Details

Time bar (total: 5.1s)

analyze112.0ms (2.2%)

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
25%74.9%0.1%5
31.2%68.7%0.1%6
67.1%32.8%0.1%7
71%28.9%0.1%8
82.3%17.6%0.1%9
84.9%15%0.1%10
90.8%9.1%0.1%11
92.2%7.7%0.1%12
95.3%4.6%0.1%13
96%3.9%0.1%14
Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.2s (23.3%)

Results
695.0ms6468×body128valid
215.0ms644×body1024valid
174.0ms699×body512valid
80.0ms436×body256valid
3.0ms9×body2048valid
Compiler

Compiled 28 to 22 computations (21.4% saved)

preprocess41.0ms (0.8%)

Algorithm
2×egg-herbie
Rules
1040×fma-neg_binary64
720×times-frac_binary64
361×associate-/l*_binary64
246×div-sub_binary64
203×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01432
13232
27932
320328
464828
5198128
6467228
022
Stop Event
1×saturated
1×node limit
Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify31.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
777×fma-def_binary64
611×fma-neg_binary64
471×div-sub_binary64
314×distribute-rgt-in_binary64
295×distribute-lft-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0916
11916
24316
311114
432614
589314
6237814
7363814
Stop Event
1×node limit
Counts
1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
13.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
20.1b
(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
▶13.3b
(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
Compiler

Compiled 73 to 55 computations (24.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 y (-.f64 -1 y))
✓2.8b
(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)

series10.0ms (0.2%)

Counts
2 → 36
Calls

9 calls:

2.0ms
(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
x
-inf
2.0ms
(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
x
inf
2.0ms
(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
x
0
1.0ms
(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
y
-inf
1.0ms
(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
y
inf

rewrite50.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
443×log-prod_binary64
234×prod-diff_binary64
173×expm1-udef_binary64
172×log1p-udef_binary64
150×fma-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0921
119521
2260021
Stop Event
1×node limit
Counts
2 → 64

simplify31.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
547×associate-+l-_binary64
449×cancel-sign-sub-inv_binary64
416×fma-neg_binary64
397×sub-neg_binary64
385×associate--r+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
059624
1177613
2555587
32124547
Stop Event
1×node limit
Counts
100 → 98

prune65.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New95398
Fresh101
Picked011
Done000
Total964100
Error
0.0b
Counts
100 → 4
Alt Table
StatusErrorProgram
36.9b
(*.f64 (/.f64 x (+.f64 1 y)) y)
▶31.5b
(pow.f64 (pow.f64 (fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1) 3) 1/3)
✓13.3b
(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
33.9b
(-.f64 (+.f64 (/.f64 1 y) (+.f64 (/.f64 1 (pow.f64 y 3)) (+.f64 (/.f64 x (pow.f64 y 2)) x))) (+.f64 (/.f64 x y) (+.f64 (/.f64 x (pow.f64 y 3)) (/.f64 1 (pow.f64 y 2)))))
Compiler

Compiled 1646 to 1183 computations (28.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 y (-.f64 -1 y))
✓0.1b
(pow.f64 (fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1) 3)
2.8b
(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
✓11.7b
(pow.f64 (pow.f64 (fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1) 3) 1/3)

series273.0ms (5.4%)

Counts
2 → 48
Calls

12 calls:

138.0ms
(pow.f64 (pow.f64 (fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1) 3) 1/3)
x
-inf
40.0ms
(pow.f64 (pow.f64 (fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1) 3) 1/3)
x
0
36.0ms
(pow.f64 (pow.f64 (fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1) 3) 1/3)
x
inf
16.0ms
(pow.f64 (pow.f64 (fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1) 3) 1/3)
y
-inf
12.0ms
(pow.f64 (pow.f64 (fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1) 3) 1/3)
y
inf

rewrite57.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
234×prod-diff_binary64
217×expm1-udef_binary64
216×log1p-udef_binary64
180×log-pow_binary64
162×fma-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01331
127231
2329631
Stop Event
1×node limit
Counts
2 → 60

simplify138.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
834×times-frac_binary64
293×*-commutative_binary64
290×+-commutative_binary64
250×associate-+r+_binary64
221×fma-def_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
09298512
133878304
Stop Event
1×node limit
Counts
108 → 125

prune308.0ms (6.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2221223
Fresh022
Picked101
Done011
Total2234227
Error
0.0b
Counts
227 → 4
Alt Table
StatusErrorProgram
▶31.4b
(pow.f64 (exp.f64 (*.f64 3 (log1p.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))))) 1/3)
36.9b
(*.f64 (/.f64 x (+.f64 1 y)) y)
✓13.3b
(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
33.9b
(-.f64 (+.f64 (/.f64 1 y) (+.f64 (/.f64 1 (pow.f64 y 3)) (+.f64 (/.f64 x (pow.f64 y 2)) x))) (+.f64 (/.f64 x y) (+.f64 (/.f64 x (pow.f64 y 3)) (/.f64 1 (pow.f64 y 2)))))
Compiler

Compiled 13831 to 10617 computations (23.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 3 (log1p.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))))
✓0.6b
(exp.f64 (*.f64 3 (log1p.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))))))
✓2.3b
(log1p.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))))
✓6.9b
(pow.f64 (exp.f64 (*.f64 3 (log1p.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))))) 1/3)

series512.0ms (10.1%)

Counts
4 → 96
Calls

24 calls:

178.0ms
(pow.f64 (exp.f64 (*.f64 3 (log1p.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))))) 1/3)
x
inf
141.0ms
(pow.f64 (exp.f64 (*.f64 3 (log1p.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))))) 1/3)
x
-inf
23.0ms
(exp.f64 (*.f64 3 (log1p.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))))))
x
-inf
22.0ms
(exp.f64 (*.f64 3 (log1p.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))))))
x
inf
19.0ms
(log1p.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))))
x
-inf

rewrite62.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
520×prod-diff_binary64
151×add-sqr-sqrt_binary64
144×expm1-log1p-u_binary64
143×add-cbrt-cube_binary64
143×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01575
131868
2393568
Stop Event
1×node limit
Counts
4 → 85

simplify155.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
588×+-commutative_binary64
501×*-commutative_binary64
493×associate-+r+_binary64
470×fma-def_binary64
242×associate-*r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0138621977
Stop Event
1×node limit
Counts
181 → 236

prune582.0ms (11.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2351236
Fresh022
Picked101
Done011
Total2364240
Error
0.0b
Counts
240 → 4
Alt Table
StatusErrorProgram
▶22.8b
(/.f64 (-.f64 1 (pow.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))) 2)) (-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))))
36.9b
(*.f64 (/.f64 x (+.f64 1 y)) y)
✓13.3b
(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
33.9b
(-.f64 (+.f64 (/.f64 1 y) (+.f64 (/.f64 1 (pow.f64 y 3)) (+.f64 (/.f64 x (pow.f64 y 2)) x))) (+.f64 (/.f64 x y) (+.f64 (/.f64 x (pow.f64 y 3)) (/.f64 1 (pow.f64 y 2)))))
Compiler

Compiled 29183 to 21936 computations (24.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))
✓0.1b
(pow.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))) 2)
✓2.7b
(-.f64 1 (pow.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))) 2))
✓9.0b
(/.f64 (-.f64 1 (pow.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))) 2)) (-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))))

series207.0ms (4.1%)

Counts
4 → 96
Calls

24 calls:

33.0ms
(/.f64 (-.f64 1 (pow.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))) 2)) (-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))))
y
-inf
29.0ms
(/.f64 (-.f64 1 (pow.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))) 2)) (-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))))
x
inf
28.0ms
(/.f64 (-.f64 1 (pow.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))) 2)) (-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))))
x
-inf
23.0ms
(/.f64 (-.f64 1 (pow.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))) 2)) (-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))))
y
inf
16.0ms
(-.f64 1 (pow.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))) 2))
x
inf

rewrite79.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
277×log1p-udef_binary64
162×add-sqr-sqrt_binary64
159×log1p-expm1-u_binary64
159×expm1-log1p-u_binary64
158×add-cbrt-cube_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01485
133264
2474264
Stop Event
1×node limit
Counts
4 → 138

simplify105.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
850×fma-def_binary64
463×times-frac_binary64
287×associate-/l*_binary64
278×+-commutative_binary64
226×associate-+r+_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
06158300
123628088
Stop Event
1×node limit
Counts
234 → 246

prune383.0ms (7.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3062308
Fresh022
Picked101
Done011
Total3075312
Error
0.0b
Counts
312 → 5
Alt Table
StatusErrorProgram
42.1b
(/.f64 (+.f64 (/.f64 2 y) (-.f64 (fma.f64 2 (/.f64 x (/.f64 y x)) (fma.f64 2 x (*.f64 (/.f64 6 y) (/.f64 x y)))) (+.f64 (fma.f64 4 (/.f64 x y) (/.f64 3 (*.f64 y y))) (fma.f64 x x (*.f64 3 (*.f64 (/.f64 x y) (/.f64 x y))))))) (-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))))
36.9b
(*.f64 (/.f64 x (+.f64 1 y)) y)
23.1b
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))))) 2)) (/.f64 (-.f64 1 (pow.f64 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y))) 2)) (cbrt.f64 (-.f64 1 (*.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)))))))
✓13.3b
(fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1)
33.9b
(-.f64 (+.f64 (/.f64 1 y) (+.f64 (/.f64 1 (pow.f64 y 3)) (+.f64 (/.f64 x (pow.f64 y 2)) x))) (+.f64 (/.f64 x y) (+.f64 (/.f64 x (pow.f64 y 3)) (/.f64 1 (pow.f64 y 2)))))
Compiler

Compiled 16332 to 11833 computations (27.5% saved)

regimes460.0ms (9.1%)

Accuracy

Total 0.0b remaining (19%)

Threshold costs 0.0b (19%)

Counts
48 → 3
Compiler

Compiled 5764 to 4403 computations (23.6% saved)

bsearch42.0ms (0.8%)

Algorithm
2×binary-search
Calls

2 calls:

20.0ms
y
20.0ms
y
Steps
ItersPointRange
16093.960005574929
∈ [
764.6076184464732
, 
3569911252515.528
]
-11212.03429386349
∈ [
-3460624.3474320844
, 
-1.3196114914278487e-6
]
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
17×+-commutative_binary64
10×sub-neg_binary64
9×*-commutative_binary64
8×neg-sub0_binary64
8×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033132
147132
260132
378132
497132
5106132
6109132
Stop Event
1×saturated

end137.0ms (2.7%)

Stop Event
1×fuel
Compiler

Compiled 342 to 237 computations (30.7% saved)

Profiling

Loading profile data...