Details

Time bar (total: 4.7s)

analyze228.0ms (4.8%)

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%74.9%25.1%4
12.5%62.4%25.1%5
31.2%31.2%37.6%6
37.5%25%37.6%7
40.6%15.6%43.8%8
42.9%11.7%45.4%9
44.1%7.4%48.5%10
45.1%5.7%49.3%11
45.6%3.6%50.8%12
46%2.8%51.2%13
46.2%1.8%52%14
Compiler

Compiled 17 to 14 computations (17.6% saved)

sample22.0ms (0.5%)

Algorithm
intervals
Results
12.0ms256×body128valid
0.0msbody128nan
0.0msbody128invalid
Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify149.0ms (3.1%)

Algorithm
egg-herbie
Rules
326×associate-/l*_binary64
318×cancel-sign-sub-inv_binary64
290×distribute-rgt-neg-in_binary64
248×distribute-rgt-in_binary64
231×unsub-neg_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01321
12818
26818
313718
419718
529718
667118
7106518
8154418
9165718
10183918
11177118
12174518
13174518
14194318
15177618
16177618
17177618
18158318

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.4b
Counts
2 → 2
Alt Table
StatusErrorProgram
0.4b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.4b
(*.f64 (*.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (+.f64 y -1)))
Compiler

Compiled 74 to 59 computations (20.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 y (/.f64 1 (*.f64 x 9)))
0.2b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.3b
(/.f64 1 (*.f64 x 9))
0.4b
(*.f64 3 (sqrt.f64 x))

rewrite164.0ms (3.5%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
23×*-un-lft-identity_binary64
22×add-exp-log_binary64
20×add-sqr-sqrt_binary64
16×add-cbrt-cube_binary64
15×associate-*r*_binary64
Counts
4 → 99
Calls

4 calls:

14.0ms
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
5.0ms
(+.f64 y (/.f64 1 (*.f64 x 9)))
5.0ms
(*.f64 3 (sqrt.f64 x))
4.0ms
(/.f64 1 (*.f64 x 9))
Compiler

Compiled 1852 to 1376 computations (25.7% saved)

series78.0ms (1.6%)

Error
0.2b
Counts
4 → 27
Calls

4 calls:

32.0ms
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
22.0ms
(+.f64 y (/.f64 1 (*.f64 x 9)))
7.0ms
(/.f64 1 (*.f64 x 9))
7.0ms
(*.f64 3 (sqrt.f64 x))
Compiler

Compiled 816 to 639 computations (21.7% saved)

simplify126.0ms (2.7%)

Algorithm
egg-herbie
Rules
599×times-frac_binary64
452×distribute-rgt-in_binary64
422×distribute-lft-in_binary64
285×associate-/l*_binary64
252×associate-/r*_binary64
Counts
126 → 90
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01601708
13801406
212071401
348591401
449961401
549201401

prune76.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New81990
Fresh101
Picked101
Done000
Total83992
Error
0.0b
Counts
92 → 9
Alt Table
StatusErrorProgram
0.4b
(*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y (-.f64 (/.f64 1/9 x) 1))))
1.2b
(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1)))) (cbrt.f64 (*.f64 (*.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1))))) (cbrt.f64 (*.f64 (*.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1)))))
32.0b
(cbrt.f64 (pow.f64 (*.f64 (*.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1))) 3))
17.2b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (*.f64 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)) (sqrt.f64 (+.f64 (/.f64 1/9 x) y))) 1))
1.0b
(*.f64 (*.f64 (*.f64 3 (sqrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1))) (cbrt.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1))))) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
0.3b
(+.f64 (*.f64 1/3 (sqrt.f64 (/.f64 1 x))) (*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))
0.5b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (*.f64 (/.f64 1 x) 1/9)) 1))
1.0b
(*.f64 (*.f64 (*.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.7b
(*.f64 (*.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 x) (sqrt.f64 3))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
Compiler

Compiled 1250 to 930 computations (25.6% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (/.f64 1 x))
0.2b
(*.f64 (sqrt.f64 x) (+.f64 y -1))
0.3b
(*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1)))
0.4b
(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

rewrite195.0ms (4.1%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
42×add-sqr-sqrt_binary64
33×sqrt-prod_binary64
28×*-un-lft-identity_binary64
24×add-cube-cbrt_binary64
22×times-frac_binary64 associate-*r*_binary64
Counts
4 → 115
Calls

4 calls:

9.0ms
(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
9.0ms
(*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1)))
8.0ms
(*.f64 (sqrt.f64 x) (+.f64 y -1))
3.0ms
(sqrt.f64 (/.f64 1 x))
Compiler

Compiled 2210 to 1625 computations (26.5% saved)

series74.0ms (1.6%)

Error
0.0b
Counts
4 → 24
Calls

4 calls:

27.0ms
(*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1)))
22.0ms
(*.f64 (sqrt.f64 x) (+.f64 y -1))
8.0ms
(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
7.0ms
(sqrt.f64 (/.f64 1 x))
Compiler

Compiled 945 to 730 computations (22.8% saved)

simplify106.0ms (2.2%)

Algorithm
egg-herbie
Rules
451×distribute-rgt-in_binary64
433×distribute-lft-in_binary64
351×times-frac_binary64
298×*-commutative_binary64
253×+-commutative_binary64
Counts
139 → 88
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01611607
13421523
29561516
323791516
442171516
550191516

prune87.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New84488
Fresh268
Picked101
Done000
Total871097
Error
0.0b
Counts
97 → 10
Alt Table
StatusErrorProgram
0.4b
(*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y (-.f64 (/.f64 1/9 x) 1))))
32.0b
(cbrt.f64 (pow.f64 (*.f64 (*.f64 3 (sqrt.f64 x)) (+.f64 y (-.f64 (/.f64 1/9 x) 1))) 3))
0.7b
(+.f64 (*.f64 1/3 (sqrt.f64 (/.f64 1 x))) (*.f64 3 (*.f64 (sqrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (+.f64 y -1) (sqrt.f64 (cbrt.f64 x))))))
0.8b
(+.f64 (*.f64 1/3 (sqrt.f64 (/.f64 1 x))) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y)))) (cbrt.f64 (*.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y))))) (cbrt.f64 (*.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y))))))
17.2b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (*.f64 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)) (sqrt.f64 (+.f64 (/.f64 1/9 x) y))) 1))
1.0b
(*.f64 (*.f64 (*.f64 3 (sqrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1))) (cbrt.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1))))) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
0.6b
(+.f64 (*.f64 1/3 (sqrt.f64 (/.f64 1 x))) (*.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 x) (*.f64 (+.f64 y -1) (sqrt.f64 3)))))
0.5b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (*.f64 (/.f64 1 x) 1/9)) 1))
1.0b
(*.f64 (*.f64 (*.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.4b
(+.f64 (/.f64 1/3 (sqrt.f64 x)) (*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))
Compiler

Compiled 1401 to 1035 computations (26.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (/.f64 1/3 (sqrt.f64 x)) (*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))
0.2b
(*.f64 (sqrt.f64 x) (+.f64 y -1))
0.3b
(*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1)))
0.4b
(/.f64 1/3 (sqrt.f64 x))

rewrite170.0ms (3.6%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
28×add-sqr-sqrt_binary64
25×*-un-lft-identity_binary64
23×add-cube-cbrt_binary64
18×times-frac_binary64
16×sqrt-prod_binary64
Counts
4 → 108
Calls

4 calls:

11.0ms
(+.f64 (/.f64 1/3 (sqrt.f64 x)) (*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))
8.0ms
(*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1)))
8.0ms
(*.f64 (sqrt.f64 x) (+.f64 y -1))
4.0ms
(/.f64 1/3 (sqrt.f64 x))
Compiler

Compiled 2024 to 1277 computations (36.9% saved)

series104.0ms (2.2%)

Error
0.0b
Counts
4 → 30
Calls

4 calls:

39.0ms
(+.f64 (/.f64 1/3 (sqrt.f64 x)) (*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))
26.0ms
(*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1)))
21.0ms
(*.f64 (sqrt.f64 x) (+.f64 y -1))
7.0ms
(/.f64 1/3 (sqrt.f64 x))
Compiler

Compiled 1073 to 778 computations (27.5% saved)

simplify109.0ms (2.3%)

Algorithm
egg-herbie
Rules
757×distribute-rgt-in_binary64
715×distribute-lft-in_binary64
153×associate-*r*_binary64
145×associate-*l*_binary64
105×cancel-sign-sub-inv_binary64
Counts
138 → 89
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01992051
14671972
214061920
347231920
449981920

prune95.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New86389
Fresh279
Picked101
Done000
Total891099
Error
0b
Counts
99 → 10
Alt Table
StatusErrorProgram
0.4b
(*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y (-.f64 (/.f64 1/9 x) 1))))
31.9b
(cbrt.f64 (pow.f64 (+.f64 (*.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y))) (/.f64 1/3 (sqrt.f64 x))) 3))
0.4b
(+.f64 (/.f64 1/3 (sqrt.f64 x)) (*.f64 (/.f64 (sqrt.f64 x) 1/3) (+.f64 y -1)))
0.7b
(+.f64 (*.f64 1/3 (sqrt.f64 (/.f64 1 x))) (*.f64 3 (*.f64 (sqrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (+.f64 y -1) (sqrt.f64 (cbrt.f64 x))))))
0.8b
(+.f64 (*.f64 1/3 (sqrt.f64 (/.f64 1 x))) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y)))) (cbrt.f64 (*.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y))))) (cbrt.f64 (*.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y))))))
17.2b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (*.f64 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)) (sqrt.f64 (+.f64 (/.f64 1/9 x) y))) 1))
1.0b
(*.f64 (*.f64 (*.f64 3 (sqrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1))) (cbrt.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1))))) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
0.6b
(+.f64 (*.f64 1/3 (sqrt.f64 (/.f64 1 x))) (*.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 x) (*.f64 (+.f64 y -1) (sqrt.f64 3)))))
0.5b
(*.f64 (*.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (*.f64 (/.f64 1 x) 1/9)) 1))
14.4b
(/.f64 (-.f64 (/.f64 1/9 x) (*.f64 (*.f64 (+.f64 y -1) (+.f64 y -1)) (*.f64 x 9))) (+.f64 (/.f64 1/3 (sqrt.f64 x)) (*.f64 (*.f64 -3 (sqrt.f64 x)) (+.f64 y -1))))
Compiler

Compiled 1427 to 982 computations (31.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 y (-.f64 (/.f64 1/9 x) 1))
0.2b
(*.f64 (sqrt.f64 x) (+.f64 y (-.f64 (/.f64 1/9 x) 1)))
0.3b
(*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y (-.f64 (/.f64 1/9 x) 1))))
0.4b
(/.f64 1/9 x)

rewrite179.0ms (3.8%)

Algorithm
rewrite-expression-head
Error
0b
Rules
27×*-un-lft-identity_binary64
21×add-sqr-sqrt_binary64
17×add-cube-cbrt_binary64
13×add-exp-log_binary64 add-cbrt-cube_binary64
11×pow1_binary64
Counts
4 → 98
Calls

4 calls:

17.0ms
(*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y (-.f64 (/.f64 1/9 x) 1))))
14.0ms
(*.f64 (sqrt.f64 x) (+.f64 y (-.f64 (/.f64 1/9 x) 1)))
10.0ms
(+.f64 y (-.f64 (/.f64 1/9 x) 1))
3.0ms
(/.f64 1/9 x)
Compiler

Compiled 1741 to 1202 computations (31% saved)

series95.0ms (2%)

Error
0b
Counts
4 → 33
Calls

4 calls:

31.0ms
(*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y (-.f64 (/.f64 1/9 x) 1))))
26.0ms
(*.f64 (sqrt.f64 x) (+.f64 y (-.f64 (/.f64 1/9 x) 1)))
23.0ms
(+.f64 y (-.f64 (/.f64 1/9 x) 1))
6.0ms
(/.f64 1/9 x)
Compiler

Compiled 952 to 723 computations (24.1% saved)

simplify146.0ms (3.1%)

Algorithm
egg-herbie
Rules
526×times-frac_binary64
336×*-commutative_binary64
329×associate-/l*_binary64
324×associate-/l/_binary64
302×associate-*l/_binary64
Counts
131 → 66
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01652007
13701818
212461799
322251799
441521796
548161796
649101796

prune58.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New64266
Fresh369
Picked011
Done000
Total67976
Error
0b
Counts
76 → 9
Alt Table
StatusErrorProgram
0.4b
(*.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y (-.f64 (/.f64 1/9 x) 1))))
0.4b
(+.f64 (/.f64 1/3 (sqrt.f64 x)) (*.f64 (/.f64 (sqrt.f64 x) 1/3) (+.f64 y -1)))
0.6b
(*.f64 3 (*.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1)) (sqrt.f64 (sqrt.f64 x)))))
0.7b
(+.f64 (*.f64 1/3 (sqrt.f64 (/.f64 1 x))) (*.f64 3 (*.f64 (sqrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (+.f64 y -1) (sqrt.f64 (cbrt.f64 x))))))
0.8b
(+.f64 (*.f64 1/3 (sqrt.f64 (/.f64 1 x))) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y)))) (cbrt.f64 (*.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y))))) (cbrt.f64 (*.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y))))))
1.0b
(*.f64 (*.f64 (*.f64 3 (sqrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1))) (cbrt.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1))))) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
0.6b
(+.f64 (*.f64 1/3 (sqrt.f64 (/.f64 1 x))) (*.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 x) (*.f64 (+.f64 y -1) (sqrt.f64 3)))))
14.4b
(/.f64 (-.f64 (/.f64 1/9 x) (*.f64 (*.f64 (+.f64 y -1) (+.f64 y -1)) (*.f64 x 9))) (+.f64 (/.f64 1/3 (sqrt.f64 x)) (*.f64 (*.f64 -3 (sqrt.f64 x)) (+.f64 y -1))))
0.4b
(+.f64 (*.f64 3 (*.f64 y (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (+.f64 (/.f64 1/3 x) -3)))
Compiler

Compiled 755 to 534 computations (29.3% saved)

regimes1.4s (29.5%)

Accuracy

Total 0.3b remaining (92.4%)

Threshold costs 0.3b (92.4%)

Compiler

Compiled 19439 to 15125 computations (22.2% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01821
12521
22221

end1.0ms (0%)

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.0s (21.6%)

Algorithm
intervals
Results
562.0ms8000×body128valid
6.0ms141×body128nan
3.0ms60×body128invalid
Compiler

Compiled 250 to 192 computations (23.2% saved)

Profiling

Loading profile data...