Details

Time bar (total: 4.8s)

analyze633.0ms (13.2%)

Algorithm
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
6.2%93.6%0.1%6
12.5%87.4%0.1%7
15.6%84.3%0.1%8
18.7%71.8%9.5%9
23.4%56%20.6%10
26.3%52.2%21.5%11
31%40.1%28.9%12
35.6%28.9%35.5%13
36.8%27.5%35.7%14
Compiler

Compiled 18 to 12 computations (33.3% saved)

sample41.0ms (0.9%)

Algorithm
intervals
Results
11.0ms256×body128valid
2.0ms60×body128nan
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify10.0ms (0.2%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
distribute-rgt-out_binary64
associate-+r+_binary64
associate-+l+_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01218
12218
23218
33818
43818
53818

prune9.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
22.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
22.1b
(*.f64 2 (sqrt.f64 (+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z))))
Compiler

Compiled 45 to 30 computations (33.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 x (+.f64 y z))
1.2b
(+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z))
20.9b
(sqrt.f64 (+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z)))

rewrite92.0ms (1.9%)

Algorithm
rewrite-expression-head
Error
22.1b
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
pow1_binary64
add-cbrt-cube_binary64
Counts
3 → 51
Calls

3 calls:

7.0ms
(*.f64 x (+.f64 y z))
6.0ms
(sqrt.f64 (+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z)))
6.0ms
(+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z))
Compiler

Compiled 977 to 297 computations (69.6% saved)

series136.0ms (2.8%)

Error
21.6b
Counts
3 → 47
Calls

3 calls:

55.0ms
(sqrt.f64 (+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z)))
35.0ms
(+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z))
27.0ms
(*.f64 x (+.f64 y z))
Compiler

Compiled 1930 to 1292 computations (33.1% saved)

simplify95.0ms (2%)

Algorithm
egg-herbie
Rules
527×distribute-rgt-in_binary64
494×distribute-lft-in_binary64
359×associate-+l+_binary64
354×sub-neg_binary64
248×cancel-sign-sub-inv_binary64
Counts
98 → 76
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01831535
14471448
214391433
346771433
451161433

prune84.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New641276
Fresh000
Picked101
Done000
Total651277
Error
21.6b
Counts
77 → 12
Alt Table
StatusErrorProgram
46.5b
(*.f64 2 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 z y)) 3) (pow.f64 (*.f64 z y) 3))) (sqrt.f64 (+.f64 (*.f64 (*.f64 z y) (*.f64 z y)) (*.f64 (*.f64 x (+.f64 z y)) (-.f64 (*.f64 x (+.f64 z y)) (*.f64 z y)))))))
40.4b
(*.f64 2 (sqrt.f64 (*.f64 y x)))
22.4b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))))
23.0b
(*.f64 2 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))) (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))) (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))))
22.6b
(*.f64 2 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))) (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))))
44.7b
(*.f64 2 (sqrt.f64 (*.f64 z (+.f64 y x))))
63.6b
(*.f64 2 (+.f64 (sqrt.f64 (*.f64 z x)) (*.f64 (*.f64 y 1/2) (+.f64 (sqrt.f64 (/.f64 x z)) (sqrt.f64 (/.f64 z x))))))
22.1b
(*.f64 2 (sqrt.f64 (+.f64 (*.f64 1 (*.f64 x (+.f64 z y))) (*.f64 y z))))
45.0b
(*.f64 2 (+.f64 (sqrt.f64 (*.f64 y x)) (*.f64 (*.f64 z 1/2) (+.f64 (sqrt.f64 (/.f64 y x)) (sqrt.f64 (/.f64 x y))))))
62.0b
(*.f64 2 (sqrt.f64 (*.f64 z x)))
31.8b
(*.f64 2 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))) 3)))
22.4b
(*.f64 2 (sqrt.f64 (+.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 z y) (cbrt.f64 x))) (*.f64 y z))))
Compiler

Compiled 1494 to 660 computations (55.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 x (+.f64 z y))
1.2b
(+.f64 (*.f64 1 (*.f64 x (+.f64 z y))) (*.f64 y z))
20.9b
(sqrt.f64 (+.f64 (*.f64 1 (*.f64 x (+.f64 z y))) (*.f64 y z)))

rewrite112.0ms (2.3%)

Algorithm
rewrite-expression-head
Error
21.6b
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
pow1_binary64
distribute-lft-in_binary64
Counts
3 → 53
Calls

3 calls:

9.0ms
(+.f64 (*.f64 1 (*.f64 x (+.f64 z y))) (*.f64 y z))
8.0ms
(sqrt.f64 (+.f64 (*.f64 1 (*.f64 x (+.f64 z y))) (*.f64 y z)))
6.0ms
(*.f64 x (+.f64 z y))
Compiler

Compiled 1155 to 523 computations (54.7% saved)

series138.0ms (2.9%)

Error
21.6b
Counts
3 → 47
Calls

3 calls:

52.0ms
(sqrt.f64 (+.f64 (*.f64 1 (*.f64 x (+.f64 z y))) (*.f64 y z)))
37.0ms
(+.f64 (*.f64 1 (*.f64 x (+.f64 z y))) (*.f64 y z))
25.0ms
(*.f64 x (+.f64 z y))
Compiler

Compiled 1986 to 1348 computations (32.1% saved)

simplify90.0ms (1.9%)

Algorithm
egg-herbie
Rules
563×distribute-rgt-in_binary64
537×distribute-lft-in_binary64
360×associate-+l+_binary64
254×cancel-sign-sub-inv_binary64
218×associate--l+_binary64
Counts
100 → 70
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01901549
14581462
214681447
349271447
450541447

prune64.0ms (1.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New70070
Fresh01111
Picked011
Done000
Total701282
Error
21.6b
Counts
82 → 12
Alt Table
StatusErrorProgram
46.5b
(*.f64 2 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 z y)) 3) (pow.f64 (*.f64 z y) 3))) (sqrt.f64 (+.f64 (*.f64 (*.f64 z y) (*.f64 z y)) (*.f64 (*.f64 x (+.f64 z y)) (-.f64 (*.f64 x (+.f64 z y)) (*.f64 z y)))))))
40.4b
(*.f64 2 (sqrt.f64 (*.f64 y x)))
22.4b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))))
23.0b
(*.f64 2 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))) (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))) (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))))
22.6b
(*.f64 2 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))) (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))))
44.7b
(*.f64 2 (sqrt.f64 (*.f64 z (+.f64 y x))))
63.6b
(*.f64 2 (+.f64 (sqrt.f64 (*.f64 z x)) (*.f64 (*.f64 y 1/2) (+.f64 (sqrt.f64 (/.f64 x z)) (sqrt.f64 (/.f64 z x))))))
22.1b
(*.f64 2 (sqrt.f64 (+.f64 (*.f64 1 (*.f64 x (+.f64 z y))) (*.f64 y z))))
45.0b
(*.f64 2 (+.f64 (sqrt.f64 (*.f64 y x)) (*.f64 (*.f64 z 1/2) (+.f64 (sqrt.f64 (/.f64 y x)) (sqrt.f64 (/.f64 x y))))))
62.0b
(*.f64 2 (sqrt.f64 (*.f64 z x)))
31.8b
(*.f64 2 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))) 3)))
22.4b
(*.f64 2 (sqrt.f64 (+.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 z y) (cbrt.f64 x))) (*.f64 y z))))
Compiler

Compiled 1405 to 644 computations (54.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 x)
0.6b
(cbrt.f64 x)
1.2b
(+.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 z y) (cbrt.f64 x))) (*.f64 y z))
20.9b
(sqrt.f64 (+.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 z y) (cbrt.f64 x))) (*.f64 y z)))

rewrite101.0ms (2.1%)

Algorithm
rewrite-expression-head
Error
21.6b
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
cbrt-prod_binary64
add-log-exp_binary64
Counts
4 → 48
Calls

4 calls:

14.0ms
(+.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 z y) (cbrt.f64 x))) (*.f64 y z))
13.0ms
(sqrt.f64 (+.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 z y) (cbrt.f64 x))) (*.f64 y z)))
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
Compiler

Compiled 1420 to 311 computations (78.1% saved)

series168.0ms (3.5%)

Error
21.6b
Counts
4 → 38
Calls

4 calls:

64.0ms
(sqrt.f64 (+.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 z y) (cbrt.f64 x))) (*.f64 y z)))
49.0ms
(+.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 z y) (cbrt.f64 x))) (*.f64 y z))
15.0ms
(cbrt.f64 x)
15.0ms
(cbrt.f64 x)
Compiler

Compiled 2009 to 1374 computations (31.6% saved)

simplify116.0ms (2.4%)

Algorithm
egg-herbie
Rules
348×distribute-rgt-in_binary64
330×distribute-lft-in_binary64
320×cancel-sign-sub-inv_binary64
273×associate-+l+_binary64
205×associate--l+_binary64
Counts
86 → 61
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01781883
14401290
214331270
346521270
449701270
549741270

prune56.0ms (1.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New61061
Fresh01010
Picked011
Done011
Total611273
Error
21.6b
Counts
73 → 12
Alt Table
StatusErrorProgram
46.5b
(*.f64 2 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 z y)) 3) (pow.f64 (*.f64 z y) 3))) (sqrt.f64 (+.f64 (*.f64 (*.f64 z y) (*.f64 z y)) (*.f64 (*.f64 x (+.f64 z y)) (-.f64 (*.f64 x (+.f64 z y)) (*.f64 z y)))))))
40.4b
(*.f64 2 (sqrt.f64 (*.f64 y x)))
22.4b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))))
23.0b
(*.f64 2 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))) (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))) (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))))
22.6b
(*.f64 2 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))) (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))))
44.7b
(*.f64 2 (sqrt.f64 (*.f64 z (+.f64 y x))))
63.6b
(*.f64 2 (+.f64 (sqrt.f64 (*.f64 z x)) (*.f64 (*.f64 y 1/2) (+.f64 (sqrt.f64 (/.f64 x z)) (sqrt.f64 (/.f64 z x))))))
22.1b
(*.f64 2 (sqrt.f64 (+.f64 (*.f64 1 (*.f64 x (+.f64 z y))) (*.f64 y z))))
45.0b
(*.f64 2 (+.f64 (sqrt.f64 (*.f64 y x)) (*.f64 (*.f64 z 1/2) (+.f64 (sqrt.f64 (/.f64 y x)) (sqrt.f64 (/.f64 x y))))))
62.0b
(*.f64 2 (sqrt.f64 (*.f64 z x)))
31.8b
(*.f64 2 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))) 3)))
22.4b
(*.f64 2 (sqrt.f64 (+.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 z y) (cbrt.f64 x))) (*.f64 y z))))
Compiler

Compiled 1389 to 615 computations (55.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
1.8b
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
20.9b
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
20.9b
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))

rewrite104.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
21.6b
Rules
add-sqr-sqrt_binary64
add-log-exp_binary64
*-un-lft-identity_binary64
sqrt-prod_binary64
add-cube-cbrt_binary64
Counts
4 → 56
Calls

4 calls:

5.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
4.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
4.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
Compiler

Compiled 1917 to 333 computations (82.6% saved)

series239.0ms (5%)

Error
21.6b
Counts
4 → 64
Calls

4 calls:

59.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
57.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
40.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
40.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
Compiler

Compiled 4607 to 2848 computations (38.2% saved)

simplify116.0ms (2.4%)

Algorithm
egg-herbie
Rules
583×associate-*l*_binary64
496×associate-*r*_binary64
418×distribute-rgt-in_binary64
393×distribute-lft-in_binary64
329×sub-neg_binary64
Counts
120 → 78
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01512448
13682274
211932256
347022256
450212256

prune94.0ms (2%)

Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New77178
Fresh099
Picked011
Done022
Total771390
Error
21.6b
Counts
90 → 13
Alt Table
StatusErrorProgram
46.5b
(*.f64 2 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 z y)) 3) (pow.f64 (*.f64 z y) 3))) (sqrt.f64 (+.f64 (*.f64 (*.f64 z y) (*.f64 z y)) (*.f64 (*.f64 x (+.f64 z y)) (-.f64 (*.f64 x (+.f64 z y)) (*.f64 z y)))))))
40.4b
(*.f64 2 (sqrt.f64 (*.f64 y x)))
22.4b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))))
23.0b
(*.f64 2 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))) (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))) (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))))
22.6b
(*.f64 2 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))) (sqrt.f64 (cbrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))))
44.7b
(*.f64 2 (sqrt.f64 (*.f64 z (+.f64 y x))))
63.6b
(*.f64 2 (+.f64 (sqrt.f64 (*.f64 z x)) (*.f64 (*.f64 y 1/2) (+.f64 (sqrt.f64 (/.f64 x z)) (sqrt.f64 (/.f64 z x))))))
22.1b
(*.f64 2 (sqrt.f64 (+.f64 (*.f64 1 (*.f64 x (+.f64 z y))) (*.f64 y z))))
22.7b
(*.f64 2 (*.f64 (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 x y) (*.f64 z (+.f64 x y))))) (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 x y) (*.f64 z (+.f64 x y)))))) (cbrt.f64 (sqrt.f64 (+.f64 (*.f64 x y) (*.f64 z (+.f64 x y))))))) (sqrt.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))))))
45.0b
(*.f64 2 (+.f64 (sqrt.f64 (*.f64 y x)) (*.f64 (*.f64 z 1/2) (+.f64 (sqrt.f64 (/.f64 y x)) (sqrt.f64 (/.f64 x y))))))
62.0b
(*.f64 2 (sqrt.f64 (*.f64 z x)))
31.8b
(*.f64 2 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))) 3)))
22.4b
(*.f64 2 (sqrt.f64 (+.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (+.f64 z y) (cbrt.f64 x))) (*.f64 y z))))
Compiler

Compiled 2334 to 692 computations (70.4% saved)

regimes627.0ms (13.1%)

Accuracy

Total 0.5b remaining (2.5%)

Threshold costs 0.5b (2.5%)

Compiler

Compiled 11450 to 6284 computations (45.1% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01118
11618
21618

end13.0ms (0.3%)

Compiler

Compiled 45 to 30 computations (33.3% saved)

sample1.6s (33.7%)

Algorithm
intervals
Results
334.0ms8000×body128valid
121.0ms2335×body128nan
Compiler

Compiled 361 to 196 computations (45.7% saved)

Profiling

Loading profile data...