Details

Time bar (total: 3.7s)

analyze5.0ms (0.1%)

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)

sample1.4s (38.8%)

Results
1.4s8256×body128valid
0.0msbody128invalid
Compiler

Compiled 142 to 66 computations (53.5% saved)

preprocess28.0ms (0.8%)

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: 0 (0.0ms)

IterNodesCost
03275
17459
225141
3120837
4239437
011
Stop Event
saturated
node limit
Compiler

Compiled 68 to 31 computations (54.4% saved)

simplify22.0ms (0.6%)

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 (0.1%)

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)

localize23.0ms (0.6%)

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 (*.f64 (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))

series27.0ms (0.7%)

Counts
4 → 36
Calls

9 calls:

4.0ms
(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
x
-inf
4.0ms
(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
x
inf
3.0ms
(*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
x
0
3.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
x
-inf
3.0ms
(*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
x
inf

rewrite47.0ms (1.3%)

Algorithm
batch-egg-rewrite
Rules
633×log-prod_binary64
240×expm1-udef_binary64
240×log1p-udef_binary64
207×log-pow_binary64
148×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01938
134422
2353522
Stop Event
node limit
Counts
4 → 77

simplify73.0ms (2%)

Algorithm
egg-herbie
Rules
684×sqr-pow_binary64
547×unswap-sqr_binary64
336×*-commutative_binary64
334×associate-*l*_binary64
285×pow-sqr_binary64
Iterations

Useful iterations: 8 (0.0ms)

IterNodesCost
013288
130288
263288
3139288
4342264
51090264
62254264
72395264
82588216
92854216
103197216
113652216
124235216
134971216
Stop Event
node limit
Counts
113 → 82

prune162.0ms (4.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1002102
Fresh011
Picked101
Done000
Total1013104
Error
0.0b
Counts
104 → 3
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 (pow.f64 (*.f64 x x) 2) (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))))
1.1b
(fabs.f64 (*.f64 (/.f64 1 (expm1.f64 (log1p.f64 (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))))))
Compiler

Compiled 6859 to 2826 computations (58.8% saved)

localize27.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (*.f64 (*.f64 (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)))
0.2b
(pow.f64 (*.f64 x x) 2)
1.0b
(sqrt.f64 (PI.f64))

series3.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

1.0ms
(pow.f64 (*.f64 x x) 2)
x
-inf
1.0ms
(pow.f64 (*.f64 x x) 2)
x
inf
1.0ms
(pow.f64 (*.f64 x x) 2)
x
0

rewrite28.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
347×log1p-expm1-u_binary64
347×expm1-log1p-u_binary64
309×add-log-exp_binary64
309×pow1_binary64
237×unpow-prod-down_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
057
11014
210614
Stop Event
node limit
Counts
1 → 28

simplify62.0ms (1.7%)

Algorithm
egg-herbie
Rules
787×sqr-pow_binary64
390×cube-prod_binary64
342×unswap-sqr_binary64
327×pow-sqr_binary64
260×fabs-mul_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0448
1848
21448
32548
45048
513548
648448
7113348
8125748
9142648
10162548
11189848
12225548
13270448
14322648
15385448
16460548
17491148
Stop Event
node limit
Counts
40 → 29

prune125.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New92193
Fresh112
Picked011
Done000
Total93396
Error
0.0b
Counts
96 → 3
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 (pow.f64 (*.f64 x x) 2) (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))))
1.1b
(fabs.f64 (*.f64 (/.f64 1 (expm1.f64 (log1p.f64 (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 (pow.f64 (*.f64 x x) 2) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))
Compiler

Compiled 5964 to 2939 computations (50.7% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
0.1b
(*.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 (0.4%)

Counts
3 → 24
Calls

9 calls:

3.0ms
(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))
x
inf
3.0ms
(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))
x
0
3.0ms
(/.f64 (fabs.f64 x) (sqrt.f64 (PI.f64)))
x
-inf
1.0ms
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
x
-inf
1.0ms
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
x
inf

rewrite48.0ms (1.3%)

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
2345528
Stop Event
node limit
Counts
3 → 81

simplify67.0ms (1.8%)

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

prune117.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1111112
Fresh101
Picked011
Done011
Total1123115
Error
0b
Counts
115 → 3
Alt Table
StatusErrorProgram
0.3b
(fabs.f64 (*.f64 (/.f64 (fabs.f64 x) (exp.f64 (*.f64 (log.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
(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 (pow.f64 (*.f64 x x) 2) (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 3343 to 2147 computations (35.8% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (/.f64 (fabs.f64 x) (exp.f64 (*.f64 (log.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
(fma.f64 1/5 (pow.f64 x 4) (*.f64 1/21 (pow.f64 x 6)))
0.1b
(*.f64 1/21 (pow.f64 x 6))
0.3b
(/.f64 (fabs.f64 x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))

series17.0ms (0.5%)

Counts
2 → 24
Calls

6 calls:

4.0ms
(*.f64 (/.f64 (fabs.f64 x) (exp.f64 (*.f64 (log.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)))
x
-inf
3.0ms
(*.f64 (/.f64 (fabs.f64 x) (exp.f64 (*.f64 (log.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)))
x
inf
3.0ms
(/.f64 (fabs.f64 x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
x
-inf
3.0ms
(/.f64 (fabs.f64 x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
x
0
3.0ms
(/.f64 (fabs.f64 x) (exp.f64 (*.f64 (log.f64 (PI.f64)) 1/2)))
x
inf

rewrite33.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
224×add-sqr-sqrt_binary64
224×log1p-expm1-u_binary64
224×expm1-log1p-u_binary64
220×add-cbrt-cube_binary64
218×add-log-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02346
149240
Stop Event
node limit
Counts
2 → 61

simplify35.0ms (1%)

Algorithm
egg-herbie
Rules
817×fma-def_binary64
674×distribute-rgt-out_binary64
592×associate-*l*_binary64
439×associate-*r*_binary64
377×unswap-sqr_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
035738
191738
2242531
3891432
43722432
Stop Event
node limit
Counts
85 → 78

prune142.0ms (3.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1260126
Fresh000
Picked011
Done022
Total1263129
Error
0b
Counts
129 → 3
Alt Table
StatusErrorProgram
0.3b
(fabs.f64 (*.f64 (/.f64 (fabs.f64 x) (exp.f64 (*.f64 (log.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
(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 (pow.f64 (*.f64 x x) 2) (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 4290 to 2925 computations (31.8% saved)

regimes963.0ms (26.3%)

Accuracy

Total 0.1b remaining (91.3%)

Threshold costs 0.1b (91.3%)

Counts
121 → 1
Compiler

Compiled 29270 to 18973 computations (35.2% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Rules
11×*-commutative_binary64
+-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03186
14786
Stop Event
saturated

end128.0ms (3.5%)

Stop Event
done
Compiler

Compiled 221 to 158 computations (28.5% saved)

Profiling

Loading profile data...