Details

Time bar (total: 5.2s)

analyze1.0ms (0%)

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)

sample1.7s (33.3%)

Results
849.0ms2287×body1024valid
465.0ms4402×body128valid
269.0ms1012×body512valid
102.0ms555×body256valid
Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify10.0ms (0.2%)

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 → 2
Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
19.7b
Counts
3 → 1
Alt Table
StatusErrorProgram
19.7b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 47 to 38 computations (19.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
0.1b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b
(/.f64 1 (sqrt.f64 x))
2.6b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series41.0ms (0.8%)

Counts
4 → 8
Calls

4 calls:

14.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
12.0ms
(/.f64 1 (sqrt.f64 x))
8.0ms
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
7.0ms
(sqrt.f64 (+.f64 x 1))

rewrite101.0ms (2%)

Algorithm
batch-egg-rewrite
Rules
198×egg-rr
Counts
4 → 198
Calls

2 calls:

97.0ms
((-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (+.f64 x 1)))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0938
120530
2257030
3475730
4494830
000
100

simplify64.0ms (1.2%)

Algorithm
egg-herbie
Rules
914×fma-neg_binary64
743×cancel-sign-sub-inv_binary64
601×distribute-rgt-neg-in_binary64
443×fma-def_binary64
382×unsub-neg_binary64
Counts
206 → 211
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02794
17986
220376
356664
4170664
5323964
6440164
7511964

prune275.0ms (5.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New20011211
Fresh000
Picked011
Done000
Total20012212
Error
19.2b
Counts
212 → 12
Alt Table
StatusErrorProgram
29.0b
(fma.f64 (*.f64 (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 x -1/2))
29.2b
(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -1)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -1) (pow.f64 (+.f64 1 x) -1/2)))
29.5b
(+.f64 (fma.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2) (neg.f64 (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
29.3b
(+.f64 (fma.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 x))) (neg.f64 (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
29.2b
(+.f64 (fma.f64 1 (pow.f64 x -1/2) (neg.f64 (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
29.8b
(fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
29.2b
(fma.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) (neg.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (pow.f64 x -1/2))
29.5b
(fma.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
19.7b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
29.9b
(fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
25.2b
(/.f64 (-.f64 (/.f64 1 x) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
30.4b
(/.f64 (+.f64 (pow.f64 (sqrt.f64 x) -3) (pow.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) 3)) (+.f64 (/.f64 1 x) (-.f64 (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (*.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))))
Compiler

Compiled 5219 to 4196 computations (19.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 -1 (sqrt.f64 (+.f64 1 x)))
0.3b
(*.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
2.5b
(/.f64 (-.f64 (/.f64 1 x) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
15.7b
(-.f64 (/.f64 1 x) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))

series134.0ms (2.6%)

Counts
4 → 34
Calls

4 calls:

106.0ms
(/.f64 (-.f64 (/.f64 1 x) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
23.0ms
(/.f64 -1 (sqrt.f64 (+.f64 1 x)))
3.0ms
(-.f64 (/.f64 1 x) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
3.0ms
(*.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

rewrite122.0ms (2.4%)

Algorithm
batch-egg-rewrite
Rules
331×egg-rr
Counts
4 → 331
Calls

2 calls:

114.0ms
((-.f64 (/.f64 1 x) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))) (/.f64 (-.f64 (/.f64 1 x) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))) (*.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 x))) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01459
133140
2371740
3504240
000
100

simplify76.0ms (1.5%)

Algorithm
egg-herbie
Rules
573×fma-neg_binary64
464×sub-neg_binary64
292×associate-+l+_binary64
236×fma-def_binary64
234×associate--l+_binary64
Counts
365 → 375
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0102785
1284733
2880707
33266691
44704691
54982691

prune507.0ms (9.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New4643467
Fresh9110
Picked101
Done101
Total4754479
Error
5.9b
Counts
479 → 4
Alt Table
StatusErrorProgram
48.8b
(/.f64 1 (pow.f64 x 3/2))
39.8b
(/.f64 (-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3))) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
29.2b
(fma.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) (neg.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (pow.f64 x -1/2))
19.7b
(/.f64 (/.f64 (-.f64 (+.f64 1 x) x) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
Compiler

Compiled 14897 to 12129 computations (18.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
0.1b
(/.f64 -1 (sqrt.f64 (+.f64 1 x)))
0.3b
(/.f64 (/.f64 (-.f64 (+.f64 1 x) x) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
2.4b
(-.f64 (+.f64 1 x) x)

series59.0ms (1.1%)

Counts
3 → 24
Calls

3 calls:

50.0ms
(/.f64 (/.f64 (-.f64 (+.f64 1 x) x) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
7.0ms
(-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
1.0ms
(-.f64 (+.f64 1 x) x)

rewrite84.0ms (1.6%)

Algorithm
batch-egg-rewrite
Rules
75×egg-rr
Counts
3 → 75
Calls

2 calls:

82.0ms
((-.f64 (+.f64 1 x) x) (/.f64 (/.f64 (-.f64 (+.f64 1 x) x) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01455
133339
2434039
3494339
000
100

simplify50.0ms (1%)

Algorithm
egg-herbie
Rules
536×associate-+l+_binary64
453×fma-neg_binary64
405×associate-+r+_binary64
403×fma-def_binary64
296×associate--l+_binary64
Counts
99 → 97
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
093696
1277515
2952464
34616460
44992460

prune156.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1367143
Fresh213
Picked101
Done000
Total1398147
Error
0.0b
Counts
147 → 8
Alt Table
StatusErrorProgram
29.2b
(fma.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) (neg.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (pow.f64 x -1/2))
6.9b
(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x)))))
0.7b
(pow.f64 (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (sqrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))) 2)
1.1b
(*.f64 (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 2)) (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (cbrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))
0.4b
(*.f64 (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) 1) (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
7.1b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))) (/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (sqrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))
7.6b
(*.f64 (pow.f64 (/.f64 1 (cbrt.f64 (*.f64 x (+.f64 1 x)))) 2) (*.f64 (/.f64 1 (cbrt.f64 (*.f64 x (+.f64 1 x)))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))
6.9b
(*.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
Compiler

Compiled 4690 to 3606 computations (23.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
0.1b
(/.f64 1 (hypot.f64 (sqrt.f64 x) x))
0.1b
(*.f64 (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) 1) (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
0.3b
(/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))

series572.0ms (11.1%)

Counts
4 → 22
Calls

4 calls:

278.0ms
(/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
264.0ms
(*.f64 (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) 1) (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
25.0ms
(/.f64 1 (hypot.f64 (sqrt.f64 x) x))
5.0ms
(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))

rewrite118.0ms (2.3%)

Algorithm
batch-egg-rewrite
Rules
156×egg-rr
Counts
4 → 156
Calls

2 calls:

114.0ms
((/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (*.f64 (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) 1) (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))) (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
0.0ms
()
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01481
130670
2372370
3533870
000
100

simplify58.0ms (1.1%)

Algorithm
egg-herbie
Rules
648×fma-def_binary64
615×associate-/r*_binary64
546×fma-neg_binary64
371×times-frac_binary64
362×cancel-sign-sub-inv_binary64
Counts
178 → 196
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
084632
1226618
2582500
31652366
44992366
55220366

prune354.0ms (6.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2276233
Fresh437
Picked101
Done000
Total2329241
Error
0b
Counts
241 → 9
Alt Table
StatusErrorProgram
6.9b
(*.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
6.6b
(/.f64 (/.f64 (pow.f64 (hypot.f64 (sqrt.f64 x) x) -2) (hypot.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4))) (hypot.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 1 x) -1/4)))
29.2b
(fma.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) (neg.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (pow.f64 x -1/2))
0.4b
(/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (*.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
0.7b
(pow.f64 (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (sqrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))) 2)
0.3b
(*.f64 (/.f64 (*.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 1) (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
0.7b
(/.f64 1 (*.f64 (hypot.f64 (sqrt.f64 x) x) (*.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))))
6.6b
(/.f64 (pow.f64 (hypot.f64 (sqrt.f64 x) x) -2) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
0.7b
(*.f64 (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) 1) (/.f64 (/.f64 1 (hypot.f64 (sqrt.f64 x) x)) (fma.f64 (cbrt.f64 (pow.f64 x -1)) (cbrt.f64 (pow.f64 x -1/2)) (pow.f64 (+.f64 1 x) -1/2))))
Compiler

Compiled 6911 to 4496 computations (34.9% saved)

regimes408.0ms (7.9%)

Accuracy

Total 0.3b remaining (97.2%)

Threshold costs 0.3b (97.2%)

Counts
163 → 1
Compiler

Compiled 6668 to 5234 computations (21.5% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
/-rgt-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01539
12139
22039

end194.0ms (3.8%)

Compiler

Compiled 260 to 196 computations (24.6% saved)

Profiling

Loading profile data...