saved)

sample2.6s (20.4%)

Algorithm
intervals
Results
766.0ms8000×body128valid
310.0ms3118×body128invalid
Compiler

Compiled 287 to 201 computations (30% saved)

Profiling

Loading profile data...