Details

Time bar (total: 6.6s)

analyze54.0ms (0.8%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%14%86%0
0%14%86%1
0%14%86%2
0%14%86%3
0%14%86%4
0%14%86%5
0%14%86%6
8.1%5.9%86%7
10.3%3.7%86%8
12.6%1.5%86%9
13.9%0.1%86%10
14%0%86%11
14%0%86%12
14%0%86%13
14%0%86%14
Compiler

Compiled 67 to 35 computations (47.8% saved)

sample1.5s (22.7%)

Results
1.5s8256×body128valid
Compiler

Compiled 134 to 70 computations (47.8% saved)

preprocess29.0ms (0.4%)

Algorithm
2×egg-herbie
Rules
915×distribute-rgt-in_binary64
897×distribute-lft-in_binary64
304×fma-def_binary64
241×times-frac_binary64
202×associate-/l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
053300
1246268
21026268
033
133
Stop Event
1×unsound
1×node limit
Symmetry

(sort alpha beta)

Compiler

Compiled 56 to 27 computations (51.8% saved)

simplify21.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
684×associate-+l+_binary64
483×associate-*l*_binary64
418×associate-*r*_binary64
369×times-frac_binary64
337×associate-/l*_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01875
16767
233267
3216967
Stop Event
1×node limit
Counts
1 → 2

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
48.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
54.3b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (*.f64 beta alpha) (*.f64 i (+.f64 (+.f64 alpha beta) i)))) (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))) (-.f64 (*.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) 1))
▶48.9b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (*.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))
Compiler

Compiled 315 to 155 computations (50.8% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta)))
✓0.1b
(*.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))
✓7.1b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (*.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))
✓46.8b
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (*.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1)))

series1.4s (20.4%)

Counts
4 → 144
Calls

36 calls:

310.0ms
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (*.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))
beta
0
304.0ms
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (*.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))
alpha
0
245.0ms
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (*.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))
i
0
115.0ms
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (*.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1)))
beta
0
112.0ms
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (*.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1)))
alpha
0

rewrite52.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
211×add-sqr-sqrt_binary64
200×add-cbrt-cube_binary64
200×log1p-expm1-u_binary64
200×expm1-log1p-u_binary64
195×add-log-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
018161
1411146
Stop Event
1×node limit
Counts
4 → 107

simplify373.0ms (5.6%)

Algorithm
1×egg-herbie
Rules
855×fma-def_binary64
511×times-frac_binary64
68×sub-neg_binary64
56×sqr-pow_binary64
12×distribute-lft-out_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0295251722
Stop Event
1×node limit
Counts
251 → 283

prune1.5s (23.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2758283
Fresh101
Picked101
Done000
Total2778285
Error
14.0b
Counts
285 → 8
Alt Table
StatusErrorProgram
45.3b
(*.f64 (/.f64 (fma.f64 i alpha (*.f64 i i)) (+.f64 (fma.f64 4 (*.f64 i alpha) (+.f64 (*.f64 alpha alpha) (*.f64 4 (*.f64 i i)))) -1)) (/.f64 (*.f64 i (+.f64 i alpha)) (pow.f64 (fma.f64 2 i alpha) 2)))
59.3b
(-.f64 (fma.f64 6 (/.f64 (*.f64 i (pow.f64 alpha 3)) (pow.f64 beta 4)) (fma.f64 25 (/.f64 (pow.f64 i 4) (pow.f64 beta 4)) (+.f64 (/.f64 (*.f64 i i) (pow.f64 beta 4)) (+.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) (fma.f64 50 (/.f64 (*.f64 (pow.f64 i 3) alpha) (pow.f64 beta 4)) (fma.f64 31 (/.f64 (*.f64 (*.f64 i i) (*.f64 alpha alpha)) (pow.f64 beta 4)) (+.f64 (/.f64 (*.f64 i alpha) (*.f64 beta beta)) (/.f64 (*.f64 i alpha) (pow.f64 beta 4))))))))) (fma.f64 196 (/.f64 (*.f64 (pow.f64 i 3) (*.f64 alpha alpha)) (pow.f64 beta 5)) (fma.f64 220 (/.f64 (*.f64 (pow.f64 i 4) alpha) (pow.f64 beta 5)) (fma.f64 74 (/.f64 (*.f64 (*.f64 i i) (pow.f64 alpha 3)) (pow.f64 beta 5)) (fma.f64 15 (/.f64 (*.f64 (*.f64 i i) alpha) (pow.f64 beta 5)) (fma.f64 9 (/.f64 (*.f64 (*.f64 i i) alpha) (pow.f64 beta 3)) (fma.f64 5 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 5)) (fma.f64 3 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 88 (/.f64 (pow.f64 i 5) (pow.f64 beta 5)) (fma.f64 10 (/.f64 (pow.f64 i 3) (pow.f64 beta 5)) (fma.f64 10 (/.f64 (*.f64 i (pow.f64 alpha 4)) (pow.f64 beta 5)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))))))))))
55.0b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (+.f64 i alpha) (pow.f64 beta 2)))
40.5b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
▶22.2b
1/16
25.9b
(-.f64 (+.f64 1/16 (*.f64 1/64 (/.f64 1 (*.f64 i i)))) (*.f64 1/32 (+.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) (/.f64 (*.f64 alpha alpha) (*.f64 i i)))))
42.1b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (exp.f64 (log.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)))))
40.6b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (pow.f64 (sqrt.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))) 2))
Compiler

Compiled 76494 to 46943 computations (38.6% saved)

localize0.0ms (0%)

prune19.0ms (0.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New000
Fresh077
Picked011
Done000
Total088
Error
14.0b
Counts
8 → 8
Alt Table
StatusErrorProgram
45.3b
(*.f64 (/.f64 (fma.f64 i alpha (*.f64 i i)) (+.f64 (fma.f64 4 (*.f64 i alpha) (+.f64 (*.f64 alpha alpha) (*.f64 4 (*.f64 i i)))) -1)) (/.f64 (*.f64 i (+.f64 i alpha)) (pow.f64 (fma.f64 2 i alpha) 2)))
59.3b
(-.f64 (fma.f64 6 (/.f64 (*.f64 i (pow.f64 alpha 3)) (pow.f64 beta 4)) (fma.f64 25 (/.f64 (pow.f64 i 4) (pow.f64 beta 4)) (+.f64 (/.f64 (*.f64 i i) (pow.f64 beta 4)) (+.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) (fma.f64 50 (/.f64 (*.f64 (pow.f64 i 3) alpha) (pow.f64 beta 4)) (fma.f64 31 (/.f64 (*.f64 (*.f64 i i) (*.f64 alpha alpha)) (pow.f64 beta 4)) (+.f64 (/.f64 (*.f64 i alpha) (*.f64 beta beta)) (/.f64 (*.f64 i alpha) (pow.f64 beta 4))))))))) (fma.f64 196 (/.f64 (*.f64 (pow.f64 i 3) (*.f64 alpha alpha)) (pow.f64 beta 5)) (fma.f64 220 (/.f64 (*.f64 (pow.f64 i 4) alpha) (pow.f64 beta 5)) (fma.f64 74 (/.f64 (*.f64 (*.f64 i i) (pow.f64 alpha 3)) (pow.f64 beta 5)) (fma.f64 15 (/.f64 (*.f64 (*.f64 i i) alpha) (pow.f64 beta 5)) (fma.f64 9 (/.f64 (*.f64 (*.f64 i i) alpha) (pow.f64 beta 3)) (fma.f64 5 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 5)) (fma.f64 3 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 88 (/.f64 (pow.f64 i 5) (pow.f64 beta 5)) (fma.f64 10 (/.f64 (pow.f64 i 3) (pow.f64 beta 5)) (fma.f64 10 (/.f64 (*.f64 i (pow.f64 alpha 4)) (pow.f64 beta 5)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))))))))))
55.0b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (+.f64 i alpha) (pow.f64 beta 2)))
40.5b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
✓22.2b
1/16
▶25.9b
(-.f64 (+.f64 1/16 (*.f64 1/64 (/.f64 1 (*.f64 i i)))) (*.f64 1/32 (+.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) (/.f64 (*.f64 alpha alpha) (*.f64 i i)))))
42.1b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (exp.f64 (log.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)))))
40.6b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (pow.f64 (sqrt.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))) 2))
Compiler

Compiled 878 to 538 computations (38.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.5b
(/.f64 1 (*.f64 i i))
✓0.6b
(*.f64 1/32 (+.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) (/.f64 (*.f64 alpha alpha) (*.f64 i i))))
✓3.2b
(/.f64 (*.f64 alpha alpha) (*.f64 i i))
✓18.4b
(/.f64 (*.f64 beta beta) (*.f64 i i))

series125.0ms (1.9%)

Counts
4 → 96
Calls

24 calls:

11.0ms
(*.f64 1/32 (+.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) (/.f64 (*.f64 alpha alpha) (*.f64 i i))))
beta
inf
10.0ms
(*.f64 1/32 (+.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) (/.f64 (*.f64 alpha alpha) (*.f64 i i))))
alpha
inf
10.0ms
(*.f64 1/32 (+.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) (/.f64 (*.f64 alpha alpha) (*.f64 i i))))
beta
0
10.0ms
(*.f64 1/32 (+.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) (/.f64 (*.f64 alpha alpha) (*.f64 i i))))
alpha
0
9.0ms
(*.f64 1/32 (+.f64 (/.f64 (*.f64 beta beta) (*.f64 i i)) (/.f64 (*.f64 alpha alpha) (*.f64 i i))))
beta
-inf

rewrite41.0ms (0.6%)

Algorithm
1×batch-egg-rewrite
Rules
156×add-sqr-sqrt_binary64
149×add-cbrt-cube_binary64
149×log1p-expm1-u_binary64
149×expm1-log1p-u_binary64
147×add-log-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01452
131834
Stop Event
1×node limit
Counts
4 → 121

simplify45.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
751×associate-/l/_binary64
609×associate-*l/_binary64
554×associate-*l*_binary64
432×associate-*r/_binary64
430×associate-/r/_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0191392
1451392
21101302
33091152
414741152
Stop Event
1×node limit
Counts
217 → 134

prune189.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1322134
Fresh066
Picked101
Done011
Total1339142
Error
13.9b
Counts
142 → 9
Alt Table
StatusErrorProgram
55.0b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (+.f64 i alpha) (pow.f64 beta 2)))
▶22.1b
(-.f64 (+.f64 1/16 (*.f64 1/64 (/.f64 1 (*.f64 i i)))) (*.f64 1/32 (/.f64 (pow.f64 alpha 2) (pow.f64 i 2))))
45.3b
(*.f64 (/.f64 (fma.f64 i alpha (*.f64 i i)) (+.f64 (fma.f64 4 (*.f64 i alpha) (+.f64 (*.f64 alpha alpha) (*.f64 4 (*.f64 i i)))) -1)) (/.f64 (*.f64 i (+.f64 i alpha)) (pow.f64 (fma.f64 2 i alpha) 2)))
59.3b
(-.f64 (fma.f64 6 (/.f64 (*.f64 i (pow.f64 alpha 3)) (pow.f64 beta 4)) (fma.f64 25 (/.f64 (pow.f64 i 4) (pow.f64 beta 4)) (+.f64 (/.f64 (*.f64 i i) (pow.f64 beta 4)) (+.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) (fma.f64 50 (/.f64 (*.f64 (pow.f64 i 3) alpha) (pow.f64 beta 4)) (fma.f64 31 (/.f64 (*.f64 (*.f64 i i) (*.f64 alpha alpha)) (pow.f64 beta 4)) (+.f64 (/.f64 (*.f64 i alpha) (*.f64 beta beta)) (/.f64 (*.f64 i alpha) (pow.f64 beta 4))))))))) (fma.f64 196 (/.f64 (*.f64 (pow.f64 i 3) (*.f64 alpha alpha)) (pow.f64 beta 5)) (fma.f64 220 (/.f64 (*.f64 (pow.f64 i 4) alpha) (pow.f64 beta 5)) (fma.f64 74 (/.f64 (*.f64 (*.f64 i i) (pow.f64 alpha 3)) (pow.f64 beta 5)) (fma.f64 15 (/.f64 (*.f64 (*.f64 i i) alpha) (pow.f64 beta 5)) (fma.f64 9 (/.f64 (*.f64 (*.f64 i i) alpha) (pow.f64 beta 3)) (fma.f64 5 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 5)) (fma.f64 3 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 88 (/.f64 (pow.f64 i 5) (pow.f64 beta 5)) (fma.f64 10 (/.f64 (pow.f64 i 3) (pow.f64 beta 5)) (fma.f64 10 (/.f64 (*.f64 i (pow.f64 alpha 4)) (pow.f64 beta 5)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))))))))))
40.5b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
✓22.2b
1/16
42.1b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (exp.f64 (log.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)))))
22.9b
(-.f64 (+.f64 1/16 (*.f64 1/64 (/.f64 1 (*.f64 i i)))) (*.f64 (/.f64 1/32 i) (/.f64 beta (/.f64 i beta))))
40.6b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (pow.f64 (sqrt.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))) 2))
Compiler

Compiled 4814 to 2635 computations (45.3% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.5b
(/.f64 1 (*.f64 i i))
✓3.2b
(/.f64 (pow.f64 alpha 2) (pow.f64 i 2))

series31.0ms (0.5%)

Counts
1 → 0
Calls

6 calls:

12.0ms
(/.f64 (pow.f64 alpha 2) (pow.f64 i 2))
alpha
0
7.0ms
(/.f64 (pow.f64 alpha 2) (pow.f64 i 2))
alpha
-inf
6.0ms
(/.f64 (pow.f64 alpha 2) (pow.f64 i 2))
alpha
inf
2.0ms
(/.f64 (pow.f64 alpha 2) (pow.f64 i 2))
i
0
2.0ms
(/.f64 (pow.f64 alpha 2) (pow.f64 i 2))
i
-inf

rewrite35.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
610×log1p-expm1-u_binary64
610×expm1-log1p-u_binary64
319×log-prod_binary64
120×expm1-udef_binary64
120×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0710
11487
217777
Stop Event
1×node limit
Counts
1 → 36

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
36 → 36

prune85.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New60161
Fresh077
Picked101
Done011
Total61970
Error
13.9b
Counts
70 → 9
Alt Table
StatusErrorProgram
55.0b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (+.f64 i alpha) (pow.f64 beta 2)))
22.1b
(-.f64 (+.f64 1/16 (*.f64 1/64 (/.f64 1 (*.f64 i i)))) (*.f64 1/32 (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 alpha i) 2))) (cbrt.f64 (exp.f64 (pow.f64 (/.f64 alpha i) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (/.f64 alpha i) 2)))))))
45.3b
(*.f64 (/.f64 (fma.f64 i alpha (*.f64 i i)) (+.f64 (fma.f64 4 (*.f64 i alpha) (+.f64 (*.f64 alpha alpha) (*.f64 4 (*.f64 i i)))) -1)) (/.f64 (*.f64 i (+.f64 i alpha)) (pow.f64 (fma.f64 2 i alpha) 2)))
59.3b
(-.f64 (fma.f64 6 (/.f64 (*.f64 i (pow.f64 alpha 3)) (pow.f64 beta 4)) (fma.f64 25 (/.f64 (pow.f64 i 4) (pow.f64 beta 4)) (+.f64 (/.f64 (*.f64 i i) (pow.f64 beta 4)) (+.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) (fma.f64 50 (/.f64 (*.f64 (pow.f64 i 3) alpha) (pow.f64 beta 4)) (fma.f64 31 (/.f64 (*.f64 (*.f64 i i) (*.f64 alpha alpha)) (pow.f64 beta 4)) (+.f64 (/.f64 (*.f64 i alpha) (*.f64 beta beta)) (/.f64 (*.f64 i alpha) (pow.f64 beta 4))))))))) (fma.f64 196 (/.f64 (*.f64 (pow.f64 i 3) (*.f64 alpha alpha)) (pow.f64 beta 5)) (fma.f64 220 (/.f64 (*.f64 (pow.f64 i 4) alpha) (pow.f64 beta 5)) (fma.f64 74 (/.f64 (*.f64 (*.f64 i i) (pow.f64 alpha 3)) (pow.f64 beta 5)) (fma.f64 15 (/.f64 (*.f64 (*.f64 i i) alpha) (pow.f64 beta 5)) (fma.f64 9 (/.f64 (*.f64 (*.f64 i i) alpha) (pow.f64 beta 3)) (fma.f64 5 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 5)) (fma.f64 3 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 88 (/.f64 (pow.f64 i 5) (pow.f64 beta 5)) (fma.f64 10 (/.f64 (pow.f64 i 3) (pow.f64 beta 5)) (fma.f64 10 (/.f64 (*.f64 i (pow.f64 alpha 4)) (pow.f64 beta 5)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))))))))))
40.5b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
✓22.2b
1/16
42.1b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (exp.f64 (log.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)))))
22.9b
(-.f64 (+.f64 1/16 (*.f64 1/64 (/.f64 1 (*.f64 i i)))) (*.f64 (/.f64 1/32 i) (/.f64 beta (/.f64 i beta))))
40.6b
(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (pow.f64 (sqrt.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))) 2))
Compiler

Compiled 1784 to 1265 computations (29.1% saved)

regimes736.0ms (11.1%)

Accuracy

Total 1.7b remaining (13.3%)

Threshold costs 0b (0%)

Counts
73 → 2
Compiler

Compiled 20112 to 12277 computations (39% saved)

bsearch26.0ms (0.4%)

Algorithm
1×binary-search
Calls

1 calls:

19.0ms
i
Steps
ItersPointRange
8.433203281924905e+119
∈ [
6.0383310138928436e+119
, 
2.2327974709211004e+120
]
Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Rules
6×+-commutative_binary64
4×*-commutative_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02872
14072
Stop Event
1×saturated

end319.0ms (4.8%)

Stop Event
1×fuel
Remove

(sort alpha beta)

Compiler

Compiled 685 to 431 computations (37.1% saved)

Profiling

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