Details

Time bar (total: 8.6s)

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 (13.2%)

Results
1.1s8256×body128valid
Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify37.0ms (0.4%)

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)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series10.0ms (0.1%)

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))))

rewrite23.0ms (0.3%)

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:

7.0ms
(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
7.0ms
(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0ms
(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify137.0ms (1.6%)

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

prune120.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1282130
Fresh000
Picked101
Done000
Total1292131
Error
0.0b
Counts
131 → 2
Alt Table
StatusErrorProgram
0.0b
(*.f64 2 (atan.f64 (*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))))))
▶0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x))))))
Compiler

Compiled 2607 to 2130 computations (18.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series28.0ms (0.3%)

Counts
4 → 32
Calls

4 calls:

11.0ms
(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
9.0ms
(sqrt.f64 (+.f64 1 x))
6.0ms
(sqrt.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x))))
3.0ms
(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x)))

rewrite238.0ms (2.8%)

Algorithm
1×rewrite-expression-head
Rules
1354×times-frac_binary64
1252×*-un-lft-identity_binary64
1127×sqrt-prod_binary64
883×add-sqr-sqrt_binary64
522×add-cube-cbrt_binary64
Counts
4 → 867
Calls

4 calls:

34.0ms
(sqrt.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x))))
20.0ms
(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x)))
8.0ms
(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
3.0ms
(sqrt.f64 (+.f64 1 x))

simplify995.0ms (11.6%)

Algorithm
1×egg-herbie
Rules
606×times-frac_binary64
399×associate-/l*_binary64
334×fma-neg_binary64
322×associate-/l/_binary64
322×fma-def_binary64
Counts
899 → 677
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
055233268
1104631666
2230429872
3460229379
4499029379
5494629379

prune949.0ms (11.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New7032705
Fresh101
Picked011
Done000
Total7043707
Error
0b
Counts
707 → 3
Alt Table
StatusErrorProgram
0.3b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (*.f64 x (fma.f64 7/8 x -3/2))) (sqrt.f64 (+.f64 1 x))))))
▶0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)) (sqrt.f64 (+.f64 1 x))))))
✓0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x))))))
Compiler

Compiled 22312 to 18347 computations (17.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)) (sqrt.f64 (+.f64 1 x))))
✓0.0b
(/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)) (sqrt.f64 (+.f64 1 x)))
0.0b
(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
✓0.0b
(pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)

series31.0ms (0.4%)

Counts
3 → 28
Calls

3 calls:

22.0ms
(pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)
6.0ms
(sqrt.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)) (sqrt.f64 (+.f64 1 x))))
3.0ms
(/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)) (sqrt.f64 (+.f64 1 x)))

rewrite734.0ms (8.6%)

Algorithm
1×rewrite-expression-head
Rules
2840×times-frac_binary64
2575×*-un-lft-identity_binary64
2366×sqrt-prod_binary64
1812×add-sqr-sqrt_binary64
1546×cbrt-prod_binary64
Counts
3 → 1754
Calls

3 calls:

73.0ms
(sqrt.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)) (sqrt.f64 (+.f64 1 x))))
39.0ms
(/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)) (sqrt.f64 (+.f64 1 x)))
11.0ms
(pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)

simplify1.9s (22.4%)

Algorithm
1×egg-herbie
Rules
322×associate-/l/_binary64
304×fma-def_binary64
275×div-sub_binary64
232×fma-neg_binary64
194×log-prod_binary64
Counts
1782 → 802
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
073574546
1114765410
2333358825
3426358785
4493858785

prune1.2s (14.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New8780878
Fresh011
Picked011
Done011
Total8783881
Error
0b
Counts
881 → 3
Alt Table
StatusErrorProgram
▶0.3b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (*.f64 x (fma.f64 7/8 x -3/2))) (sqrt.f64 (+.f64 1 x))))))
✓0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)) (sqrt.f64 (+.f64 1 x))))))
✓0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x))))))
Compiler

Compiled 31707 to 26713 computations (15.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 1 x))
✓0.0b
(/.f64 (+.f64 1 (*.f64 x (fma.f64 7/8 x -3/2))) (sqrt.f64 (+.f64 1 x)))
✓0.0b
(sqrt.f64 (/.f64 (+.f64 1 (*.f64 x (fma.f64 7/8 x -3/2))) (sqrt.f64 (+.f64 1 x))))
✓0.0b
(*.f64 x (fma.f64 7/8 x -3/2))

series36.0ms (0.4%)

Counts
3 → 28
Calls

3 calls:

21.0ms
(sqrt.f64 (/.f64 (+.f64 1 (*.f64 x (fma.f64 7/8 x -3/2))) (sqrt.f64 (+.f64 1 x))))
12.0ms
(/.f64 (+.f64 1 (*.f64 x (fma.f64 7/8 x -3/2))) (sqrt.f64 (+.f64 1 x)))
3.0ms
(*.f64 x (fma.f64 7/8 x -3/2))

rewrite27.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
56×sqrt-prod_binary64
49×*-un-lft-identity_binary64
44×times-frac_binary64
42×add-sqr-sqrt_binary64
35×add-cube-cbrt_binary64
Counts
3 → 113
Calls

3 calls:

7.0ms
(sqrt.f64 (/.f64 (+.f64 1 (*.f64 x (fma.f64 7/8 x -3/2))) (sqrt.f64 (+.f64 1 x))))
6.0ms
(/.f64 (+.f64 1 (*.f64 x (fma.f64 7/8 x -3/2))) (sqrt.f64 (+.f64 1 x)))
5.0ms
(*.f64 x (fma.f64 7/8 x -3/2))

simplify153.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
613×times-frac_binary64
507×fma-neg_binary64
394×cancel-sign-sub-inv_binary64
231×distribute-rgt-in_binary64
180×fma-def_binary64
Counts
141 → 198
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02944423
17103818
222553724
344313612
449753612
549053612

prune277.0ms (3.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2260226
Fresh000
Picked011
Done022
Total2263229
Error
0b
Counts
229 → 3
Alt Table
StatusErrorProgram
✓0.3b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (+.f64 1 (*.f64 x (fma.f64 7/8 x -3/2))) (sqrt.f64 (+.f64 1 x))))))
✓0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)) (sqrt.f64 (+.f64 1 x))))))
✓0.0b
(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x))))))
Compiler

Compiled 6637 to 5528 computations (16.7% saved)

regimes382.0ms (4.4%)

Accuracy

Total 0.0b remaining (42.9%)

Threshold costs 0.0b (42.9%)

Counts
94 → 1
Compiler

Compiled 8557 to 7219 computations (15.6% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01532
12132
22532
32732
42832
52732

end78.0ms (0.9%)

Compiler

Compiled 99 to 84 computations (15.2% saved)

Profiling

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