Details

Time bar (total: 3.8s)

analyze525.0ms (13.9%)

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%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
14%85.8%0.1%7
22.6%77.2%0.1%8
23.8%74.5%1.7%9
40%56%4%10
47.3%48.7%4%11
48.4%45.8%5.8%12
58.6%32.4%9%13
63.4%27.5%9%14
Compiler

Compiled 11 to 7 computations (36.4% saved)

sample913.0ms (24.2%)

Results
821.0ms8256×body128valid
78.0ms743×body128invalid
Compiler

Compiled 22 to 14 computations (36.4% saved)

preprocess138.0ms (3.7%)

Algorithm
2×egg-herbie
Rules
2118×associate-/l/_binary64
1625×fma-def_binary64
405×*-commutative_binary64
364×distribute-rgt-out_binary64
238×swap-sqr_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01640
14640
28240
313040
416840
518940
620132
726232
8142932
9233032
10289532
11294432
12294732
13294732
14411832
15423132
16431532
17433032
18437432
19437932
20437932
033
Stop Event
1×saturated
1×node limit
Compiler

Compiled 10 to 6 computations (40% saved)

simplify29.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
756×associate-/l*_binary64
731×associate-/l/_binary64
589×associate-/r/_binary64
532×associate-*l/_binary64
346×associate-/r*_binary64
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
0710
11710
22810
34110
45010
55610
6608
7758
82578
911908
1014488
1115858
1215988
1316038
1416088
Stop Event
1×node limit
Counts
1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶3.6b
(fma.f64 x (/.f64 y z) x)
12.6b
(/.f64 (*.f64 x (+.f64 y z)) z)
Compiler

Compiled 54 to 30 computations (44.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓3.4b
(fma.f64 x (/.f64 y z) x)

series13.0ms (0.3%)

Counts
1 → 36
Calls

9 calls:

2.0ms
(fma.f64 x (/.f64 y z) x)
x
-inf
2.0ms
(fma.f64 x (/.f64 y z) x)
x
inf
2.0ms
(fma.f64 x (/.f64 y z) x)
x
0
1.0ms
(fma.f64 x (/.f64 y z) x)
z
inf
1.0ms
(fma.f64 x (/.f64 y z) x)
y
-inf

rewrite39.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
616×log1p-expm1-u_binary64
616×expm1-log1p-u_binary64
323×log-prod_binary64
119×expm1-udef_binary64
119×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
11248
216388
Stop Event
1×node limit
Counts
1 → 29

simplify19.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
20×fma-def_binary64
10×associate-*r*_binary64
9×associate-/r/_binary64
8×associate-/l*_binary64
6×associate-*l*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
011324
119324
231264
342264
472264
586264
6106264
7115264
8117264
Stop Event
1×saturated
Counts
65 → 35

prune22.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New31435
Fresh101
Picked011
Done000
Total32537
Error
0.0b
Counts
37 → 5
Alt Table
StatusErrorProgram
4.9b
(fma.f64 y (/.f64 x z) x)
34.0b
(pow.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) 2)
▶4.8b
(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) 3)
✓3.6b
(fma.f64 x (/.f64 y z) x)
5.2b
(+.f64 (/.f64 (*.f64 y x) z) x)
Compiler

Compiled 479 to 162 computations (66.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.6b
(cbrt.f64 (fma.f64 x (/.f64 y z) x))
✓0.7b
(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) 3)
3.4b
(fma.f64 x (/.f64 y z) x)

series507.0ms (13.5%)

Counts
2 → 24
Calls

18 calls:

170.0ms
(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) 3)
y
0
146.0ms
(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) 3)
z
-inf
145.0ms
(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) 3)
z
inf
6.0ms
(cbrt.f64 (fma.f64 x (/.f64 y z) x))
y
0
5.0ms
(cbrt.f64 (fma.f64 x (/.f64 y z) x))
z
inf

rewrite48.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
784×log1p-expm1-u_binary64
784×expm1-log1p-u_binary64
87×prod-diff_binary64
84×add-sqr-sqrt_binary64
79×add-cbrt-cube_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0918
118518
2213918
Stop Event
1×node limit
Counts
2 → 49

simplify35.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
710×associate-/r*_binary64
662×fma-def_binary64
263×unswap-sqr_binary64
257×associate-/r/_binary64
181×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
041750
1131732
2391711
31936699
Stop Event
1×node limit
Counts
73 → 60

prune46.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New94195
Fresh033
Picked011
Done011
Total946100
Error
0.0b
Counts
100 → 6
Alt Table
StatusErrorProgram
▶4.9b
(fma.f64 y (/.f64 x z) x)
34.0b
(pow.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) 2)
✓4.8b
(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) 3)
✓3.6b
(fma.f64 x (/.f64 y z) x)
5.2b
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))) 2)) (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))))
5.2b
(+.f64 (/.f64 (*.f64 y x) z) x)
Compiler

Compiled 1602 to 653 computations (59.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓4.8b
(fma.f64 y (/.f64 x z) x)

series14.0ms (0.4%)

Counts
1 → 36
Calls

9 calls:

4.0ms
(fma.f64 y (/.f64 x z) x)
x
0
2.0ms
(fma.f64 y (/.f64 x z) x)
x
-inf
2.0ms
(fma.f64 y (/.f64 x z) x)
x
inf
1.0ms
(fma.f64 y (/.f64 x z) x)
y
-inf
1.0ms
(fma.f64 y (/.f64 x z) x)
y
inf

rewrite42.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
616×log1p-expm1-u_binary64
616×expm1-log1p-u_binary64
323×log-prod_binary64
119×expm1-udef_binary64
119×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
11248
216388
Stop Event
1×node limit
Counts
1 → 29

simplify20.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
20×fma-def_binary64
10×associate-*r*_binary64
9×associate-/r/_binary64
8×associate-/l*_binary64
6×associate-*l*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
011324
119324
231264
342264
472264
586264
6106264
7115264
8117264
Stop Event
1×saturated
Counts
65 → 35

prune17.0ms (0.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New35035
Fresh033
Picked011
Done022
Total35641
Error
0.0b
Counts
41 → 6
Alt Table
StatusErrorProgram
✓4.9b
(fma.f64 y (/.f64 x z) x)
34.0b
(pow.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) 2)
✓4.8b
(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) 3)
✓3.6b
(fma.f64 x (/.f64 y z) x)
▶5.2b
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))) 2)) (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))))
5.2b
(+.f64 (/.f64 (*.f64 y x) z) x)
Compiler

Compiled 522 to 173 computations (66.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.5b
(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))) 2)
0.6b
(cbrt.f64 (fma.f64 x (/.f64 y z) x))
✓0.6b
(cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
3.4b
(fma.f64 x (/.f64 y z) x)

series615.0ms (16.3%)

Counts
2 → 72
Calls

18 calls:

115.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))) 2)
x
-inf
101.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
x
-inf
89.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
x
0
86.0ms
(cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
x
inf
86.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))) 2)
x
inf

rewrite51.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
856×log1p-expm1-u_binary64
856×expm1-log1p-u_binary64
97×add-sqr-sqrt_binary64
91×add-cube-cbrt_binary64
91×add-cbrt-cube_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01027
120227
2239627
Stop Event
1×node limit
Counts
2 → 42

simplify69.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
686×associate-/l*_binary64
469×fma-def_binary64
462×associate-/r*_binary64
195×associate-/r/_binary64
155×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01863448
15833101
221172689
Stop Event
1×node limit
Counts
114 → 108

prune222.0ms (5.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New3600360
Fresh022
Picked011
Done033
Total3606366
Error
0.0b
Counts
366 → 6
Alt Table
StatusErrorProgram
✓4.9b
(fma.f64 y (/.f64 x z) x)
34.0b
(pow.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) 2)
✓4.8b
(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) 3)
✓3.6b
(fma.f64 x (/.f64 y z) x)
✓5.2b
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))) 2)) (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))))
5.2b
(+.f64 (/.f64 (*.f64 y x) z) x)
Compiler

Compiled 14613 to 5203 computations (64.4% saved)

regimes204.0ms (5.4%)

Accuracy

Total 1.6b remaining (99.1%)

Threshold costs 0b (0%)

Counts
21 → 5
Compiler

Compiled 1512 to 838 computations (44.6% saved)

bsearch51.0ms (1.3%)

Algorithm
4×binary-search
Calls

4 calls:

18.0ms
x
16.0ms
x
11.0ms
x
5.0ms
x
Steps
ItersPointRange
1.1147993284127676e-87
∈ [
4.2017530616152036e-88
, 
1.8204299919059153e-87
]
3.162995441140994e-151
∈ [
1.1942149943023898e-159
, 
2.133541830397882e-148
]
-6.363410517185796e-300
∈ [
-6.791053444696439e-300
, 
-3.023280644887128e-307
]
-2.041895623003483e-62
∈ [
-7.092321156861636e-62
, 
-6.032591974008712e-66
]
Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02468
12668
Stop Event
1×saturated

end99.0ms (2.6%)

Stop Event
1×fuel
Compiler

Compiled 186 to 89 computations (52.2% saved)

Profiling

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