Details

Time bar (total: 3.3s)

analyze319.0ms (9.6%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
25%74.9%0.1%6
25%74.9%0.1%7
43.7%56.2%0.1%8
62.4%37.4%0.1%9
65.5%34.3%0.1%10
71.8%27.7%0.5%11
79.2%19.7%1.1%12
80.2%18.7%1.1%13
82.8%15%2.2%14
Compiler

Compiled 15 to 11 computations (26.7% saved)

sample951.0ms (28.6%)

Symmetry

(sort x y)

Results
865.0ms8256×body128valid
48.0ms450×body128invalid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify10.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
44×fma-def_binary64
31×associate-*l*_binary64
30×associate-*r*_binary64
19×distribute-lft-in_binary64
19×distribute-rgt-in_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01016
12414
24614
310714
417314
523414
623814
Stop Event
1×saturated
Counts
1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
6.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
7.5b
(/.f64 1 (*.f64 x (*.f64 y (fma.f64 z z 1))))
▶7.0b
(/.f64 (/.f64 1 x) (*.f64 y (+.f64 1 (*.f64 z z))))
Compiler

Compiled 78 to 54 computations (30.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓3.8b
(/.f64 (/.f64 1 x) (*.f64 y (+.f64 1 (*.f64 z z))))
✓5.0b
(*.f64 y (+.f64 1 (*.f64 z z)))

series77.0ms (2.3%)

Counts
2 → 60
Calls

2 calls:

68.0ms
(/.f64 (/.f64 1 x) (*.f64 y (+.f64 1 (*.f64 z z))))
9.0ms
(*.f64 y (+.f64 1 (*.f64 z z)))

rewrite52.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
289×prod-diff_binary64
220×fma-def_binary64
187×expm1-udef_binary64
187×log1p-udef_binary64
170×log-pow_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01026
122222
2313422
Stop Event
1×node limit
Counts
2 → 98
Calls

2 calls:

51.0ms
(/.f64 (/.f64 1 x) (*.f64 y (+.f64 1 (*.f64 z z))))
51.0ms
(*.f64 y (+.f64 1 (*.f64 z z)))

simplify45.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
671×times-frac_binary64
428×distribute-neg-frac_binary64
318×associate-/l*_binary64
199×sub-neg_binary64
189×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
055993
1151903
2366901
31295897
44292897
Stop Event
1×node limit
Counts
158 → 124

prune92.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1159124
Fresh101
Picked101
Done000
Total1179126
Error
0.0b
Counts
126 → 9
Alt Table
StatusErrorProgram
22.6b
(/.f64 (/.f64 1 x) (pow.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) 2))
32.8b
(/.f64 (/.f64 (/.f64 1 y) z) (*.f64 z x))
27.8b
(/.f64 (/.f64 1 y) x)
5.9b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
33.9b
(/.f64 (/.f64 1 x) (*.f64 z (*.f64 y z)))
▶5.8b
(pow.f64 (*.f64 (fma.f64 z z 1) (*.f64 y x)) -1)
7.0b
(/.f64 (/.f64 1 x) (fma.f64 y (*.f64 z z) y))
22.8b
(*.f64 (/.f64 (/.f64 1 (*.f64 y x)) (-.f64 1 (pow.f64 z 4))) (-.f64 1 (*.f64 z z)))
25.2b
(*.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
Compiler

Compiled 2184 to 1278 computations (41.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.9b
(pow.f64 (*.f64 (fma.f64 z z 1) (*.f64 y x)) -1)
✓5.0b
(*.f64 (fma.f64 z z 1) (*.f64 y x))

series95.0ms (2.9%)

Counts
2 → 72
Calls

2 calls:

73.0ms
(pow.f64 (*.f64 (fma.f64 z z 1) (*.f64 y x)) -1)
22.0ms
(*.f64 (fma.f64 z z 1) (*.f64 y x))

rewrite46.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
832×log1p-expm1-u_binary64
832×expm1-log1p-u_binary64
96×add-sqr-sqrt_binary64
88×add-cbrt-cube_binary64
87×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01025
119725
2230025
Stop Event
1×node limit
Counts
2 → 44
Calls

2 calls:

45.0ms
(pow.f64 (*.f64 (fma.f64 z z 1) (*.f64 y x)) -1)
45.0ms
(*.f64 (fma.f64 z z 1) (*.f64 y x))

simplify47.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
555×times-frac_binary64
418×distribute-neg-frac_binary64
297×associate-/l*_binary64
199×sub-neg_binary64
195×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0561107
11481107
23711105
312311101
439961101
Stop Event
1×node limit
Counts
116 → 73

prune69.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New72173
Fresh088
Picked011
Done000
Total721082
Error
0.0b
Counts
82 → 10
Alt Table
StatusErrorProgram
22.6b
(/.f64 (/.f64 1 x) (pow.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) 2))
32.8b
(/.f64 (/.f64 (/.f64 1 y) z) (*.f64 z x))
25.9b
(pow.f64 (cbrt.f64 (pow.f64 (*.f64 (fma.f64 z z 1) (*.f64 y x)) 3)) -1)
27.8b
(/.f64 (/.f64 1 y) x)
▶5.9b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
33.9b
(/.f64 (/.f64 1 x) (*.f64 z (*.f64 y z)))
✓5.8b
(pow.f64 (*.f64 (fma.f64 z z 1) (*.f64 y x)) -1)
7.0b
(/.f64 (/.f64 1 x) (fma.f64 y (*.f64 z z) y))
22.8b
(*.f64 (/.f64 (/.f64 1 (*.f64 y x)) (-.f64 1 (pow.f64 z 4))) (-.f64 1 (*.f64 z z)))
25.2b
(*.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
Compiler

Compiled 1352 to 817 computations (39.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.9b
(/.f64 1 (*.f64 y x))
✓5.3b
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))

series90.0ms (2.7%)

Counts
2 → 36
Calls

2 calls:

83.0ms
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
7.0ms
(/.f64 1 (*.f64 y x))

rewrite45.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
865×log1p-expm1-u_binary64
865×expm1-log1p-u_binary64
93×add-sqr-sqrt_binary64
85×add-cbrt-cube_binary64
85×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0921
118621
2243721
Stop Event
1×node limit
Counts
2 → 59
Calls

2 calls:

44.0ms
(/.f64 1 (*.f64 y x))
44.0ms
(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))

simplify39.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
555×times-frac_binary64
420×distribute-neg-frac_binary64
298×associate-/l*_binary64
199×sub-neg_binary64
195×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
054720
1146720
2369718
31233714
43999714
Stop Event
1×node limit
Counts
95 → 79

prune68.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New77279
Fresh178
Picked101
Done101
Total80989
Error
0.0b
Counts
89 → 9
Alt Table
StatusErrorProgram
▶5.5b
(*.f64 (/.f64 (/.f64 1 y) x) (/.f64 1 (fma.f64 z z 1)))
25.2b
(*.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
28.9b
(/.f64 1 (*.f64 z (*.f64 z (*.f64 y x))))
22.6b
(/.f64 (/.f64 1 x) (pow.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) 2))
32.8b
(/.f64 (/.f64 (/.f64 1 y) z) (*.f64 z x))
25.9b
(pow.f64 (cbrt.f64 (pow.f64 (*.f64 (fma.f64 z z 1) (*.f64 y x)) 3)) -1)
33.9b
(/.f64 (/.f64 1 x) (*.f64 z (*.f64 y z)))
7.0b
(/.f64 (/.f64 1 x) (fma.f64 y (*.f64 z z) y))
22.8b
(*.f64 (/.f64 (/.f64 1 (*.f64 y x)) (-.f64 1 (pow.f64 z 4))) (-.f64 1 (*.f64 z z)))
Compiler

Compiled 1520 to 943 computations (38% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (/.f64 1 y) x)
✓0.8b
(/.f64 1 (fma.f64 z z 1))
✓5.1b
(*.f64 (/.f64 (/.f64 1 y) x) (/.f64 1 (fma.f64 z z 1)))

series80.0ms (2.4%)

Counts
3 → 72
Calls

3 calls:

68.0ms
(*.f64 (/.f64 (/.f64 1 y) x) (/.f64 1 (fma.f64 z z 1)))
9.0ms
(/.f64 (/.f64 1 y) x)
2.0ms
(/.f64 1 (fma.f64 z z 1))

rewrite51.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
546×log-prod_binary64
185×expm1-udef_binary64
185×log1p-udef_binary64
175×log-div_binary64
174×log-pow_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01029
121629
2304429
Stop Event
1×node limit
Counts
3 → 119
Calls

3 calls:

49.0ms
(/.f64 (/.f64 1 y) x)
49.0ms
(/.f64 1 (fma.f64 z z 1))
49.0ms
(*.f64 (/.f64 (/.f64 1 y) x) (/.f64 1 (fma.f64 z z 1)))

simplify37.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
697×times-frac_binary64
396×fma-def_binary64
334×associate-/l*_binary64
239×associate-/l/_binary64
179×fma-neg_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0681092
11851090
24881088
316061078
Stop Event
1×node limit
Counts
191 → 153

prune140.0ms (4.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1503153
Fresh268
Picked011
Done000
Total15210162
Error
0.0b
Counts
162 → 10
Alt Table
StatusErrorProgram
✓5.5b
(*.f64 (/.f64 (/.f64 1 y) x) (/.f64 1 (fma.f64 z z 1)))
25.2b
(*.f64 (/.f64 (cbrt.f64 (pow.f64 x -2)) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
28.9b
(/.f64 1 (*.f64 z (*.f64 z (*.f64 y x))))
22.6b
(/.f64 (/.f64 1 x) (pow.f64 (*.f64 (sqrt.f64 y) (hypot.f64 1 z)) 2))
32.8b
(/.f64 (/.f64 (/.f64 1 y) z) (*.f64 z x))
25.9b
(pow.f64 (cbrt.f64 (pow.f64 (*.f64 (fma.f64 z z 1) (*.f64 y x)) 3)) -1)
23.3b
(*.f64 (*.f64 (pow.f64 y -1/2) (*.f64 (pow.f64 y -1/2) (/.f64 1 x))) (/.f64 1 (fma.f64 z z 1)))
7.1b
(/.f64 (*.f64 (/.f64 -1 y) (/.f64 1 (fma.f64 z z 1))) (neg.f64 x))
2.6b
(/.f64 (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)) (hypot.f64 1 z))
7.0b
(/.f64 (/.f64 1 x) (fma.f64 y (*.f64 z z) y))
Compiler

Compiled 2615 to 1696 computations (35.1% saved)

regimes766.0ms (23.1%)

Accuracy

Total 1.7b remaining (98.1%)

Threshold costs 0b (0%)

Counts
81 → 2
Compiler

Compiled 9919 to 7200 computations (27.4% saved)

bsearch2.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify28.0ms (0.8%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01839
12239
Stop Event
1×saturated

end144.0ms (4.3%)

Remove

(sort x y)

Compiler

Compiled 275 to 193 computations (29.8% saved)

Profiling

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