Details

Time bar (total: 4.9s)

analyze115.0ms (2.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%24.7%75.3%0
0%24.7%75.3%1
0%24.7%75.3%2
12.4%12.4%75.3%3
12.4%12.4%75.3%4
18.5%6.2%75.3%5
18.5%6.2%75.3%6
21.6%3.1%75.3%7
21.6%3.1%75.3%8
23.2%1.5%75.3%9
23.2%1.5%75.3%10
23.9%0.8%75.3%11
23.9%0.8%75.3%12
24.3%0.4%75.3%13
24.3%0.4%75.3%14
Compiler

Compiled 35 to 18 computations (48.6% saved)

sample1.4s (29.3%)

Results
1.4s8256×body128valid
Compiler

Compiled 98 to 49 computations (50% saved)

simplify35.0ms (0.7%)

Algorithm
egg-herbie
Rules
505×fma-def_binary32
440×times-frac_binary32
346×distribute-rgt-in_binary32
272×distribute-rgt-out_binary32
271×distribute-lft-in_binary32
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
01243
13843
210741
324641
451839
5107530
6343029
7494629
Stop Event
node limit
Counts
1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.1b
(/.f32 (/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
0.1b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
Compiler

Compiled 142 to 78 computations (45.1% saved)

localize44.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))
0.0b
(/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2)))
0.0b
(exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s)))
0.1b
(exp.f32 (/.f32 (fabs.f32 x) s))

series94.0ms (1.9%)

Counts
4 → 80
Calls

4 calls:

55.0ms
(/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2)))
17.0ms
(+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))
14.0ms
(exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s)))
8.0ms
(exp.f32 (/.f32 (fabs.f32 x) s))

rewrite58.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
654×prod-diff_binary32
152×add-sqr-sqrt_binary32
144×log1p-expm1-u_binary32
144×expm1-log1p-u_binary32
143×add-cbrt-cube_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01465
130549
2441949
Stop Event
node limit
Counts
4 → 107
Calls

4 calls:

56.0ms
(+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))
56.0ms
(/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2)))
56.0ms
(exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s)))
56.0ms
(exp.f32 (/.f32 (fabs.f32 x) s))

simplify47.0ms (1%)

Algorithm
egg-herbie
Rules
704×cancel-sign-sub-inv_binary32
351×times-frac_binary32
311×unswap-sqr_binary32
297×distribute-rgt-neg-in_binary32
217×distribute-neg-frac_binary32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0641626
11741578
25051558
325741522
Stop Event
node limit
Counts
187 → 119

prune109.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1154119
Fresh011
Picked011
Done000
Total1156121
Error
0.0b
Counts
121 → 6
Alt Table
StatusErrorProgram
11.0b
(/.f32 (/.f32 1 (+.f32 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 x s)))) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
6.5b
(/.f32 (/.f32 1 (+.f32 (*.f32 (/.f32 x s) (/.f32 x s)) 4)) s)
23.2b
(/.f32 (fma.f32 (*.f32 (/.f32 x s) (/.f32 x s)) -1/16 1/4) s)
0.1b
(/.f32 (/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
8.6b
(/.f32 (/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (-.f32 (fma.f32 1/2 (*.f32 (/.f32 x s) (/.f32 x s)) 1) (/.f32 (fabs.f32 x) s)) 2))) s)
0.1b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
Compiler

Compiled 3050 to 1452 computations (52.4% saved)

localize34.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))
0.0b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
0.0b
(*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))))
0.0b
(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))

series148.0ms (3%)

Counts
4 → 96
Calls

4 calls:

101.0ms
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
22.0ms
(*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))))
13.0ms
(+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))
11.0ms
(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))

rewrite64.0ms (1.3%)

Algorithm
batch-egg-rewrite
Rules
726×prod-diff_binary32
135×add-sqr-sqrt_binary32
129×egg-rr
126×log1p-expm1-u_binary32
126×expm1-log1p-u_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01297
126853
2411353
Stop Event
node limit
Counts
4 → 129
Calls

4 calls:

61.0ms
(+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))
61.0ms
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
61.0ms
(*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))))
61.0ms
(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))

simplify54.0ms (1.1%)

Algorithm
egg-herbie
Rules
386×fma-neg_binary32
329×unswap-sqr_binary32
306×distribute-rgt-neg-in_binary32
281×times-frac_binary32
277×distribute-neg-frac_binary32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0781948
12281892
26771842
330581832
Stop Event
node limit
Counts
225 → 168

prune312.0ms (6.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2615266
Fresh314
Picked101
Done101
Total2666272
Error
0.0b
Counts
272 → 6
Alt Table
StatusErrorProgram
11.9b
(*.f32 (/.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 2) (*.f32 (sqrt.f32 s) (+.f32 (exp.f32 (/.f32 x s)) 1))) (/.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) (*.f32 (sqrt.f32 s) (+.f32 (exp.f32 (/.f32 x s)) 1))))
11.0b
(/.f32 (/.f32 1 (+.f32 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 x s)))) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
11.8b
(*.f32 (/.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 2) (+.f32 s (*.f32 s (exp.f32 (/.f32 x s))))) (/.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) (+.f32 (exp.f32 (/.f32 x s)) 1)))
0.1b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
13.0b
(/.f32 (pow.f32 (exp.f32 (*.f32 (/.f32 x s) 3)) 1/3) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
12.9b
(/.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 3) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
Compiler

Compiled 7851 to 2963 computations (62.3% saved)

localize59.0ms (1.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
0.0b
(exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))
0.0b
(exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s))
0.1b
(pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)

series170.0ms (3.5%)

Counts
3 → 40
Calls

3 calls:

144.0ms
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
17.0ms
(pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)
9.0ms
(exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))

rewrite35.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
182×add-sqr-sqrt_binary32
174×log1p-expm1-u_binary32
174×expm1-log1p-u_binary32
172×add-cbrt-cube_binary32
169×add-log-exp_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01967
142146
Stop Event
node limit
Counts
3 → 84
Calls

3 calls:

34.0ms
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
33.0ms
(exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))
33.0ms
(pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)

simplify42.0ms (0.9%)

Algorithm
egg-herbie
Rules
376×fma-neg_binary32
335×distribute-rgt-neg-in_binary32
332×distribute-lft-neg-in_binary32
285×distribute-neg-frac_binary32
283×times-frac_binary32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0671242
11991194
26021118
328221100
Stop Event
node limit
Counts
124 → 105

prune212.0ms (4.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1661167
Fresh235
Picked011
Done000
Total1685173
Error
0.0b
Counts
173 → 5
Alt Table
StatusErrorProgram
11.9b
(*.f32 (/.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 2) (*.f32 (sqrt.f32 s) (+.f32 (exp.f32 (/.f32 x s)) 1))) (/.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) (*.f32 (sqrt.f32 s) (+.f32 (exp.f32 (/.f32 x s)) 1))))
11.0b
(/.f32 (/.f32 1 (+.f32 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 x s)))) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
11.8b
(*.f32 (sqrt.f32 (exp.f32 (/.f32 x s))) (*.f32 (sqrt.f32 (exp.f32 (/.f32 x s))) (/.f32 1 (+.f32 s (*.f32 (*.f32 (exp.f32 (/.f32 x s)) (+.f32 (exp.f32 (/.f32 x s)) 2)) s)))))
0.1b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
13.0b
(/.f32 (pow.f32 (exp.f32 (*.f32 (/.f32 x s) 3)) 1/3) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
Compiler

Compiled 5515 to 2680 computations (51.4% saved)

localize54.0ms (1.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 x s))))
0.0b
(exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s)))
0.0b
(exp.f32 (/.f32 x s))
1.3b
(log1p.f32 (exp.f32 (/.f32 x s)))

series247.0ms (5.1%)

Counts
3 → 60
Calls

3 calls:

236.0ms
(log1p.f32 (exp.f32 (/.f32 x s)))
6.0ms
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 x s))))
4.0ms
(exp.f32 (/.f32 x s))

rewrite40.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
561×expm1-log1p-u_binary32
560×log1p-expm1-u_binary32
301×log-prod_binary32
157×pow2_binary32
110×pow1/3_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0720
111920
2152220
Stop Event
node limit
Counts
3 → 79
Calls

3 calls:

38.0ms
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 x s))))
38.0ms
(exp.f32 (/.f32 x s))
38.0ms
(log1p.f32 (exp.f32 (/.f32 x s)))

simplify27.0ms (0.6%)

Algorithm
egg-herbie
Rules
796×associate-/l*_binary32
551×associate-/r*_binary32
538×fma-def_binary32
474×associate-*l/_binary32
157×associate-/r/_binary32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
040786
1106768
2280732
31095699
Stop Event
node limit
Counts
139 → 67

prune71.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New74074
Fresh033
Picked011
Done011
Total74579
Error
0.0b
Counts
79 → 5
Alt Table
StatusErrorProgram
11.9b
(*.f32 (/.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 2) (*.f32 (sqrt.f32 s) (+.f32 (exp.f32 (/.f32 x s)) 1))) (/.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) (*.f32 (sqrt.f32 s) (+.f32 (exp.f32 (/.f32 x s)) 1))))
11.0b
(/.f32 (/.f32 1 (+.f32 (expm1.f32 (log1p.f32 (exp.f32 (/.f32 x s)))) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
11.8b
(*.f32 (sqrt.f32 (exp.f32 (/.f32 x s))) (*.f32 (sqrt.f32 (exp.f32 (/.f32 x s))) (/.f32 1 (+.f32 s (*.f32 (*.f32 (exp.f32 (/.f32 x s)) (+.f32 (exp.f32 (/.f32 x s)) 2)) s)))))
0.1b
(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 s (+.f32 1 (+.f32 (*.f32 2 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s)))) (pow.f32 (exp.f32 (*.f32 -1 (/.f32 (fabs.f32 x) s))) 2)))))
13.0b
(/.f32 (pow.f32 (exp.f32 (*.f32 (/.f32 x s) 3)) 1/3) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
Compiler

Compiled 2038 to 1019 computations (50% saved)

regimes1.3s (26.2%)

Accuracy

Total 0.0b remaining (28.6%)

Threshold costs 0.0b (28.6%)

Counts
240 → 1
Compiler

Compiled 30682 to 19170 computations (37.5% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary32
*-commutative_binary32
sub-neg_binary32
neg-sub0_binary32
neg-mul-1_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01529
12229
22429
32529
Stop Event
saturated

end96.0ms (2%)

Compiler

Compiled 189 to 116 computations (38.6% saved)

Profiling

Loading profile data...