Details

Time bar (total: 4.5s)

analyze2.0ms (0%)

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

Compiled 13 to 11 computations (15.4% saved)

sample2.0s (45.2%)

Results
1.0s2331×body1024valid
532.0ms4393×body128valid
326.0ms1038×body512valid
113.0ms494×body256valid
Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify10.0ms (0.2%)

Algorithm
1×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
18.4b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶18.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 47 to 38 computations (19.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓0.3b
(/.f64 1 (sqrt.f64 x))
✓1.8b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series40.0ms (0.9%)

Counts
3 → 4
Calls

3 calls:

19.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
13.0ms
(/.f64 1 (sqrt.f64 x))
8.0ms
(/.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite104.0ms (2.3%)

Algorithm
2×batch-egg-rewrite
Rules
776×prod-diff_binary64
428×fma-def_binary64
246×fma-neg_binary64
170×log1p-udef_binary64
169×expm1-udef_binary64
Counts
3 → 167
Calls

3 calls:

100.0ms
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
100.0ms
(/.f64 1 (sqrt.f64 x))
100.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0932
120524
2257024
3475724
4494824
000
100

simplify131.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
695×fma-neg_binary64
559×cancel-sign-sub-inv_binary64
543×unsub-neg_binary64
474×distribute-rgt-neg-in_binary64
424×sub-neg_binary64
Counts
171 → 174
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01847
15143
212239
333031
4105831
5209331
6352631
7413931
8486431
9494931
10500031
11480231

prune239.0ms (5.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New16014174
Fresh000
Picked101
Done000
Total16114175
Error
17.9b
Counts
175 → 14
Alt Table
StatusErrorProgram
28.2b
(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))
▶18.5b
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
28.3b
(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))
28.6b
(+.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))))
28.2b
(fma.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x))) (neg.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2))) (pow.f64 x -1/2))
28.2b
(+.f64 (fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 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))))
32.5b
(pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) 3) 1/3)
31.2b
(/.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)))))))
29.0b
(fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
41.1b
(fma.f64 (-.f64 (pow.f64 (sqrt.f64 x) -3) (pow.f64 (sqrt.f64 (+.f64 1 x)) -3)) (/.f64 1 (+.f64 (/.f64 1 x) (fma.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2) (/.f64 1 (+.f64 1 x))))) (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)))
28.6b
(fma.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
29.0b
(fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
28.4b
(+.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))))
28.3b
(+.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))))
Compiler

Compiled 4853 to 3933 computations (19% saved)

localize13.0ms (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))
✓0.2b
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
✓0.3b
(/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
✓1.8b
(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

series32.0ms (0.7%)

Counts
4 → 48
Calls

4 calls:

13.0ms
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
11.0ms
(/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
5.0ms
(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
3.0ms
(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite94.0ms (2.1%)

Algorithm
2×batch-egg-rewrite
Rules
323×fma-neg_binary64
251×expm1-udef_binary64
251×log1p-udef_binary64
190×egg-rr
153×log1p-expm1-u_binary64
Counts
4 → 190
Calls

4 calls:

90.0ms
(+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
90.0ms
(*.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
90.0ms
(/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
90.0ms
(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01370
131455
2390355
3487355
000
100

simplify93.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
638×fma-def_binary64
404×associate-/r*_binary64
403×times-frac_binary64
369×fma-neg_binary64
255×associate-/l*_binary64
Counts
238 → 271
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01901903
15771779
217901565
346131318
449771318
549291318

prune244.0ms (5.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2665271
Fresh13013
Picked101
Done000
Total2805285
Error
0.5b
Counts
285 → 5
Alt Table
StatusErrorProgram
18.3b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
40.6b
(*.f64 (-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
▶17.9b
(*.f64 (/.f64 (-.f64 (+.f64 1 x) x) (+.f64 x (*.f64 x x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
34.3b
(-.f64 (/.f64 1/2 (pow.f64 x 3/2)) (/.f64 3/8 (*.f64 x (pow.f64 x 3/2))))
45.9b
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
Compiler

Compiled 7925 to 6356 computations (19.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (-.f64 (+.f64 1 x) x) (+.f64 x (*.f64 x x)))
✓0.2b
(*.f64 (/.f64 (-.f64 (+.f64 1 x) x) (+.f64 x (*.f64 x x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
0.3b
(/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
✓1.2b
(-.f64 (+.f64 1 x) x)

series29.0ms (0.7%)

Counts
3 → 36
Calls

3 calls:

24.0ms
(*.f64 (/.f64 (-.f64 (+.f64 1 x) x) (+.f64 x (*.f64 x x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
3.0ms
(/.f64 (-.f64 (+.f64 1 x) x) (+.f64 x (*.f64 x x)))
1.0ms
(-.f64 (+.f64 1 x) x)

rewrite101.0ms (2.3%)

Algorithm
2×batch-egg-rewrite
Rules
270×expm1-udef_binary64
270×log1p-udef_binary64
171×add-sqr-sqrt_binary64
169×log1p-expm1-u_binary64
169×expm1-log1p-u_binary64
Counts
3 → 72
Calls

3 calls:

99.0ms
(/.f64 (-.f64 (+.f64 1 x) x) (+.f64 x (*.f64 x x)))
99.0ms
(*.f64 (/.f64 (-.f64 (+.f64 1 x) x) (+.f64 x (*.f64 x x))) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
99.0ms
(-.f64 (+.f64 1 x) x)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01454
134532
2416932
3498932
4480132
000
100

simplify63.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
564×associate-+l+_binary64
500×fma-neg_binary64
449×fma-def_binary64
365×associate-/r*_binary64
323×associate--l+_binary64
Counts
108 → 110
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01361160
1401972
21227881
34959881
45363881

prune151.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1524156
Fresh134
Picked101
Done000
Total1547161
Error
0.0b
Counts
161 → 7
Alt Table
StatusErrorProgram
7.0b
(*.f64 (pow.f64 (fma.f64 x x x) -1) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
0.5b
(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 1 (hypot.f64 x (sqrt.f64 x)))))
18.3b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
▶0.4b
(/.f64 (/.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (hypot.f64 x (sqrt.f64 x))) (hypot.f64 x (sqrt.f64 x)))
34.3b
(-.f64 (/.f64 1/2 (pow.f64 x 3/2)) (/.f64 3/8 (*.f64 x (pow.f64 x 3/2))))
45.9b
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
0.6b
(pow.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) -1/2) (hypot.f64 x (sqrt.f64 x))) 2)
Compiler

Compiled 4855 to 3510 computations (27.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(hypot.f64 x (sqrt.f64 x))
✓0.2b
(/.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (hypot.f64 x (sqrt.f64 x)))
✓0.2b
(/.f64 (/.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (hypot.f64 x (sqrt.f64 x))) (hypot.f64 x (sqrt.f64 x)))
0.3b
(/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))

series411.0ms (9.2%)

Counts
3 → 10
Calls

3 calls:

199.0ms
(/.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (hypot.f64 x (sqrt.f64 x)))
197.0ms
(/.f64 (/.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (hypot.f64 x (sqrt.f64 x))) (hypot.f64 x (sqrt.f64 x)))
15.0ms
(hypot.f64 x (sqrt.f64 x))

rewrite76.0ms (1.7%)

Algorithm
2×batch-egg-rewrite
Rules
847×prod-diff_binary64
146×add-sqr-sqrt_binary64
143×log1p-expm1-u_binary64
143×expm1-log1p-u_binary64
138×add-log-exp_binary64
Counts
3 → 91
Calls

3 calls:

74.0ms
(hypot.f64 x (sqrt.f64 x))
74.0ms
(/.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (hypot.f64 x (sqrt.f64 x)))
74.0ms
(/.f64 (/.f64 (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) (hypot.f64 x (sqrt.f64 x))) (hypot.f64 x (sqrt.f64 x)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01362
130153
2381053
3533153
000
100

simplify67.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
718×unswap-sqr_binary64
493×fma-neg_binary64
452×associate-/r*_binary64
371×fma-def_binary64
313×distribute-neg-frac_binary64
Counts
101 → 108
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
047220
1109218
2237184
3645124
42303112
54350112
64910112
74983112

prune145.0ms (3.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1751176
Fresh156
Picked101
Done000
Total1776183
Error
0b
Counts
183 → 6
Alt Table
StatusErrorProgram
7.0b
(*.f64 (pow.f64 (fma.f64 x x x) -1) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))))
0.5b
(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (/.f64 1 (hypot.f64 x (sqrt.f64 x)))))
18.3b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
31.9b
(/.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (hypot.f64 x (sqrt.f64 x)))
34.3b
(-.f64 (/.f64 1/2 (pow.f64 x 3/2)) (/.f64 3/8 (*.f64 x (pow.f64 x 3/2))))
45.9b
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
Compiler

Compiled 4918 to 2997 computations (39.1% saved)

regimes252.0ms (5.7%)

Accuracy

Total 0.4b remaining (96.1%)

Threshold costs 0.4b (96.1%)

Counts
123 → 1
Compiler

Compiled 4614 to 3776 computations (18.2% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01125
11525
21425

end107.0ms (2.4%)

Compiler

Compiled 132 to 101 computations (23.5% saved)

Profiling

Loading profile data...