Details

Time bar (total: 3.2s)

analyze4.0ms (0.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
50%12.5%37.5%4
50%6.2%43.8%5
50%3.1%46.9%6
50%1.6%48.5%7
50%0.8%49.2%8
50%0.4%49.6%9
50%0.2%49.8%10
50%0.1%49.9%11
50%0%50%12
50%0%50%13
50%0%50%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample44.0ms (1.4%)

Algorithm
intervals
Results
7.0ms47×body1024valid
6.0ms155×body128valid
3.0ms30×body512valid
1.0msbody2048valid
1.0ms16×body256valid
Compiler

Compiled 18 to 14 computations (22.2% 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
26.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
26.1b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
2.3b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series25.0ms (0.8%)

Counts
2 → 5
Calls

2 calls:

17.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
8.0ms
(sqrt.f64 (+.f64 x 1))

rewrite18.0ms (0.6%)

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))

simplify157.0ms (4.9%)

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

prune120.0ms (3.8%)

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
0.1b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
25.8b
(/.f64 (-.f64 (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (*.f64 (sqrt.f64 x) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
26.2b
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
27.7b
(log.f64 (/.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))) (exp.f64 (sqrt.f64 x))))
Compiler

Compiled 1966 to 1060 computations (46.1% saved)

localize7.0ms (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))
0.1b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series32.0ms (1%)

Counts
3 → 6
Calls

3 calls:

14.0ms
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
8.0ms
(sqrt.f64 (+.f64 1 x))

rewrite24.0ms (0.8%)

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:

10.0ms
(/.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))

simplify133.0ms (4.2%)

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

prune112.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New89695
Fresh213
Picked101
Done000
Total92799
Error
0.0b
Counts
99 → 7
Alt Table
StatusErrorProgram
0.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
26.2b
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
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 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.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))))
0.1b
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
8.1b
(*.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)))))
Compiler

Compiled 1850 to 1336 computations (27.8% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.0b
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b
(/.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))))

series47.0ms (1.5%)

Counts
2 → 2
Calls

2 calls:

31.0ms
(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 (2.5%)

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

prune129.0ms (4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New991100
Fresh156
Picked011
Done000
Total1007107
Error
0.0b
Counts
107 → 7
Alt Table
StatusErrorProgram
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)))))
26.2b
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))
0.3b
(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
8.0b
(log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)))
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))))
0.1b
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
8.1b
(*.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)))))
Compiler

Compiled 2059 to 1544 computations (25% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series44.0ms (1.4%)

Counts
2 → 2
Calls

2 calls:

30.0ms
(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
14.0ms
(*.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)))))

rewrite104.0ms (3.3%)

Algorithm
rewrite-expression-head
Rules
258×sqrt-prod_binary64
236×*-un-lft-identity_binary64
148×times-frac_binary64
144×add-sqr-sqrt_binary64
84×distribute-lft-out_binary64
Counts
2 → 204
Calls

2 calls:

33.0ms
(*.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)))))
9.0ms
(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

simplify236.0ms (7.4%)

Algorithm
egg-herbie
Rules
635×unswap-sqr_binary64
539×times-frac_binary64
411×div-sub_binary64
403×fma-def_binary64
378×associate-/l*_binary64
Counts
206 → 200
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
01114253
11864015
24933961
312303833
425213833
542433833
642563829
749263829
847883829

prune600.0ms (18.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New3723375
Fresh325
Picked011
Done011
Total3757382
Error
0.0b
Counts
382 → 7
Alt Table
StatusErrorProgram
8.1b
(*.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
(sqrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4))
0.3b
(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4) (/.f64 -1 2))
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)))))
0.2b
(/.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.3b
(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
0.1b
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
Compiler

Compiled 11256 to 8315 computations (26.1% saved)

regimes238.0ms (7.5%)

Accuracy

Total 0.1b remaining (78.2%)

Threshold costs 0.1b (78.2%)

Counts
136 → 1
Compiler

Compiled 5736 to 4140 computations (27.8% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11418
21318

end0.0ms (0%)

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample988.0ms (31.1%)

Algorithm
intervals
Results
313.0ms2006×body1024valid
184.0ms4342×body128valid
104.0ms948×body512valid
43.0ms226×body2048valid
35.0ms478×body256valid
Compiler

Compiled 163 to 127 computations (22.1% saved)

Profiling

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