Details

Time bar (total: 4.8s)

analyze1.8s (36.9%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.7%0.3%0
0%99.7%0.3%1
0%99.7%0.3%2
0%99.7%0.3%3
0%99.7%0.3%4
0%99.7%0.3%5
0%99.7%0.3%6
0%99.7%0.3%7
0%99.7%0.3%8
0%99.7%0.3%9
0%99.7%0.3%10
0%99.7%0.3%11
0%99.7%0.3%12
1.6%98.1%0.3%13
3.1%96.6%0.3%14
Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.8s (37.9%)

Symmetry

(sort x y)

(sort z t)

(sort a b)

Results
1.2s8256×body128valid
562.0ms4127×body128invalid
Compiler

Compiled 53 to 35 computations (34% saved)

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
18×fma-def_binary64
5×+-commutative_binary64
3×*-commutative_binary64
3×associate-+r+_binary64
3×associate-+l+_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01214
12012
23512
34312
44312

prune8.0ms (0.2%)

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
▶0.0b
(fma.f64 a b (fma.f64 x y (*.f64 z t)))
0.0b
(+.f64 (+.f64 (*.f64 x y) (*.f64 z t)) (*.f64 a b))
Compiler

Compiled 90 to 53 computations (41.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 a b (fma.f64 x y (*.f64 z t)))
✓0.0b
(fma.f64 x y (*.f64 z t))

series28.0ms (0.6%)

Counts
2 → 120
Calls

2 calls:

19.0ms
(fma.f64 a b (fma.f64 x y (*.f64 z t)))
8.0ms
(fma.f64 x y (*.f64 z t))

rewrite1.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
2×*-un-lft-identity_binary64
2×add-sqr-sqrt_binary64
2×add-cube-cbrt_binary64
2×add-cbrt-cube_binary64
2×add-exp-log_binary64
Counts
2 → 20
Calls

2 calls:

0.0ms
(fma.f64 x y (*.f64 z t))
0.0ms
(fma.f64 a b (fma.f64 x y (*.f64 z t)))

simplify144.0ms (3%)

Algorithm
1×egg-herbie
Rules
914×distribute-lft-in_binary64
914×distribute-rgt-in_binary64
738×unswap-sqr_binary64
682×distribute-rgt-out_binary64
377×fma-def_binary64
Counts
140 → 47
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0371376
1501334
21361334
35451334
430271334
531171334
634541334
738271334
843051334
944211334
1056411334

prune29.0ms (0.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New45247
Fresh101
Picked101
Done000
Total47249
Error
0b
Counts
49 → 2
Alt Table
StatusErrorProgram
▶0.0b
(fma.f64 a b (fma.f64 t z (*.f64 y x)))
32.6b
(fma.f64 a b (*.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t)))))
Compiler

Compiled 697 to 158 computations (77.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 t z (*.f64 y x))
✓0.0b
(fma.f64 a b (fma.f64 t z (*.f64 y x)))

series28.0ms (0.6%)

Counts
2 → 120
Calls

2 calls:

20.0ms
(fma.f64 a b (fma.f64 t z (*.f64 y x)))
8.0ms
(fma.f64 t z (*.f64 y x))

rewrite1.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
2×*-un-lft-identity_binary64
2×add-sqr-sqrt_binary64
2×add-cube-cbrt_binary64
2×add-cbrt-cube_binary64
2×add-exp-log_binary64
Counts
2 → 20
Calls

2 calls:

0.0ms
(fma.f64 a b (fma.f64 t z (*.f64 y x)))
0.0ms
(fma.f64 t z (*.f64 y x))

simplify149.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
914×distribute-lft-in_binary64
914×distribute-rgt-in_binary64
738×unswap-sqr_binary64
682×distribute-rgt-out_binary64
377×fma-def_binary64
Counts
140 → 46
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0351376
1501334
21361334
35451334
430411334
531311334
634681334
738411334
843191334
944351334
1056411334

prune23.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New46046
Fresh011
Picked011
Done000
Total46248
Error
0b
Counts
48 → 2
Alt Table
StatusErrorProgram
✓0.0b
(fma.f64 a b (fma.f64 t z (*.f64 y x)))
▶32.6b
(fma.f64 a b (*.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t)))))
Compiler

Compiled 660 to 142 computations (78.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 a b (*.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t)))))
0.0b
(fma.f64 x y (*.f64 z t))
✓0.2b
(*.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))))
✓1.5b
(sqrt.f64 (fma.f64 x y (*.f64 z t)))

series77.0ms (1.6%)

Counts
3 → 136
Calls

3 calls:

48.0ms
(sqrt.f64 (fma.f64 x y (*.f64 z t)))
19.0ms
(fma.f64 a b (*.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t)))))
9.0ms
(*.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))))

rewrite11.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
29×add-sqr-sqrt_binary64
21×sqrt-prod_binary64
19×pow1_binary64
12×*-un-lft-identity_binary64
12×add-cube-cbrt_binary64
Counts
3 → 78
Calls

3 calls:

5.0ms
(*.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t))))
1.0ms
(sqrt.f64 (fma.f64 x y (*.f64 z t)))
0.0ms
(fma.f64 a b (*.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t)))))

simplify111.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
405×associate-/r*_binary64
395×associate-+l+_binary64
346×fma-neg_binary64
338×unswap-sqr_binary64
288×*-commutative_binary64
Counts
214 → 129
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01312945
12912767
29042705
322512677
449132677
550752677

prune94.0ms (2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New2100210
Fresh000
Picked011
Done011
Total2102212
Error
0b
Counts
212 → 2
Alt Table
StatusErrorProgram
✓0.0b
(fma.f64 a b (fma.f64 t z (*.f64 y x)))
✓32.6b
(fma.f64 a b (*.f64 (sqrt.f64 (fma.f64 x y (*.f64 z t))) (sqrt.f64 (fma.f64 x y (*.f64 z t)))))
Compiler

Compiled 5236 to 1185 computations (77.4% saved)

regimes335.0ms (6.9%)

Accuracy

Total 0.0b remaining (11.8%)

Threshold costs 0.0b (11.8%)

Counts
26 → 1
Compiler

Compiled 5174 to 3456 computations (33.2% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01012
11112
21112

end138.0ms (2.9%)

Remove

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 159 to 92 computations (42.1% saved)

Profiling

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