Details

Time bar (total: 12.7s)

analyze22.0ms (0.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%0%50%2
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample33.0ms (0.3%)

Algorithm
intervals
Results
13.0ms69×body1024valid
7.0ms134×body128valid
6.0ms37×body512valid
1.0ms16×body256valid
Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify14.0ms (0.1%)

Algorithm
egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
14×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
11417
22017
32817
43617
55417
67917
79617
811317
912317
1012717
1112917
1211517

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
20.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
20.3b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 36 to 30 computations (16.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (+.f64 x 1))
0.1b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b
(/.f64 1 (sqrt.f64 x))
1.7b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite1.5s (11.8%)

Algorithm
rewrite-expression-head
Error
19.7b
Rules
1084×times-frac_binary64
922×*-un-lft-identity_binary64
802×add-sqr-sqrt_binary64
728×add-cube-cbrt_binary64
594×prod-diff_binary64
Counts
4 → 815
Calls

4 calls:

40.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
5.0ms
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms
(/.f64 1 (sqrt.f64 x))
3.0ms
(sqrt.f64 (+.f64 x 1))
Compiler

Compiled 28085 to 22877 computations (18.5% saved)

series28.0ms (0.2%)

Error
20.0b
Counts
4 → 18
Calls

4 calls:

6.0ms
(sqrt.f64 (+.f64 x 1))
6.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 515 to 413 computations (19.8% saved)

simplify879.0ms (6.9%)

Algorithm
egg-herbie
Rules
762×fma-neg_binary64
623×fma-def_binary64
483×cancel-sign-sub-inv_binary64
358×associate-*r*_binary64
265×times-frac_binary64
Counts
833 → 796
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
024936541
151625707
2125118791
3354317889
4454917879
5496717879
6471417879

prune125.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New78610796
Fresh000
Picked101
Done000
Total78710797
Error
19.7b
Counts
797 → 10
Alt Table
StatusErrorProgram
29.0b
(/.f64 (+.f64 (/.f64 1 (pow.f64 x 3/2)) (/.f64 -1 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 1 (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))))
30.2b
(fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
29.8b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))))
24.8b
(+.f64 (+.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))) 0)
30.5b
(fma.f64 (/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
30.1b
(fma.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 1 (sqrt.f64 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
30.7b
(fma.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))) (/.f64 1 (cbrt.f64 (sqrt.f64 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
23.3b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
62.0b
(+.f64 (/.f64 1 (sqrt.f64 x)) (neg.f64 (/.f64 (sqrt.f64 (+.f64 -1 x)) (sqrt.f64 (fma.f64 x x -1)))))
20.4b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
Compiler

Compiled 2381 to 1747 computations (26.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b
(/.f64 1 (sqrt.f64 x))
0.3b
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
1.6b
(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite1.4s (11.2%)

Algorithm
rewrite-expression-head
Error
19.5b
Rules
1647×*-un-lft-identity_binary64
1576×times-frac_binary64
962×add-sqr-sqrt_binary64
530×add-cube-cbrt_binary64
468×distribute-lft-out_binary64
Counts
4 → 809
Calls

4 calls:

59.0ms
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
21.0ms
(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
5.0ms
(/.f64 1 (sqrt.f64 (+.f64 1 x)))
5.0ms
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 23559 to 18916 computations (19.7% saved)

series43.0ms (0.3%)

Error
5.5b
Counts
4 → 24
Calls

4 calls:

11.0ms
(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
7.0ms
(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
6.0ms
(/.f64 1 (sqrt.f64 (+.f64 1 x)))
4.0ms
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 1003 to 806 computations (19.6% saved)

simplify808.0ms (6.4%)

Algorithm
egg-herbie
Rules
857×fma-def_binary64
709×times-frac_binary64
485×div-sub_binary64
458×fma-neg_binary64
213×cancel-sign-sub-inv_binary64
Counts
833 → 802
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
033832940
173827865
2208325683
3417025677
4445625677
5487925677

prune142.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New8002802
Fresh819
Picked101
Done000
Total8093812
Error
5.4b
Counts
812 → 3
Alt Table
StatusErrorProgram
22.9b
(/.f64 (expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (/.f64 -1 (+.f64 1 x))))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
23.3b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
5.7b
(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
Compiler

Compiled 4118 to 3217 computations (21.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b
(/.f64 1 (sqrt.f64 x))
0.4b
(/.f64 1 (fma.f64 x x x))
5.1b
(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite470.0ms (3.7%)

Algorithm
rewrite-expression-head
Error
5.3b
Rules
661×times-frac_binary64
618×*-un-lft-identity_binary64
260×add-sqr-sqrt_binary64
260×add-cube-cbrt_binary64
228×distribute-lft-out_binary64
Counts
4 → 392
Calls

4 calls:

34.0ms
(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
5.0ms
(/.f64 1 (sqrt.f64 (+.f64 1 x)))
4.0ms
(/.f64 1 (fma.f64 x x x))
3.0ms
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 8323 to 5391 computations (35.2% saved)

series39.0ms (0.3%)

Error
5.4b
Counts
4 → 24
Calls

4 calls:

10.0ms
(/.f64 1 (fma.f64 x x x))
8.0ms
(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
7.0ms
(/.f64 1 (sqrt.f64 (+.f64 1 x)))
4.0ms
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 951 to 732 computations (23% saved)

simplify368.0ms (2.9%)

Algorithm
egg-herbie
Rules
766×fma-neg_binary64
404×cancel-sign-sub-inv_binary64
234×associate-*l*_binary64
214×associate-/r*_binary64
212×associate-*r*_binary64
Counts
416 → 346
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
022311933
146511551
2108011545
3299611534
4438311515
5500411515

prune99.0ms (0.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3397346
Fresh112
Picked011
Done000
Total3409349
Error
0.0b
Counts
349 → 9
Alt Table
StatusErrorProgram
23.3b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
5.1b
(/.f64 (*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 1 (hypot.f64 x (sqrt.f64 x)))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
7.8b
(*.f64 (/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b
(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
0.6b
(*.f64 (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (sqrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (sqrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))))
1.2b
(*.f64 (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (*.f64 (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))))
6.4b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (/.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
5.7b
(/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
6.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (fma.f64 x x x))) (cbrt.f64 (/.f64 1 (fma.f64 x x x)))) (/.f64 (cbrt.f64 (/.f64 1 (fma.f64 x x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
Compiler

Compiled 2444 to 1554 computations (36.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 1 (hypot.f64 x (sqrt.f64 x)))
0.1b
(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
0.2b
(/.f64 1 (sqrt.f64 x))
0.3b
(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite1.0s (8.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
1258×times-frac_binary64
1137×*-un-lft-identity_binary64
495×add-sqr-sqrt_binary64
455×add-cube-cbrt_binary64
432×distribute-lft-out_binary64
Counts
4 → 619
Calls

4 calls:

89.0ms
(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
34.0ms
(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
5.0ms
(/.f64 1 (sqrt.f64 x))
2.0ms
(/.f64 1 (hypot.f64 x (sqrt.f64 x)))
Compiler

Compiled 16653 to 10020 computations (39.8% saved)

series146.0ms (1.2%)

Error
0.0b
Counts
4 → 12
Calls

4 calls:

85.0ms
(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
33.0ms
(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
16.0ms
(/.f64 1 (hypot.f64 x (sqrt.f64 x)))
5.0ms
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 858 to 665 computations (22.5% saved)

simplify997.0ms (7.9%)

Algorithm
egg-herbie
Rules
481×distribute-rgt-in_binary64
465×fma-def_binary64
459×distribute-lft-in_binary64
364×associate-/r*_binary64
245×*-commutative_binary64
Counts
631 → 572
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
023420419
157519047
2150518906
3261718893
4480318784
5496618784

prune228.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New5684572
Fresh347
Picked101
Done101
Total5738581
Error
0b
Counts
581 → 8
Alt Table
StatusErrorProgram
1.2b
(*.f64 (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (*.f64 (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))) (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (cbrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))))
0.3b
(/.f64 (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) (hypot.f64 x (sqrt.f64 x)))
23.3b
(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
0.6b
(*.f64 (/.f64 (/.f64 (sqrt.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x)))) (sqrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))) (sqrt.f64 (hypot.f64 x (sqrt.f64 x)))) (/.f64 (/.f64 (sqrt.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x)))) (sqrt.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))) (sqrt.f64 (hypot.f64 x (sqrt.f64 x)))))
0.4b
(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (cbrt.f64 (pow.f64 (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))) 3)))
7.8b
(*.f64 (/.f64 (/.f64 1 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
6.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (fma.f64 x x x))) (cbrt.f64 (/.f64 1 (fma.f64 x x x)))) (/.f64 (cbrt.f64 (/.f64 1 (fma.f64 x x x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
0.4b
(*.f64 (/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (sqrt.f64 (hypot.f64 x (sqrt.f64 x)))) (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 x (sqrt.f64 x)))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))
Compiler

Compiled 5381 to 3089 computations (42.6% saved)

regimes3.1s (24.4%)

Accuracy

Total 0.3b remaining (93.5%)

Threshold costs 0.3b (93.5%)

Compiler

Compiled 69067 to 54414 computations (21.2% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01336
11736
21636

end1.0ms (0%)

Compiler

Compiled 24 to 15 computations (37.5% saved)

sample1.1s (8.8%)

Algorithm
intervals
Results
412.0ms2247×body1024valid
210.0ms4305×body128valid
133.0ms986×body512valid
42.0ms462×body256valid
Compiler

Compiled 301 to 199 computations (33.9% saved)

Profiling

Loading profile data...