Details

Time bar (total: 3.1s)

analyze7.0ms (0.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%74.9%25.1%0
0%74.9%25.1%1
37.5%37.5%25.1%2
37.5%18.7%43.8%3
46.8%9.4%43.8%4
51.5%4.7%43.8%5
51.5%2.3%46.1%6
52.7%1.2%46.1%7
53.3%0.6%46.1%8
53.3%0.3%46.4%9
53.4%0.1%46.4%10
53.5%0.1%46.4%11
53.5%0%46.5%12
53.5%0%46.5%13
53.5%0%46.5%14
Compiler

Compiled 71 to 33 computations (53.5% saved)

sample1.6s (50.9%)

Results
1.6s8256×body128valid
0.0msbody128invalid
Compiler

Compiled 210 to 97 computations (53.8% saved)

simplify22.0ms (0.7%)

Algorithm
egg-herbie
Rules
642×distribute-lft-out_binary64
588×associate-/l*_binary64
406×associate-/r*_binary64
400×*-commutative_binary64
244×distribute-rgt-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03275
17459
225141
3120837
4239437
Stop Event
node limit
Counts
1 → 2

prune5.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.1b
(fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
0.5b
(fabs.f64 (*.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))
Compiler

Compiled 278 to 149 computations (46.4% saved)

localize22.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
0.1b
(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
0.2b
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b
(sqrt.f64 (PI.f64))

series88.0ms (2.8%)

Counts
4 → 36
Calls

4 calls:

56.0ms
(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
19.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
14.0ms
(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
0.0ms
(sqrt.f64 (PI.f64))

rewrite38.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
274×add-cbrt-cube_binary64
274×log1p-expm1-u_binary64
274×expm1-log1p-u_binary64
265×add-cube-cbrt_binary64
265×add-log-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03189
161966
Stop Event
node limit
Counts
4 → 60
Calls

4 calls:

37.0ms
(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
37.0ms
(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
37.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
37.0ms
(sqrt.f64 (PI.f64))

simplify85.0ms (2.7%)

Algorithm
egg-herbie
Rules
2001×fma-def_binary64
662×associate-*l*_binary64
478×associate-*r*_binary64
213×sqr-pow_binary64
198×unswap-sqr_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
025720
163720
2161720
3504696
41327696
53626696
64007696
74106696
84236696
94434696
104725696
Stop Event
node limit
Counts
96 → 64

prune72.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New61364
Fresh011
Picked101
Done000
Total62466
Error
0b
Counts
66 → 4
Alt Table
StatusErrorProgram
1.4b
(fabs.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 1/21 (*.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6)) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (PI.f64)))) 3))
0.5b
(fabs.f64 (/.f64 (fma.f64 1/21 (*.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6)) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (PI.f64))))
0.1b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
0.5b
(fabs.f64 (*.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))
Compiler

Compiled 3764 to 1647 computations (56.2% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
0.1b
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.1b
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
0.2b
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

series93.0ms (2.9%)

Counts
4 → 0
Calls

4 calls:

56.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
15.0ms
(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
11.0ms
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
10.0ms
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

rewrite37.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
259×log1p-expm1-u_binary64
259×expm1-log1p-u_binary64
255×add-cbrt-cube_binary64
248×add-log-exp_binary64
247×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02569
156267
Stop Event
node limit
Counts
4 → 54
Calls

4 calls:

35.0ms
(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
35.0ms
(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
35.0ms
(*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))))
35.0ms
(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

simplify6.0ms (0.2%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
saturated
Counts
54 → 54

prune70.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New54054
Fresh033
Picked011
Done000
Total54458
Error
0b
Counts
58 → 4
Alt Table
StatusErrorProgram
1.4b
(fabs.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 1/21 (*.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6)) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (PI.f64)))) 3))
0.5b
(fabs.f64 (/.f64 (fma.f64 1/21 (*.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6)) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (PI.f64))))
0.1b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
0.5b
(fabs.f64 (*.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))
Compiler

Compiled 1979 to 1438 computations (27.3% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 1/21 (pow.f64 x 6))
0.1b
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
0.3b
(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))
1.0b
(sqrt.f64 (PI.f64))

series15.0ms (0.5%)

Counts
3 → 24
Calls

3 calls:

8.0ms
(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))
4.0ms
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
3.0ms
(*.f64 1/21 (pow.f64 x 6))

rewrite54.0ms (1.7%)

Algorithm
batch-egg-rewrite
Rules
534×log-prod_binary64
220×expm1-udef_binary64
220×log1p-udef_binary64
195×log-pow_binary64
138×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01430
130028
2345828
Stop Event
node limit
Counts
3 → 81
Calls

3 calls:

53.0ms
(*.f64 1/21 (pow.f64 x 6))
53.0ms
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
53.0ms
(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))

simplify67.0ms (2.1%)

Algorithm
egg-herbie
Rules
518×sqr-pow_binary64
487×associate-*l*_binary64
467×unswap-sqr_binary64
440×fma-def_binary64
300×associate-*r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
017291
132291
256291
3123267
4399267
51478267
62937267
73286267
83570267
93854267
104219267
114698267
Stop Event
node limit
Counts
105 → 86

prune101.0ms (3.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1041105
Fresh112
Picked011
Done011
Total1054109
Error
0b
Counts
109 → 4
Alt Table
StatusErrorProgram
0.1b
(fabs.f64 (*.f64 (*.f64 x (pow.f64 (PI.f64) -1/2)) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))
0.5b
(fabs.f64 (/.f64 (fma.f64 1/21 (*.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6)) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (PI.f64))))
0.1b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
0.5b
(fabs.f64 (*.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))
Compiler

Compiled 3163 to 2046 computations (35.3% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (*.f64 x (pow.f64 (PI.f64) -1/2)) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2)))
0.1b
(*.f64 x (pow.f64 (PI.f64) -1/2))
0.1b
(*.f64 1/21 (pow.f64 x 6))
0.1b
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))

series18.0ms (0.6%)

Counts
2 → 24
Calls

2 calls:

9.0ms
(*.f64 (*.f64 x (pow.f64 (PI.f64) -1/2)) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2)))
8.0ms
(*.f64 x (pow.f64 (PI.f64) -1/2))

rewrite33.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
199×log1p-expm1-u_binary64
199×expm1-log1p-u_binary64
198×add-sqr-sqrt_binary64
195×add-cbrt-cube_binary64
192×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02042
143542
Stop Event
node limit
Counts
2 → 46
Calls

2 calls:

31.0ms
(*.f64 (*.f64 x (pow.f64 (PI.f64) -1/2)) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2)))
31.0ms
(*.f64 x (pow.f64 (PI.f64) -1/2))

simplify69.0ms (2.2%)

Algorithm
egg-herbie
Rules
1014×fma-def_binary64
690×unswap-sqr_binary64
320×*-commutative_binary64
264×sqr-pow_binary64
202×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
032582
186582
2211504
3606432
41543420
52425420
62693420
73135420
84014420
94157420
104384420
114770420
Stop Event
node limit
Counts
70 → 61

prune154.0ms (4.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1090109
Fresh011
Picked011
Done022
Total1094113
Error
0b
Counts
113 → 4
Alt Table
StatusErrorProgram
0.1b
(fabs.f64 (*.f64 (*.f64 x (pow.f64 (PI.f64) -1/2)) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))
0.5b
(fabs.f64 (/.f64 (fma.f64 1/21 (*.f64 (fabs.f64 x) (pow.f64 (fabs.f64 x) 6)) (fma.f64 2 (fabs.f64 x) (fma.f64 2/3 (pow.f64 (fabs.f64 x) 3) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))))) (sqrt.f64 (PI.f64))))
0.1b
(fabs.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)) (+.f64 (*.f64 2 (fabs.f64 x)) (+.f64 (*.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5)))))))
0.5b
(fabs.f64 (*.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64))) (+.f64 (fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6))) (fma.f64 2/3 (*.f64 x x) 2))))
Compiler

Compiled 3554 to 2636 computations (25.8% saved)

regimes319.0ms (10.1%)

Accuracy

Total 0.1b remaining (95.7%)

Threshold costs 0.1b (95.7%)

Counts
43 → 1
Compiler

Compiled 7070 to 5017 computations (29% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Rules
fabs-mul_binary64
*-commutative_binary64
+-commutative_binary64
1-exp_binary64
unpow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02336
13036
23436
33836
Stop Event
saturated

end115.0ms (3.7%)

Compiler

Compiled 162 to 126 computations (22.2% saved)

Profiling

Loading profile data...