Details

Time bar (total: 4.7s)

analyze805.0ms (17.2%)

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
3.1%90.5%6.3%6
4.7%85.9%9.5%7
21.1%64%14.9%8
23.4%58.9%17.7%9
27.7%51.3%21%10
28.9%48.5%22.6%11
31.1%44.4%24.5%12
31.7%42.9%25.4%13
32.7%41%26.3%14
Compiler

Compiled 14 to 9 computations (35.7% saved)

sample2.9s (61.6%)

Results
1.1s1748×body1024valid
660.0ms4691×body128valid
433.0ms1050×body512valid
175.0ms171×body2048valid
161.0ms596×body256valid
117.0ms189×body1024invalid
94.0ms222×body512invalid
54.0ms406×body128invalid
39.0ms148×body256invalid
Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess35.0ms (0.7%)

Algorithm
2×egg-herbie
Rules
494×associate-*l*_binary64
400×times-frac_binary64
375×associate-/l*_binary64
298×associate-/l/_binary64
261×associate-/r*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01534
12926
24526
39626
424026
560226
6162926
022
Stop Event
1×saturated
1×node limit
Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify25.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
522×unswap-sqr_binary64
255×fma-def_binary64
248×associate-*l*_binary64
206×div-sub_binary64
200×times-frac_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0917
11613
22513
35413
413313
532613
687413
7324513
Stop Event
1×node limit
Counts
1 → 2

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
10.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶10.3b
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
Compiler

Compiled 44 to 22 computations (50% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
✓5.0b
(pow.f64 (/.f64 x (+.f64 x y)) x)

series60.0ms (1.3%)

Counts
2 → 48
Calls

12 calls:

7.0ms
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
y
-inf
7.0ms
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
x
-inf
7.0ms
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
x
inf
6.0ms
(pow.f64 (/.f64 x (+.f64 x y)) x)
y
inf
6.0ms
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
x
0

rewrite48.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
521×prod-diff_binary64
458×log-prod_binary64
195×fma-def_binary64
157×expm1-udef_binary64
157×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0723
116523
2252223
Stop Event
1×node limit
Counts
2 → 57

simplify70.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
309×fma-def_binary64
268×sub-neg_binary64
241×+-commutative_binary64
230×associate-+r+_binary64
199×associate-*r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03193163
110563055
241642708
Stop Event
1×node limit
Counts
105 → 127

prune104.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1243127
Fresh000
Picked011
Done000
Total1244128
Error
0b
Counts
128 → 4
Alt Table
StatusErrorProgram
✓10.3b
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
29.2b
(-.f64 (fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x x) y)) (fma.f64 1/2 (/.f64 y (/.f64 x y)) (/.f64 1 x))) (/.f64 y x))
11.7b
(/.f64 (exp.f64 (neg.f64 y)) x)
▶8.2b
(/.f64 1 x)
Compiler

Compiled 4426 to 2348 computations (46.9% saved)

localize2.0ms (0%)

prune4.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New000
Fresh022
Picked011
Done011
Total044
Error
0b
Counts
4 → 4
Alt Table
StatusErrorProgram
✓10.3b
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
29.2b
(-.f64 (fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x x) y)) (fma.f64 1/2 (/.f64 y (/.f64 x y)) (/.f64 1 x))) (/.f64 y x))
▶11.7b
(/.f64 (exp.f64 (neg.f64 y)) x)
✓8.2b
(/.f64 1 x)
Compiler

Compiled 80 to 50 computations (37.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (exp.f64 (neg.f64 y)) x)

series7.0ms (0.1%)

Counts
1 → 8
Calls

6 calls:

1.0ms
(/.f64 (exp.f64 (neg.f64 y)) x)
y
inf
1.0ms
(/.f64 (exp.f64 (neg.f64 y)) x)
y
-inf
1.0ms
(/.f64 (exp.f64 (neg.f64 y)) x)
x
-inf
1.0ms
(/.f64 (exp.f64 (neg.f64 y)) x)
y
0
1.0ms
(/.f64 (exp.f64 (neg.f64 y)) x)
x
inf

rewrite34.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
513×log1p-expm1-u_binary64
513×expm1-log1p-u_binary64
279×log-prod_binary64
140×pow2_binary64
99×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
068
11246
216726
Stop Event
1×node limit
Counts
1 → 39

simplify31.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
397×fma-neg_binary64
389×cancel-sign-sub-inv_binary64
351×associate-/l*_binary64
325×fma-def_binary64
264×associate-/r/_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
025102
16096
214396
337496
4120693
5488093
Stop Event
1×node limit
Counts
47 → 47

prune25.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New46147
Fresh101
Picked011
Done022
Total47451
Error
0b
Counts
51 → 4
Alt Table
StatusErrorProgram
✓10.3b
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
▶19.4b
(-.f64 (+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 (pow.f64 y 2) x))) (/.f64 y x))
✓11.7b
(/.f64 (exp.f64 (neg.f64 y)) x)
✓8.2b
(/.f64 1 x)
Compiler

Compiled 506 to 238 computations (53% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 1/2 (/.f64 (pow.f64 y 2) x))
✓0.0b
(+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 (pow.f64 y 2) x)))
✓2.4b
(-.f64 (+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 (pow.f64 y 2) x))) (/.f64 y x))
✓6.3b
(/.f64 (pow.f64 y 2) x)

series55.0ms (1.2%)

Counts
4 → 33
Calls

24 calls:

5.0ms
(*.f64 1/2 (/.f64 (pow.f64 y 2) x))
x
-inf
3.0ms
(/.f64 (pow.f64 y 2) x)
x
0
3.0ms
(-.f64 (+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 (pow.f64 y 2) x))) (/.f64 y x))
x
0
3.0ms
(-.f64 (+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 (pow.f64 y 2) x))) (/.f64 y x))
x
-inf
3.0ms
(-.f64 (+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 (pow.f64 y 2) x))) (/.f64 y x))
x
inf

rewrite73.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
250×expm1-udef_binary64
250×log1p-udef_binary64
153×egg-rr
142×add-sqr-sqrt_binary64
139×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01355
129550
2422750
Stop Event
1×node limit
Counts
4 → 153

simplify39.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
406×distribute-rgt-neg-in_binary64
325×associate-*l*_binary64
282×associate-*r*_binary64
266×fma-def_binary64
265×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
022438
150390
2117390
3324359
41014353
53841353
Stop Event
1×node limit
Counts
186 → 165

prune104.0ms (2.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1650165
Fresh000
Picked011
Done033
Total1654169
Error
0b
Counts
169 → 4
Alt Table
StatusErrorProgram
✓10.3b
(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
✓19.4b
(-.f64 (+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 (pow.f64 y 2) x))) (/.f64 y x))
✓11.7b
(/.f64 (exp.f64 (neg.f64 y)) x)
✓8.2b
(/.f64 1 x)
Compiler

Compiled 3729 to 1949 computations (47.7% saved)

regimes155.0ms (3.3%)

Accuracy

Total 0.4b remaining (95.1%)

Threshold costs 0.4b (95.1%)

Counts
22 → 3
Compiler

Compiled 929 to 633 computations (31.9% saved)

bsearch38.0ms (0.8%)

Algorithm
2×binary-search
Calls

2 calls:

32.0ms
x
5.0ms
x
Steps
ItersPointRange
0.8171519518008243
∈ [
1.4242323830808375e-12
, 
2536.483828574979
]
-38058680409478.88
∈ [
-63603295349163.57
, 
-23849218779313.094
]
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×*-commutative_binary64
1×+-commutative_binary64
1×/-rgt-identity_binary64
1×sub-neg_binary64
1×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02033
12633
22833
32933
Stop Event
1×saturated

end57.0ms (1.2%)

Stop Event
1×done
Compiler

Compiled 88 to 61 computations (30.7% saved)

Profiling

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