Details

Time bar (total: 2.7s)

analyze68.0ms (2.5%)

Algorithm
1×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%74.9%25.1%4
12.5%62.4%25.1%5
31.2%31.2%37.6%6
37.5%25%37.6%7
40.6%15.6%43.8%8
42.9%11.7%45.4%9
44.1%7.4%48.5%10
45.1%5.7%49.3%11
45.6%3.6%50.8%12
46%2.8%51.2%13
46.2%1.8%52%14
Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.0s (37%)

Results
966.0ms8256×body128valid
23.0ms208×body128invalid
Compiler

Compiled 34 to 28 computations (17.6% saved)

preprocess41.0ms (1.5%)

Algorithm
2×egg-herbie
Rules
880×fma-neg_binary64
408×fma-def_binary64
282×cancel-sign-sub-inv_binary64
184×distribute-rgt-in_binary64
184×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02042
14636
212636
337932
478332
5115532
6229432
7464932
022
Stop Event
1×saturated
1×node limit
Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify37.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
892×fma-def_binary64
453×fma-neg_binary64
318×cancel-sign-sub-inv_binary64
251×distribute-rgt-neg-in_binary64
168×associate-/l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01321
12818
26918
319416
440216
558616
6116416
7252716
8428116
9490516
Stop Event
1×node limit
Counts
1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.4b
(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) (fma.f64 3 y -3)))
▶0.4b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
Compiler

Compiled 85 to 66 computations (22.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)
✓0.2b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓0.3b
(*.f64 3 (sqrt.f64 x))
✓0.5b
(/.f64 1 (*.f64 x 9))

series40.0ms (1.5%)

Counts
4 → 48
Calls

18 calls:

14.0ms
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
x
-inf
4.0ms
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
x
inf
4.0ms
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
x
0
2.0ms
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
y
0
2.0ms
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
y
-inf

rewrite61.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
620×prod-diff_binary64
226×log1p-udef_binary64
134×add-sqr-sqrt_binary64
130×add-cbrt-cube_binary64
130×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01347
128338
2370638
Stop Event
1×node limit
Counts
4 → 106

simplify123.0ms (4.5%)

Algorithm
1×egg-herbie
Rules
992×fma-def_binary64
665×fma-neg_binary64
213×distribute-rgt-neg-in_binary64
188×cancel-sign-sub-inv_binary64
140×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
026516
162471
2126450
3235450
4457450
5814450
61577450
72805450
83865450
94194450
104524450
114524450
124885450
134885450
144885450
Stop Event
1×saturated
Counts
154 → 120

prune119.0ms (4.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1128120
Fresh011
Picked011
Done000
Total11210122
Error
0.0b
Counts
122 → 10
Alt Table
StatusErrorProgram
32.1b
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 x) (*.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3))
0.4b
(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) (fma.f64 3 y -3)))
0.7b
(*.f64 (pow.f64 (sqrt.f64 (*.f64 3 (sqrt.f64 x))) 2) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓0.4b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
▶0.3b
(-.f64 (+.f64 (*.f64 3 (*.f64 y (sqrt.f64 x))) (*.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (*.f64 3 (sqrt.f64 x)))
30.4b
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 x) (*.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 2)
1.3b
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (*.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 3)
16.1b
(*.f64 (*.f64 3 (sqrt.f64 x)) (fma.f64 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)) (sqrt.f64 (+.f64 (/.f64 1/9 x) y)) -1))
31.4b
(/.f64 (*.f64 (+.f64 (pow.f64 (+.f64 (/.f64 1/9 x) y) 3) -1) (*.f64 3 (sqrt.f64 x))) (+.f64 (pow.f64 (+.f64 (/.f64 1/9 x) y) 2) (+.f64 (/.f64 1/9 x) (+.f64 y 1))))
0.6b
(*.f64 (sqrt.f64 (*.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
Compiler

Compiled 2381 to 1749 computations (26.5% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 y (sqrt.f64 x))
0.3b
(*.f64 3 (sqrt.f64 x))
✓0.3b
(*.f64 3 (*.f64 y (sqrt.f64 x)))
✓0.4b
(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

series24.0ms (0.9%)

Counts
3 → 0
Calls

15 calls:

3.0ms
(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
x
-inf
3.0ms
(*.f64 y (sqrt.f64 x))
x
0
2.0ms
(*.f64 3 (*.f64 y (sqrt.f64 x)))
x
0
2.0ms
(*.f64 3 (*.f64 y (sqrt.f64 x)))
x
inf
2.0ms
(*.f64 3 (*.f64 y (sqrt.f64 x)))
x
-inf

rewrite44.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
515×log-prod_binary64
274×pow2_binary64
192×expm1-udef_binary64
192×log1p-udef_binary64
191×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01224
124121
2267221
Stop Event
1×node limit
Counts
3 → 53

simplify8.0ms (0.3%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
53 → 53

prune83.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New65368
Fresh268
Picked101
Done011
Total681078
Error
0.0b
Counts
78 → 10
Alt Table
StatusErrorProgram
32.1b
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 x) (*.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3))
0.4b
(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) (fma.f64 3 y -3)))
0.7b
(*.f64 (pow.f64 (sqrt.f64 (*.f64 3 (sqrt.f64 x))) 2) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓0.4b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
30.4b
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 x) (*.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 2)
1.3b
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (*.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 3)
0.6b
(-.f64 (+.f64 (*.f64 3 (*.f64 y (sqrt.f64 x))) (*.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 (*.f64 x 9)))
18.7b
(-.f64 (+.f64 (sqrt.f64 (*.f64 (*.f64 x (*.f64 y y)) 9)) (*.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (*.f64 3 (sqrt.f64 x)))
▶0.3b
(-.f64 (+.f64 (*.f64 3 (*.f64 y (sqrt.f64 x))) (sqrt.f64 (*.f64 (/.f64 1 x) 1/9))) (*.f64 3 (sqrt.f64 x)))
0.6b
(*.f64 (sqrt.f64 (*.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
Compiler

Compiled 1770 to 1190 computations (32.8% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 y (sqrt.f64 x))
0.3b
(*.f64 3 (sqrt.f64 x))
0.3b
(*.f64 3 (*.f64 y (sqrt.f64 x)))
✓0.4b
(*.f64 (/.f64 1 x) 1/9)

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

1.0ms
(*.f64 (/.f64 1 x) 1/9)
x
0
0.0ms
(*.f64 (/.f64 1 x) 1/9)
x
-inf
0.0ms
(*.f64 (/.f64 1 x) 1/9)
x
inf

rewrite32.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
459×log1p-expm1-u_binary64
459×expm1-log1p-u_binary64
296×unpow-prod-down_binary64
228×log-prod_binary64
135×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
064
11214
213204
Stop Event
1×node limit
Counts
1 → 23

simplify7.0ms (0.3%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0448
Stop Event
1×saturated
Counts
35 → 23

prune100.0ms (3.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New74074
Fresh088
Picked011
Done011
Total741084
Error
0.0b
Counts
84 → 10
Alt Table
StatusErrorProgram
32.1b
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 x) (*.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1)))) 3))
▶0.4b
(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) (fma.f64 3 y -3)))
0.7b
(*.f64 (pow.f64 (sqrt.f64 (*.f64 3 (sqrt.f64 x))) 2) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓0.4b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
30.4b
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 x) (*.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 2)
1.3b
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (*.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 3)
0.6b
(-.f64 (+.f64 (*.f64 3 (*.f64 y (sqrt.f64 x))) (*.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 (*.f64 x 9)))
18.7b
(-.f64 (+.f64 (sqrt.f64 (*.f64 (*.f64 x (*.f64 y y)) 9)) (*.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (*.f64 3 (sqrt.f64 x)))
✓0.3b
(-.f64 (+.f64 (*.f64 3 (*.f64 y (sqrt.f64 x))) (sqrt.f64 (*.f64 (/.f64 1 x) 1/9))) (*.f64 3 (sqrt.f64 x)))
0.6b
(*.f64 (sqrt.f64 (*.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
Compiler

Compiled 1864 to 1255 computations (32.7% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (/.f64 1/3 x) (fma.f64 3 y -3))
✓0.1b
(fma.f64 3 y -3)
✓0.3b
(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) (fma.f64 3 y -3)))
✓0.4b
(/.f64 1/3 x)

series27.0ms (1%)

Counts
4 → 48
Calls

18 calls:

5.0ms
(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) (fma.f64 3 y -3)))
x
inf
4.0ms
(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) (fma.f64 3 y -3)))
x
-inf
3.0ms
(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) (fma.f64 3 y -3)))
x
0
2.0ms
(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) (fma.f64 3 y -3)))
y
inf
2.0ms
(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) (fma.f64 3 y -3)))
y
-inf

rewrite71.0ms (2.6%)

Algorithm
1×batch-egg-rewrite
Rules
932×prod-diff_binary64
119×add-sqr-sqrt_binary64
115×log1p-expm1-u_binary64
115×expm1-log1p-u_binary64
114×add-cbrt-cube_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01136
124436
2317236
Stop Event
1×node limit
Counts
4 → 107

simplify74.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
769×fma-neg_binary64
746×fma-def_binary64
197×cancel-sign-sub-inv_binary64
133×distribute-rgt-in_binary64
104×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
026545
158482
2111482
3180482
4335482
5545482
61124482
72086482
82937482
93230482
103499482
113503482
123503482
Stop Event
1×saturated
Counts
155 → 123

prune152.0ms (5.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1203123
Fresh257
Picked101
Done022
Total12310133
Error
0b
Counts
133 → 10
Alt Table
StatusErrorProgram
0.4b
(*.f64 (sqrt.f64 x) (+.f64 (pow.f64 (*.f64 x 3) -1) (fma.f64 3 y -3)))
18.7b
(-.f64 (+.f64 (sqrt.f64 (*.f64 (*.f64 x (*.f64 y y)) 9)) (*.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (*.f64 3 (sqrt.f64 x)))
0.7b
(*.f64 (pow.f64 (sqrt.f64 (*.f64 3 (sqrt.f64 x))) 2) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓0.4b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.4b
(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y -1) (/.f64 1/3 x)))
1.3b
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (*.f64 3 (+.f64 (/.f64 1/9 x) (-.f64 y 1))))) 3)
17.3b
(*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) (cbrt.f64 (pow.f64 (fma.f64 3 y -3) 3))))
0.6b
(-.f64 (+.f64 (*.f64 3 (*.f64 y (sqrt.f64 x))) (*.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 (*.f64 x 9)))
✓0.3b
(-.f64 (+.f64 (*.f64 3 (*.f64 y (sqrt.f64 x))) (sqrt.f64 (*.f64 (/.f64 1 x) 1/9))) (*.f64 3 (sqrt.f64 x)))
0.6b
(*.f64 (sqrt.f64 (*.f64 x 9)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
Compiler

Compiled 2247 to 1615 computations (28.1% saved)

regimes413.0ms (15.2%)

Accuracy

Total 0.3b remaining (92.7%)

Threshold costs 0.3b (92.7%)

Counts
108 → 1
Compiler

Compiled 5210 to 4123 computations (20.9% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01427
12827
23827
34327
44627
54727
Stop Event
1×saturated

end142.0ms (5.2%)

Stop Event
1×fuel
Compiler

Compiled 212 to 167 computations (21.2% saved)

Profiling

Loading profile data...