Details

Time bar (total: 4.1s)

analyze6.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%50%50%3
25%25%50%4
37.5%12.5%50%5
43.7%6.2%50%6
46.9%3.1%50%7
48.4%1.6%50%8
49.2%0.8%50%9
49.6%0.4%50%10
49.8%0.2%50%11
49.9%0.1%50%12
49.9%0%50%13
49.9%0%50%14
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.1s (26.7%)

Results
1.0s8256×body128valid
Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify37.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
396×fma-neg_binary64
375×fma-def_binary64
260×div-sub_binary64
123×times-frac_binary64
116×associate-/l*_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01017
11917
22517
33517
45717
57317
610217
715817
824017
929917
1039117
1153617
1277717
1382617
1479917
1572217

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
Compiler

Compiled 36 to 30 computations (16.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
✓0.0b
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
✓0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))

series10.0ms (0.2%)

Counts
3 → 24
Calls

3 calls:

6.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
2.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
2.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

rewrite20.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
79×*-un-lft-identity_binary64
56×add-sqr-sqrt_binary64
49×times-frac_binary64
30×sqrt-prod_binary64
26×add-cube-cbrt_binary64
Counts
3 → 106
Calls

3 calls:

6.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
6.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify138.0ms (3.3%)

Algorithm
1×egg-herbie
Rules
697×fma-neg_binary64
247×associate-/r*_binary64
244×sub-neg_binary64
227×fma-def_binary64
215×associate-*l*_binary64
Counts
130 → 130
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01822612
14102466
210962454
333532449
447512449
549852449
649202449

prune134.0ms (3.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1264130
Fresh000
Picked101
Done000
Total1274131
Error
0b
Counts
131 → 4
Alt Table
StatusErrorProgram
0.4b
(*.f64 2 (atan.f64 (-.f64 1 x)))
0.0b
(*.f64 2 (log1p.f64 (expm1.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))
▶0.0b
(*.f64 2 (atan.f64 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))
0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x))) (/.f64 (cbrt.f64 (-.f64 1 x)) (+.f64 1 x))))))
Compiler

Compiled 2664 to 2177 computations (18.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
✓0.0b
(atan.f64 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))
✓0.0b
(cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

series20.0ms (0.5%)

Counts
3 → 36
Calls

3 calls:

11.0ms
(*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
5.0ms
(cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
4.0ms
(atan.f64 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))

rewrite64.0ms (1.5%)

Algorithm
1×rewrite-expression-head
Rules
156×add-sqr-sqrt_binary64
124×cbrt-prod_binary64
112×*-un-lft-identity_binary64
89×times-frac_binary64
54×sqrt-prod_binary64
Counts
3 → 173
Calls

3 calls:

34.0ms
(*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
5.0ms
(cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0ms
(atan.f64 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))

simplify297.0ms (7.2%)

Algorithm
1×egg-herbie
Rules
844×fma-neg_binary64
481×times-frac_binary64
405×fma-def_binary64
385×*-commutative_binary64
249×cancel-sign-sub-inv_binary64
Counts
209 → 253
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02927357
15726176
214225557
337075518
449705518
549655518

prune492.0ms (11.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New4392441
Fresh213
Picked101
Done000
Total4423445
Error
0b
Counts
445 → 3
Alt Table
StatusErrorProgram
0.4b
(*.f64 2 (atan.f64 (-.f64 1 x)))
▶0.0b
(*.f64 2 (atan.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/6))))
0.0b
(*.f64 2 (atan.f64 (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
Compiler

Compiled 14039 to 11464 computations (18.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/6))
0.0b
(/.f64 (-.f64 1 x) (+.f64 1 x))
✓0.0b
(atan.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/6)))
0.0b
(cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

series7.0ms (0.2%)

Counts
2 → 24
Calls

2 calls:

5.0ms
(*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/6))
2.0ms
(atan.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/6)))

rewrite44.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
78×add-sqr-sqrt_binary64
74×*-un-lft-identity_binary64
55×times-frac_binary64
38×cbrt-prod_binary64
36×unpow-prod-down_binary64
Counts
2 → 105
Calls

2 calls:

30.0ms
(*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/6))
1.0ms
(atan.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/6)))

simplify137.0ms (3.3%)

Algorithm
1×egg-herbie
Rules
582×fma-def_binary64
435×unswap-sqr_binary64
341×times-frac_binary64
318×*-commutative_binary64
271×cancel-sign-sub-inv_binary64
Counts
129 → 158
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02184405
14603705
212763445
326433425
447653397
549233397

prune517.0ms (12.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New3451346
Fresh112
Picked011
Done000
Total3463349
Error
0b
Counts
349 → 3
Alt Table
StatusErrorProgram
✓0.0b
(*.f64 2 (atan.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/6))))
▶0.0b
(*.f64 2 (atan.f64 (exp.f64 (*.f64 3 (*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))))
0.0b
(*.f64 2 (atan.f64 (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
Compiler

Compiled 10545 to 8558 computations (18.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(exp.f64 (*.f64 3 (*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))
✓0.0b
(atan.f64 (exp.f64 (*.f64 3 (*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))))
✓0.2b
(*.f64 3 (*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
✓0.4b
(*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))

series43.0ms (1%)

Counts
4 → 48
Calls

4 calls:

34.0ms
(*.f64 3 (*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
4.0ms
(*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))
3.0ms
(exp.f64 (*.f64 3 (*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))
2.0ms
(atan.f64 (exp.f64 (*.f64 3 (*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))))

rewrite42.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
117×distribute-lft-in_binary64
117×distribute-rgt-in_binary64
90×prod-diff_binary64
81×add-sqr-sqrt_binary64
79×*-un-lft-identity_binary64
Counts
4 → 197
Calls

4 calls:

7.0ms
(*.f64 3 (*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
6.0ms
(exp.f64 (*.f64 3 (*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))
5.0ms
(*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))
0.0ms
(atan.f64 (exp.f64 (*.f64 3 (*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))))

simplify158.0ms (3.8%)

Algorithm
1×egg-herbie
Rules
697×fma-def_binary64
366×distribute-rgt-in_binary64
331×fma-neg_binary64
270×distribute-lft-in_binary64
202×exp-prod_binary64
Counts
245 → 290
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
04024746
16384223
219103665
348863663
447383663

prune259.0ms (6.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2891290
Fresh101
Picked011
Done011
Total2903293
Error
0b
Counts
293 → 3
Alt Table
StatusErrorProgram
✓0.0b
(*.f64 2 (atan.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))) (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 1/6))))
✓0.0b
(*.f64 2 (atan.f64 (exp.f64 (*.f64 3 (*.f64 1/6 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))))
0.0b
(*.f64 2 (atan.f64 (*.f64 (exp.f64 (*.f64 (*.f64 (log1p.f64 (neg.f64 x)) 1/6) 3)) (exp.f64 (*.f64 (*.f64 (neg.f64 (log1p.f64 x)) 1/6) 3)))))
Compiler

Compiled 8193 to 4019 computations (50.9% saved)

regimes453.0ms (10.9%)

Accuracy

Total 0.0b remaining (79.8%)

Threshold costs 0.0b (79.8%)

Counts
102 → 1
Compiler

Compiled 8794 to 7509 computations (14.6% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
3×+-commutative_binary64
3×*-commutative_binary64
2×sub-neg_binary64
1×neg-sub0_binary64
1×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01332
12032
22432
32632
42732
52632

end123.0ms (3%)

Compiler

Compiled 102 to 86 computations (15.7% saved)

Profiling

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