Details

Time bar (total: 5.1s)

analyze159.0ms (3.1%)

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%50%50%4
0%50%50%5
12.5%37.5%50%6
18.7%31.2%50%7
28.1%21.9%50%8
32.8%17.2%50%9
38.2%11.7%50%10
41%9%50%11
43.9%6%50%12
45.4%4.6%50%13
46.9%3.1%50%14
Compiler

Compiled 31 to 22 computations (29% saved)

sample1.3s (25.8%)

Results
1.3s8256×body128valid
3.0ms19×body128invalid
Compiler

Compiled 92 to 65 computations (29.3% saved)

simplify33.0ms (0.7%)

Algorithm
egg-herbie
Rules
826×times-frac_binary64
592×fma-def_binary64
509×associate-/r*_binary64
353×associate-/l*_binary64
343×div-sub_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02043
15843
217938
382436
4388236
5502936

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
0.4b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.4b
(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))
Compiler

Compiled 114 to 77 computations (32.5% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 3 (*.f64 v v))
0.2b
(*.f64 (PI.f64) t)
0.2b
(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))
0.4b
(*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))

series327.0ms (6.4%)

Counts
4 → 60
Calls

4 calls:

289.0ms
(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))
31.0ms
(*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))
3.0ms
(*.f64 3 (*.f64 v v))
2.0ms
(*.f64 (PI.f64) t)

rewrite62.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
30×add-cbrt-cube_binary64
30×add-exp-log_binary64
18×associate-*r/_binary64
16×pow1_binary64
13×add-sqr-sqrt_binary64
Counts
4 → 102
Calls

4 calls:

39.0ms
(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))
7.0ms
(*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))
5.0ms
(*.f64 3 (*.f64 v v))
3.0ms
(*.f64 (PI.f64) t)

simplify140.0ms (2.7%)

Algorithm
egg-herbie
Rules
859×fma-def_binary64
494×associate-*l*_binary64
478×associate-*r*_binary64
436×times-frac_binary64
397×associate-/r*_binary64
Counts
162 → 186
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03395931
110385329
248965315
356425315

prune243.0ms (4.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1797186
Fresh000
Picked101
Done000
Total1807187
Error
0.1b
Counts
187 → 7
Alt Table
StatusErrorProgram
1.5b
(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t)) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))
0.4b
(*.f64 (/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (pow.f64 v 4)))) (+.f64 1 (*.f64 v v)))
39.5b
(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) (*.f64 (-.f64 1 (*.f64 v v)) (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))))) 3))
0.3b
(*.f64 (/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) (*.f64 t (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
0.4b
(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (PI.f64) (*.f64 t (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v))))))) (-.f64 1 (*.f64 v v))))
33.3b
(*.f64 (sqrt.f64 (/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))) (sqrt.f64 (/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))))
1.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))) (cbrt.f64 (/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v)))))) (cbrt.f64 (/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))))
Compiler

Compiled 8808 to 5759 computations (34.6% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 v v) 5)
0.1b
(*.f64 3 (*.f64 v v))
0.2b
(*.f64 t (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2))))
0.2b
(/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) (*.f64 t (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2)))))

series139.0ms (2.7%)

Counts
3 → 60
Calls

3 calls:

112.0ms
(/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) (*.f64 t (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2)))))
24.0ms
(*.f64 t (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2))))
3.0ms
(*.f64 (*.f64 v v) 5)

rewrite26.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
31×add-cbrt-cube_binary64
31×add-exp-log_binary64
17×pow1_binary64
15×cbrt-unprod_binary64
15×prod-exp_binary64
Counts
3 → 74
Calls

3 calls:

9.0ms
(/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) (*.f64 t (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2)))))
7.0ms
(*.f64 t (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2))))
4.0ms
(*.f64 (*.f64 v v) 5)

simplify89.0ms (1.7%)

Algorithm
egg-herbie
Rules
448×fma-def_binary64
436×distribute-rgt-in_binary64
418×distribute-lft-in_binary64
269×associate-*l*_binary64
268×associate-*r*_binary64
Counts
134 → 126
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01833822
15203127
221703019
352233019

prune195.0ms (3.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1455150
Fresh606
Picked011
Done000
Total1516157
Error
0.0b
Counts
157 → 6
Alt Table
StatusErrorProgram
0.3b
(*.f64 (/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) (*.f64 t (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
0.4b
(*.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (PI.f64) (*.f64 (*.f64 t (sqrt.f64 2)) (-.f64 1 (*.f64 v v))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
0.3b
(*.f64 (*.f64 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) t) (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v)))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
33.3b
(*.f64 (*.f64 (sqrt.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (PI.f64) (*.f64 (*.f64 t (sqrt.f64 2)) (-.f64 1 (*.f64 v v)))))) (sqrt.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (PI.f64) (*.f64 (*.f64 t (sqrt.f64 2)) (-.f64 1 (*.f64 v v))))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
0.3b
(*.f64 (/.f64 (/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) t) (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2)))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
1.3b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) (*.f64 t (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2)))))) (cbrt.f64 (/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) (*.f64 t (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2))))))) (cbrt.f64 (/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) (*.f64 t (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2))))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
Compiler

Compiled 6384 to 4291 computations (32.8% saved)

localize53.0ms (1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v)))
0.0b
(/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v)))))
0.1b
(*.f64 3 (*.f64 v v))
0.3b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) t) (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v))))))

series114.0ms (2.2%)

Counts
3 → 48
Calls

3 calls:

88.0ms
(*.f64 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) t) (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v))))))
21.0ms
(/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v)))))
5.0ms
(*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v)))

rewrite48.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
46×add-cbrt-cube_binary64
46×add-exp-log_binary64
41×add-sqr-sqrt_binary64
32×times-frac_binary64
29×*-un-lft-identity_binary64
Counts
3 → 138
Calls

3 calls:

17.0ms
(*.f64 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) t) (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v))))))
8.0ms
(/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v)))))
6.0ms
(*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v)))

simplify154.0ms (3%)

Algorithm
egg-herbie
Rules
473×fma-def_binary64
365×associate-/r*_binary64
317×associate-*r*_binary64
308×associate-*l*_binary64
227×*-commutative_binary64
Counts
186 → 227
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03347046
19446121
238056075
350246075

prune375.0ms (7.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2501251
Fresh224
Picked011
Done011
Total2525257
Error
0b
Counts
257 → 5
Alt Table
StatusErrorProgram
0.3b
(*.f64 (/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) (*.f64 t (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
0.4b
(*.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (PI.f64) (*.f64 (*.f64 t (sqrt.f64 2)) (-.f64 1 (*.f64 v v))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
0.1b
(*.f64 (/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v))))) t) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
0.3b
(*.f64 (*.f64 (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) t) (/.f64 (sqrt.f64 (fma.f64 v (*.f64 v -5) 1)) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v)))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
0.3b
(*.f64 (/.f64 (/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) t) (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2)))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
Compiler

Compiled 13239 to 9440 computations (28.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v)))
0.0b
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v)))))
0.1b
(/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v))))) t)
0.1b
(*.f64 3 (*.f64 v v))

series92.0ms (1.8%)

Counts
2 → 36
Calls

2 calls:

82.0ms
(/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v))))) t)
10.0ms
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v)))))

rewrite25.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
42×times-frac_binary64
25×add-cbrt-cube_binary64
25×add-exp-log_binary64
22×*-un-lft-identity_binary64
22×add-sqr-sqrt_binary64
Counts
2 → 87
Calls

2 calls:

9.0ms
(/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v))))) t)
6.0ms
(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v)))))

simplify169.0ms (3.3%)

Algorithm
egg-herbie
Rules
429×distribute-rgt-in_binary64
405×fma-def_binary64
261×associate-/r*_binary64
201×associate-*r*_binary64
182×cancel-sign-sub-inv_binary64
Counts
123 → 160
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02495066
16724437
224834403
347264399
449894399
549984399

prune302.0ms (5.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2341235
Fresh112
Picked011
Done112
Total2364240
Error
0b
Counts
240 → 4
Alt Table
StatusErrorProgram
0.1b
(*.f64 (/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (PI.f64) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v))))) t) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
0.3b
(*.f64 (/.f64 (/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) t) (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2)))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
0.3b
(*.f64 (*.f64 (/.f64 (/.f64 1 (PI.f64)) 1) (/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (sqrt.f64 2) (-.f64 1 (*.f64 v v)))) t)) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
0.3b
(*.f64 (/.f64 (-.f64 1 (*.f64 (*.f64 v v) 5)) (*.f64 t (*.f64 (fma.f64 v (neg.f64 v) 1) (*.f64 (PI.f64) (sqrt.f64 2))))) (sqrt.f64 (/.f64 1 (-.f64 1 (*.f64 3 (*.f64 v v))))))
Compiler

Compiled 9637 to 6530 computations (32.2% saved)

regimes878.0ms (17.2%)

Accuracy

Total 0.1b remaining (89%)

Threshold costs 0.1b (89%)

Counts
117 → 1
Compiler

Compiled 27290 to 19679 computations (27.9% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
distribute-rgt-neg-in_binary64
cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02349
14149
25249
35849
46149
55949

end110.0ms (2.1%)

Compiler

Compiled 202 to 154 computations (23.8% saved)

Profiling

Loading profile data...