Details

Time bar (total: 4.0s)

analyze380.0ms (9.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%75%25%3
12.5%50%37.5%4
18.7%37.5%43.8%5
21.9%31.2%46.9%6
21.9%29.7%48.5%7
21.9%28.9%49.2%8
22.3%28.1%49.6%9
22.3%27.9%49.8%10
22.3%27.8%49.9%11
22.4%27.7%50%12
22.4%27.6%50%13
22.4%27.6%50%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.5s (37.6%)

Results
627.0ms2080×body1024valid
410.0ms4360×body128valid
244.0ms1053×body512valid
99.0ms535×body256valid
85.0ms228×body2048valid
0.0msbody128invalid
Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify11.0ms (0.3%)

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
0711
11211
21611
32311
43011
54711
67211
79211
810911
911911
1012311
1112511
1211111

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
29.6b
Counts
2 → 1
Alt Table
StatusErrorProgram
29.6b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 24 to 18 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
2.7b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series27.0ms (0.7%)

Counts
2 → 5
Calls

2 calls:

17.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
9.0ms
(sqrt.f64 (+.f64 x 1))

rewrite19.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
64×sqrt-prod_binary64
57×*-un-lft-identity_binary64
45×add-sqr-sqrt_binary64
42×prod-diff_binary64
33×add-cube-cbrt_binary64
Counts
2 → 95
Calls

2 calls:

8.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms
(sqrt.f64 (+.f64 x 1))

simplify160.0ms (4%)

Algorithm
egg-herbie
Rules
1110×fma-neg_binary64
566×unswap-sqr_binary64
455×cancel-sign-sub-inv_binary64
444×fma-def_binary64
429×associate-*l*_binary64
Counts
100 → 98
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01192533
12241344
25921128
325271125
440991093
543811093
646631093
749491093
847301093

prune132.0ms (3.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New94498
Fresh000
Picked101
Done000
Total95499
Error
0.1b
Counts
99 → 4
Alt Table
StatusErrorProgram
29.7b
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
29.6b
(+.f64 (fma.f64 1 (sqrt.f64 (+.f64 x 1)) (neg.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
29.8b
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (*.f64 (cbrt.f64 (sqrt.f64 x)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))) (*.f64 (cbrt.f64 (sqrt.f64 x)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))))))
Compiler

Compiled 2064 to 1080 computations (47.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 1 x))
0.0b
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series34.0ms (0.9%)

Counts
3 → 6
Calls

3 calls:

15.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
9.0ms
(sqrt.f64 (+.f64 1 x))

rewrite24.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity_binary64
28×sqrt-prod_binary64
22×distribute-lft-out_binary64
22×add-sqr-sqrt_binary64
18×times-frac_binary64
Counts
3 → 91
Calls

3 calls:

8.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
6.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms
(sqrt.f64 (+.f64 1 x))

simplify132.0ms (3.3%)

Algorithm
egg-herbie
Rules
888×fma-neg_binary64
558×cancel-sign-sub-inv_binary64
538×times-frac_binary64
389×associate-*l*_binary64
311×associate-*r*_binary64
Counts
97 → 95
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0961310
12031217
24441211
311331207
425561207
542291207
649561207
749981207
848371207

prune137.0ms (3.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New88795
Fresh213
Picked011
Done000
Total90999
Error
0.0b
Counts
99 → 9
Alt Table
StatusErrorProgram
29.8b
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (*.f64 (cbrt.f64 (sqrt.f64 x)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))) (*.f64 (cbrt.f64 (sqrt.f64 x)) (*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x))))))
10.3b
(cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.3b
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.7b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.3b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
10.2b
(*.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.3b
(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
Compiler

Compiled 2002 to 1412 computations (29.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x))
0.1b
(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.2b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.3b
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

series40.0ms (1%)

Counts
4 → 18
Calls

4 calls:

17.0ms
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
10.0ms
(+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x))
8.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
5.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

rewrite61.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
102×sqrt-prod_binary64
74×add-sqr-sqrt_binary64
42×*-un-lft-identity_binary64
36×sqrt-pow1_binary64
30×pow1_binary64
Counts
4 → 171
Calls

4 calls:

16.0ms
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
14.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
12.0ms
(+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x))
3.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

simplify126.0ms (3.1%)

Algorithm
egg-herbie
Rules
729×times-frac_binary64
590×fma-neg_binary64
555×fma-def_binary64
279×cancel-sign-sub-inv_binary64
216×unswap-sqr_binary64
Counts
189 → 220
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02012748
14302530
211182395
327282341
446442341
548412341

prune421.0ms (10.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2642266
Fresh167
Picked011
Done101
Total2669275
Error
0.0b
Counts
275 → 9
Alt Table
StatusErrorProgram
0.3b
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.7b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.3b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
10.2b
(*.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
10.2b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) 3) (pow.f64 (sqrt.f64 x) 3))) (+.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))) (-.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
10.3b
(cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.2b
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.3b
(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
Compiler

Compiled 6870 to 5301 computations (22.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.0b
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.5b
(expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

series49.0ms (1.2%)

Counts
2 → 2
Calls

2 calls:

33.0ms
(expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
15.0ms
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
log1p-expm1-u_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 22
Calls

2 calls:

0.0ms
(expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.0ms
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

simplify80.0ms (2%)

Algorithm
egg-herbie
Rules
824×unswap-sqr_binary64
563×fma-def_binary64
414×associate-*l*_binary64
386×times-frac_binary64
258×associate-*r*_binary64
Counts
24 → 33
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
031445
140380
257380
375380
495380
5145380
6269380
7587380
81551380
94600380
104557380
115007380

prune172.0ms (4.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New991100
Fresh167
Picked011
Done011
Total1009109
Error
0.0b
Counts
109 → 9
Alt Table
StatusErrorProgram
0.3b
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.7b
(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.3b
(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.3b
(log1p.f64 (*.f64 (sqrt.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))
10.2b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) 3) (pow.f64 (sqrt.f64 x) 3))) (+.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))) (-.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))))
0.3b
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
10.3b
(cbrt.f64 (/.f64 (*.f64 (*.f64 1 1) 1) (*.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.2b
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.3b
(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
Compiler

Compiled 2034 to 1527 computations (24.9% saved)

regimes269.0ms (6.8%)

Accuracy

Total 0.1b remaining (79.5%)

Threshold costs 0.1b (79.5%)

Counts
145 → 1
Compiler

Compiled 6000 to 4283 computations (28.6% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01222
11622
21522

end178.0ms (4.5%)

Compiler

Compiled 267 to 209 computations (21.7% saved)

Profiling

Loading profile data...