Details

Time bar (total: 7.6s)

analyze1.3s (17.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
10.1%89.6%0.2%11
15.2%84.6%0.2%12
20.5%79.3%0.2%13
21.6%77.1%1.3%14
Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.5s (19.8%)

Results
1.0s8256×body128valid
348.0ms2716×body128invalid
Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify68.0ms (0.9%)

Algorithm
egg-herbie
Rules
946×fma-def_binary64
719×fma-neg_binary64
235×cancel-sign-sub-inv_binary64
163×distribute-rgt-in_binary64
116×distribute-lft-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01013
11613
23111
36211
413011
523111
639011
763911
895511
9127211
10138111
11144911
12147411
13147111
14147111
15139811

prune3.0ms (0%)

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
6.9b
(fma.f64 y (/.f64 (-.f64 z t) a) x)
5.8b
(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
Compiler

Compiled 76 to 45 computations (40.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
0.0b
(*.f64 y (-.f64 z t))
6.7b
(/.f64 (*.f64 y (-.f64 z t)) a)

series54.0ms (0.7%)

Counts
3 → 144
Calls

3 calls:

28.0ms
(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
19.0ms
(/.f64 (*.f64 y (-.f64 z t)) a)
7.0ms
(*.f64 y (-.f64 z t))

rewrite20.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity_binary64
26×add-sqr-sqrt_binary64
22×add-cube-cbrt_binary64
18×prod-diff_binary64
13×distribute-lft-in_binary64
Counts
3 → 92
Calls

3 calls:

6.0ms
(/.f64 (*.f64 y (-.f64 z t)) a)
5.0ms
(*.f64 y (-.f64 z t))
4.0ms
(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

simplify196.0ms (2.6%)

Algorithm
egg-herbie
Rules
599×times-frac_binary64
517×distribute-rgt-in_binary64
492×distribute-lft-in_binary64
448×fma-def_binary64
124×associate-*l*_binary64
Counts
236 → 148
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01992898
14252525
215582355
351862355

prune157.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1426148
Fresh011
Picked101
Done000
Total1437150
Error
0.0b
Counts
150 → 7
Alt Table
StatusErrorProgram
6.2b
(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
5.8b
(+.f64 x (-.f64 (/.f64 (*.f64 y z) a) (/.f64 (*.f64 y t) a)))
38.2b
(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x) 3))
6.9b
(fma.f64 y (/.f64 (-.f64 z t) a) x)
35.4b
(+.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))
3.0b
(+.f64 x (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
5.8b
(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
Compiler

Compiled 2667 to 793 computations (70.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
0.5b
(*.f64 (cbrt.f64 a) (cbrt.f64 a))
0.5b
(cbrt.f64 a)
4.9b
(*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))

series865.0ms (11.4%)

Counts
4 → 96
Calls

4 calls:

566.0ms
(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
129.0ms
(*.f64 (cbrt.f64 a) (cbrt.f64 a))
120.0ms
(cbrt.f64 a)
50.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))

rewrite37.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt_binary64
46×*-un-lft-identity_binary64
43×times-frac_binary64
40×associate-*r*_binary64
36×cbrt-prod_binary64
Counts
4 → 151
Calls

4 calls:

15.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))
4.0ms
(*.f64 (cbrt.f64 a) (cbrt.f64 a))
4.0ms
(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
1.0ms
(cbrt.f64 a)

simplify156.0ms (2.1%)

Algorithm
egg-herbie
Rules
516×fma-def_binary64
334×associate-/r/_binary64
183×associate-*r/_binary64
182×associate-/r*_binary64
179×distribute-rgt-in_binary64
Counts
247 → 234
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02064014
15052982
222582923
339382868
450422868

prune214.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2682270
Fresh066
Picked011
Done000
Total2689277
Error
0.0b
Counts
277 → 9
Alt Table
StatusErrorProgram
6.2b
(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
5.8b
(+.f64 x (-.f64 (/.f64 (*.f64 y z) a) (/.f64 (*.f64 y t) a)))
38.2b
(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x) 3))
6.9b
(fma.f64 y (/.f64 (-.f64 z t) a) x)
35.4b
(+.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))
3.0b
(+.f64 x (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
5.8b
(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
16.4b
(+.f64 x (*.f64 (*.f64 y (cbrt.f64 (/.f64 1 (*.f64 a a)))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
3.1b
(+.f64 x (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a))))))
Compiler

Compiled 6259 to 1690 computations (73% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(cbrt.f64 a)
0.5b
(cbrt.f64 (cbrt.f64 a))
0.6b
(cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
4.9b
(*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a)))))

series646.0ms (8.5%)

Counts
3 → 72
Calls

3 calls:

317.0ms
(cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
278.0ms
(cbrt.f64 (cbrt.f64 a))
51.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a)))))

rewrite31.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
39×add-exp-log_binary64
27×add-cbrt-cube_binary64
15×add-sqr-sqrt_binary64
15×cbrt-unprod_binary64
15×prod-exp_binary64
Counts
3 → 77
Calls

3 calls:

20.0ms
(*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a)))))
2.0ms
(cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
1.0ms
(cbrt.f64 (cbrt.f64 a))

simplify121.0ms (1.6%)

Algorithm
egg-herbie
Rules
719×associate-/l/_binary64
444×*-commutative_binary64
398×fma-def_binary64
191×associate-/r/_binary64
189×log-div_binary64
Counts
149 → 114
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01633546
13892803
218092448
343872448
449742448

prune163.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2040204
Fresh077
Picked011
Done011
Total2049213
Error
0.0b
Counts
213 → 9
Alt Table
StatusErrorProgram
6.2b
(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
5.8b
(+.f64 x (-.f64 (/.f64 (*.f64 y z) a) (/.f64 (*.f64 y t) a)))
38.2b
(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x) 3))
6.9b
(fma.f64 y (/.f64 (-.f64 z t) a) x)
35.4b
(+.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))
3.0b
(+.f64 x (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
5.8b
(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
16.4b
(+.f64 x (*.f64 (*.f64 y (cbrt.f64 (/.f64 1 (*.f64 a a)))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
3.1b
(+.f64 x (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a))))))
Compiler

Compiled 6348 to 1370 computations (78.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 x (-.f64 (/.f64 (*.f64 y z) a) (/.f64 (*.f64 y t) a)))
0.0b
(-.f64 (/.f64 (*.f64 y z) a) (/.f64 (*.f64 y t) a))
6.5b
(/.f64 (*.f64 y z) a)
8.1b
(/.f64 (*.f64 y t) a)

series85.0ms (1.1%)

Counts
4 → 90
Calls

4 calls:

31.0ms
(+.f64 x (-.f64 (/.f64 (*.f64 y z) a) (/.f64 (*.f64 y t) a)))
27.0ms
(-.f64 (/.f64 (*.f64 y z) a) (/.f64 (*.f64 y t) a))
14.0ms
(/.f64 (*.f64 y z) a)
14.0ms
(/.f64 (*.f64 y t) a)

rewrite50.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
105×times-frac_binary64
98×prod-diff_binary64
80×*-un-lft-identity_binary64
75×add-sqr-sqrt_binary64
73×add-cube-cbrt_binary64
Counts
4 → 207
Calls

4 calls:

13.0ms
(+.f64 x (-.f64 (/.f64 (*.f64 y z) a) (/.f64 (*.f64 y t) a)))
9.0ms
(-.f64 (/.f64 (*.f64 y z) a) (/.f64 (*.f64 y t) a))
4.0ms
(/.f64 (*.f64 y t) a)
3.0ms
(/.f64 (*.f64 y z) a)

simplify164.0ms (2.2%)

Algorithm
egg-herbie
Rules
925×times-frac_binary64
507×fma-neg_binary64
195×cancel-sign-sub-inv_binary64
182×exp-prod_binary64
174×distribute-rgt-neg-in_binary64
Counts
297 → 320
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02875726
16234778
219924266
341934266
448864266

prune252.0ms (3.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New3182320
Fresh336
Picked011
Done112
Total3227329
Error
0.0b
Counts
329 → 7
Alt Table
StatusErrorProgram
6.2b
(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
5.8b
(+.f64 x (-.f64 (/.f64 (*.f64 y z) a) (/.f64 (*.f64 y t) a)))
2.7b
(+.f64 x (*.f64 (/.f64 y a) (-.f64 z t)))
6.9b
(+.f64 (+.f64 (*.f64 (/.f64 z a) y) x) (*.f64 (neg.f64 (/.f64 y 1)) (/.f64 t a)))
16.4b
(+.f64 x (*.f64 (*.f64 y (cbrt.f64 (/.f64 1 (*.f64 a a)))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
3.1b
(+.f64 x (*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a))))))
38.2b
(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x) 3))
Compiler

Compiled 9314 to 1650 computations (82.3% saved)

regimes1.3s (16.5%)

Accuracy

Total 1.3b remaining (98.9%)

Threshold costs 0b (0%)

Counts
85 → 3
Compiler

Compiled 13653 to 8850 computations (35.2% saved)

bsearch51.0ms (0.7%)

Steps
ItersRangePoint
5
1.9562311358258616e-88
7.777938587842933e-88
6.996154411165649e-88
8
-3.876135808164779e+30
-2.274666984782897e+27
-1.681862728285677e+28
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03578
15578
27378
38878
49478
59578
69478

end107.0ms (1.4%)

Compiler

Compiled 248 to 148 computations (40.3% saved)

Profiling

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