Details

Time bar (total: 9.0s)

analyze2.9s (32.1%)

Algorithm
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
1.2%98.5%0.3%13
1.8%97.9%0.3%14
Compiler

Compiled 25 to 18 computations (28% saved)

sample70.0ms (0.8%)

Algorithm
intervals
Results
16.0ms256×body128valid
8.0ms130×body128invalid
Compiler

Compiled 56 to 42 computations (25% saved)

simplify106.0ms (1.2%)

Algorithm
egg-herbie
Rules
1251×fma-neg_binary64
530×fma-def_binary64
258×cancel-sign-sub-inv_binary64
148×distribute-rgt-in_binary64
135×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01823
13423
27722
315621
433219
567419
695919
7136519
8181519
9183519
10184519
11184619
12184619
13216219
14216619
15216619
16205519

prune4.0ms (0%)

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
(+.f64 (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) c)
0.0b
(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
Compiler

Compiled 128 to 85 computations (33.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
0.0b
(fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))
0.0b
(fma.f64 (*.f64 a b) -1/4 c)

series64.0ms (0.7%)

Counts
3 → 180
Calls

3 calls:

35.0ms
(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
22.0ms
(fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))
7.0ms
(fma.f64 (*.f64 a b) -1/4 c)

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
3 → 30
Calls

3 calls:

0.0ms
(fma.f64 (*.f64 a b) -1/4 c)
0.0ms
(fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))
0.0ms
(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))

simplify197.0ms (2.2%)

Algorithm
egg-herbie
Rules
560×distribute-lft-in_binary64
560×distribute-rgt-in_binary64
420×fma-def_binary64
395×associate-*l*_binary64
366×associate-*r*_binary64
Counts
210 → 74
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0643513
11123132
22312908
37802908
437022908
549692908
650002908
749532908

prune67.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New71374
Fresh101
Picked101
Done000
Total73376
Error
0b
Counts
76 → 3
Alt Table
StatusErrorProgram
0.0b
(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c)))
1.0b
(fma.f64 x y (*.f64 (*.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))))
26.4b
(fma.f64 x y (expm1.f64 (log1p.f64 (fma.f64 a (*.f64 b -1/4) (fma.f64 z (/.f64 t 16) c)))))
Compiler

Compiled 1564 to 789 computations (49.6% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c)))
0.0b
(fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c))

series56.0ms (0.6%)

Counts
2 → 144
Calls

2 calls:

35.0ms
(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c)))
21.0ms
(fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c))

rewrite2.0ms (0%)

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

2 calls:

0.0ms
(fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c))
0.0ms
(fma.f64 x y (fma.f64 z (/.f64 t 16) (fma.f64 a (*.f64 b -1/4) c)))

simplify115.0ms (1.3%)

Algorithm
egg-herbie
Rules
474×distribute-lft-in_binary64
474×distribute-rgt-in_binary64
356×fma-def_binary64
351×associate-*l/_binary64
329×associate-*r/_binary64
Counts
164 → 57
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0553077
11032767
22032543
36152543
426992543
546872543
652852543

prune48.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New56157
Fresh112
Picked101
Done000
Total58260
Error
0b
Counts
60 → 2
Alt Table
StatusErrorProgram
0.0b
(fma.f64 x y (fma.f64 a (*.f64 b -1/4) (fma.f64 1/16 (*.f64 t z) c)))
1.0b
(fma.f64 x y (*.f64 (*.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))))
Compiler

Compiled 1164 to 603 computations (48.2% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x y (fma.f64 a (*.f64 b -1/4) (fma.f64 1/16 (*.f64 t z) c)))
0.0b
(fma.f64 1/16 (*.f64 t z) c)

series41.0ms (0.5%)

Counts
2 → 120
Calls

2 calls:

34.0ms
(fma.f64 x y (fma.f64 a (*.f64 b -1/4) (fma.f64 1/16 (*.f64 t z) c)))
7.0ms
(fma.f64 1/16 (*.f64 t z) c)

rewrite1.0ms (0%)

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

2 calls:

0.0ms
(fma.f64 1/16 (*.f64 t z) c)
0.0ms
(fma.f64 x y (fma.f64 a (*.f64 b -1/4) (fma.f64 1/16 (*.f64 t z) c)))

simplify101.0ms (1.1%)

Algorithm
egg-herbie
Rules
982×distribute-lft-in_binary64
982×distribute-rgt-in_binary64
374×fma-def_binary64
265×associate-*l*_binary64
239×associate-*r*_binary64
Counts
140 → 47
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0502145
1911953
21941949
36981949
448341949
549881949
650131949

prune34.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New47047
Fresh011
Picked011
Done000
Total47249
Error
0b
Counts
49 → 2
Alt Table
StatusErrorProgram
0.0b
(fma.f64 x y (fma.f64 a (*.f64 b -1/4) (fma.f64 1/16 (*.f64 t z) c)))
1.0b
(fma.f64 x y (*.f64 (*.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))))
Compiler

Compiled 947 to 444 computations (53.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (*.f64 a b) -1/4 c)
0.3b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))))
0.5b
(*.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))))
0.6b
(cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))

series758.0ms (8.5%)

Counts
3 → 180
Calls

3 calls:

513.0ms
(*.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))))
220.0ms
(cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))
24.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))))

rewrite23.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
29×pow1_binary64
24×add-sqr-sqrt_binary64
23×cbrt-prod_binary64
16×pow1/3_binary64
14×*-un-lft-identity_binary64
Counts
3 → 93
Calls

3 calls:

7.0ms
(*.f64 (*.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))))
4.0ms
(*.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))))
1.0ms
(cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))

simplify257.0ms (2.9%)

Algorithm
egg-herbie
Rules
335×associate-*r*_binary64
330×fma-def_binary64
257×associate-+r+_binary64
181×associate-*r/_binary64
181×associate-/l*_binary64
Counts
273 → 312
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0163224087
1516324087

prune1.2s (13.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New6060606
Fresh000
Picked011
Done011
Total6062608
Error
0b
Counts
608 → 2
Alt Table
StatusErrorProgram
0.0b
(fma.f64 x y (fma.f64 a (*.f64 b -1/4) (fma.f64 1/16 (*.f64 t z) c)))
1.0b
(fma.f64 x y (*.f64 (*.f64 (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))) (cbrt.f64 (fma.f64 z (/.f64 t 16) (fma.f64 (*.f64 a b) -1/4 c)))))
Compiler

Compiled 66071 to 41549 computations (37.1% saved)

regimes1.2s (13.9%)

Accuracy

Total 0.1b remaining (92.2%)

Threshold costs 0.1b (92.2%)

Counts
60 → 1
Compiler

Compiled 26502 to 17916 computations (32.4% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01519
11719
21719

end69.0ms (0.8%)

Remove

(sort a b)

(sort z t)

(sort x y)

Compiler

Compiled 147 to 98 computations (33.3% saved)

sample1.5s (17.1%)

Algorithm
intervals
Results
535.0ms8000×body128valid
246.0ms3846×body128invalid
Compiler

Compiled 122 to 82 computations (32.8% saved)

Profiling

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