Details

Time bar (total: 4.1s)

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 (42.6%)

Results
848.0ms2266×body1024valid
472.0ms4402×body128valid
295.0ms1100×body512valid
87.0ms488×body256valid
Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify12.0ms (0.3%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
11417
22017
32817
43817
55617
69317
712717
817417
921017
1023617
1123817
Stop Event
saturated
Counts
1 → 2

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
20.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
20.1b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 47 to 38 computations (19.1% saved)

localize7.0ms (0.2%)

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))
2.8b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series28.0ms (0.7%)

Counts
3 → 4
Calls

3 calls:

11.0ms
(/.f64 1 (sqrt.f64 x))
10.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms
(/.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite60.0ms (1.5%)

Algorithm
batch-egg-rewrite
Rules
776×prod-diff_binary64
205×fma-neg_binary64
170×log1p-udef_binary64
169×expm1-udef_binary64
117×egg-rr
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0932
120824
2291324
Stop Event
node limit
Counts
3 → 117
Calls

3 calls:

57.0ms
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
57.0ms
(/.f64 1 (sqrt.f64 x))
57.0ms
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify40.0ms (1%)

Algorithm
egg-herbie
Rules
695×fma-neg_binary64
558×cancel-sign-sub-inv_binary64
474×distribute-rgt-neg-in_binary64
284×unswap-sqr_binary64
180×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01847
15243
213139
343431
4147831
5380031
Stop Event
node limit
Counts
121 → 124

prune177.0ms (4.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New11014124
Fresh000
Picked101
Done000
Total11114125
Error
19.4b
Counts
125 → 14
Alt Table
StatusErrorProgram
29.9b
(fma.f64 (sqrt.f64 (pow.f64 x -1/2)) (sqrt.f64 (pow.f64 x -1/2)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
25.5b
(-.f64 (/.f64 1 (sqrt.f64 x)) (pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) 2))
24.8b
(/.f64 (-.f64 (/.f64 1 x) (*.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))) (-.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))
30.1b
(fma.f64 (pow.f64 (pow.f64 x 1/4) -1) (pow.f64 (pow.f64 x 1/4) -1) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
30.3b
(fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
30.0b
(+.f64 (fma.f64 (pow.f64 (pow.f64 x 1/4) -1) (pow.f64 (pow.f64 x 1/4) -1) (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))))
29.5b
(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2))) (cbrt.f64 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
29.6b
(+.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))))
20.1b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
30.4b
(fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
29.9b
(+.f64 (fma.f64 (sqrt.f64 (pow.f64 x -1/2)) (sqrt.f64 (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))))
29.7b
(+.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)))
29.6b
(+.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))))
31.3b
(/.f64 (+.f64 (pow.f64 (sqrt.f64 x) -3) (pow.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 3)) (+.f64 (/.f64 1 x) (-.f64 (*.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (*.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))))
Compiler

Compiled 3313 to 2690 computations (18.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
0.2b
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x))
2.8b
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series63.0ms (1.5%)

Counts
3 → 1
Calls

3 calls:

28.0ms
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
22.0ms
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x))
12.0ms
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite72.0ms (1.8%)

Algorithm
batch-egg-rewrite
Rules
473×fma-def_binary64
237×fma-neg_binary64
209×log-div_binary64
182×egg-rr
178×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0951
120843
2314443
Stop Event
node limit
Counts
3 → 182
Calls

3 calls:

68.0ms
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
68.0ms
(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 x))
68.0ms
(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify12.0ms (0.3%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011
141
Stop Event
saturated
Counts
183 → 183

prune157.0ms (3.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1812183
Fresh13013
Picked101
Done000
Total1952197
Error
0.2b
Counts
197 → 2
Alt Table
StatusErrorProgram
0.4b
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
19.9b
(/.f64 (*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 x -1/2)) (sqrt.f64 (+.f64 1 x)))
Compiler

Compiled 4122 to 2774 computations (32.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series71.0ms (1.8%)

Counts
4 → 3
Calls

4 calls:

31.0ms
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
22.0ms
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x))
11.0ms
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
7.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite83.0ms (2%)

Algorithm
batch-egg-rewrite
Rules
917×prod-diff_binary64
193×egg-rr
119×add-sqr-sqrt_binary64
118×log1p-expm1-u_binary64
118×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01271
130158
2366758
Stop Event
node limit
Counts
4 → 193
Calls

4 calls:

78.0ms
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
78.0ms
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
78.0ms
(/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
78.0ms
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x))

simplify10.0ms (0.2%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
176
Stop Event
saturated
Counts
196 → 195

prune195.0ms (4.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1905195
Fresh011
Picked011
Done000
Total1907197
Error
0.0b
Counts
197 → 7
Alt Table
StatusErrorProgram
3.6b
(*.f64 1 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (+.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))))
0.7b
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (*.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 2))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
3.7b
(*.f64 (/.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (/.f64 (/.f64 1 (+.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))) (pow.f64 (+.f64 1 x) 1/4)))
0.7b
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
0.4b
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
30.4b
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
19.9b
(/.f64 (*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 x -1/2)) (sqrt.f64 (+.f64 1 x)))
Compiler

Compiled 5434 to 3432 computations (36.8% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (+.f64 1 (-.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3))
0.3b
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3)) (sqrt.f64 x))
0.3b
(cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))
0.4b
(pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3)

series647.0ms (15.9%)

Counts
4 → 3
Calls

4 calls:

298.0ms
(pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3)
163.0ms
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3)) (sqrt.f64 x))
116.0ms
(cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))
69.0ms
(/.f64 (+.f64 1 (-.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3))

rewrite70.0ms (1.7%)

Algorithm
batch-egg-rewrite
Rules
611×prod-diff_binary64
186×expm1-udef_binary64
186×log1p-udef_binary64
160×egg-rr
115×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01357
131150
2327750
Stop Event
node limit
Counts
4 → 160
Calls

4 calls:

66.0ms
(/.f64 (+.f64 1 (-.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3))
66.0ms
(/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3)) (sqrt.f64 x))
66.0ms
(cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))
66.0ms
(pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3)

simplify13.0ms (0.3%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
013
143
Stop Event
saturated
Counts
163 → 161

prune168.0ms (4.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1610161
Fresh055
Picked011
Done011
Total1617168
Error
0.0b
Counts
168 → 7
Alt Table
StatusErrorProgram
3.6b
(*.f64 1 (/.f64 (pow.f64 (+.f64 1 x) -1/2) (+.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))))
0.7b
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (*.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 2))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
3.7b
(*.f64 (/.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (/.f64 (/.f64 1 (+.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))) (pow.f64 (+.f64 1 x) 1/4)))
0.7b
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3)) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
0.4b
(/.f64 (/.f64 (/.f64 (+.f64 1 (-.f64 x x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))
30.4b
(/.f64 (/.f64 1/2 x) (sqrt.f64 (+.f64 1 x)))
19.9b
(/.f64 (*.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (pow.f64 x -1/2)) (sqrt.f64 (+.f64 1 x)))
Compiler

Compiled 4530 to 2862 computations (36.8% saved)

regimes295.0ms (7.2%)

Accuracy

Total 0.4b remaining (89.1%)

Threshold costs 0.4b (89.1%)

Counts
151 → 1
Compiler

Compiled 5692 to 4562 computations (19.9% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01127
11527
Stop Event
saturated

end117.0ms (2.9%)

Compiler

Compiled 185 to 133 computations (28.1% saved)

Profiling

Loading profile data...