Details

Time bar (total: 14.0s)

analyze391.0ms (2.8%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%28.1%71.9%0
0%28.1%71.9%1
0%28.1%71.9%2
0%28.1%71.9%3
3.5%24.6%71.9%4
5.3%22.8%71.9%5
10.5%17.5%71.9%6
14%14%71.9%7
19.1%9%71.9%8
24.6%3.5%71.9%9
25.1%3%71.9%10
25.8%2.3%71.9%11
26.3%1.8%71.9%12
26.6%1.5%71.9%13
26.9%1.2%71.9%14
Compiler

Compiled 43 to 28 computations (34.9% saved)

sample280.0ms (2%)

Algorithm
1×intervals
Results
201.0ms208×body128valid
6.0ms256×pre128true
5.0ms18×body1024valid
5.0ms21×body512valid
1.0ms3×body2048valid
1.0ms6×body256valid
Compiler

Compiled 78 to 51 computations (34.6% saved)

simplify44.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
847×times-frac_binary64
817×distribute-rgt-in_binary64
748×distribute-lft-in_binary64
537×div-sub_binary64
535×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01643
13439
211037
343537
4167237
5249437
6335837
7539237

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
19.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶19.5b
(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
22.2b
(/.f64 (+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)
Compiler

Compiled 180 to 106 computations (41.1% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 2 i (+.f64 alpha beta))
✓0.0b
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓11.9b
(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
✓19.0b
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series910.0ms (6.5%)

Counts
4 → 144
Calls

4 calls:

535.0ms
(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
349.0ms
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
19.0ms
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
6.0ms
(fma.f64 2 i (+.f64 alpha beta))

rewrite17.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
14×*-un-lft-identity_binary64
14×add-sqr-sqrt_binary64
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
8×add-cube-cbrt_binary64
Counts
4 → 77
Calls

4 calls:

7.0ms
(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
4.0ms
(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
0.0ms
(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
0.0ms
(fma.f64 2 i (+.f64 alpha beta))

simplify266.0ms (1.9%)

Algorithm
1×egg-herbie
Rules
562×+-commutative_binary64
490×fma-def_binary64
488×associate-+r+_binary64
392×*-commutative_binary64
294×associate-*r/_binary64
Counts
221 → 227
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0140520324
1545620324

prune583.0ms (4.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2427249
Fresh101
Picked101
Done000
Total2447251
Error
0.2b
Counts
251 → 7
Alt Table
StatusErrorProgram
19.5b
(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
20.9b
(/.f64 (-.f64 (+.f64 1 (/.f64 beta (+.f64 beta (+.f64 2 alpha)))) (/.f64 alpha (+.f64 beta (+.f64 2 alpha)))) 2)
19.6b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1))) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1))) 2)
54.3b
(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i i) (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i beta) (pow.f64 alpha 3)) (*.f64 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 240 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (*.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 (*.f64 beta beta) (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (*.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (*.f64 beta beta) (pow.f64 alpha 4)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha)))))))))))))))))))))))) 2)
▶12.0b
(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
50.1b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
12.2b
(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
Compiler

Compiled 26647 to 16988 computations (36.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))
✓0.0b
(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓0.1b
(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
✓11.9b
(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

series991.0ms (7.1%)

Counts
4 → 144
Calls

4 calls:

511.0ms
(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
318.0ms
(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
93.0ms
(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
67.0ms
(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))

rewrite43.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
82×*-un-lft-identity_binary64
75×add-sqr-sqrt_binary64
65×times-frac_binary64
40×add-cube-cbrt_binary64
32×add-exp-log_binary64
Counts
4 → 162
Calls

4 calls:

17.0ms
(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
7.0ms
(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
2.0ms
(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))
1.0ms
(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

simplify292.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
579×fma-def_binary64
560×associate-+r+_binary64
386×associate-*r/_binary64
174×associate-/l*_binary64
155×associate-/r*_binary64
Counts
306 → 370
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0171726289
1548426289

prune921.0ms (6.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3664370
Fresh336
Picked101
Done000
Total3707377
Error
0.2b
Counts
377 → 7
Alt Table
StatusErrorProgram
54.3b
(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i i) (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i beta) (pow.f64 alpha 3)) (*.f64 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 240 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (*.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 (*.f64 beta beta) (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (*.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (*.f64 beta beta) (pow.f64 alpha 4)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha)))))))))))))))))))))))) 2)
20.9b
(/.f64 (+.f64 1 (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 2 alpha)))) 2)
12.3b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))) 1)) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))) 1))) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))) 1))) 2)
12.3b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1))) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1))) 2)
▶11.9b
(/.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1))) 2)
50.1b
(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
12.2b
(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
Compiler

Compiled 35370 to 22183 computations (37.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
0.1b
(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
✓4.3b
(log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)))
11.9b
(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

series517.0ms (3.7%)

Counts
1 → 36
Calls

1 calls:

516.0ms
(log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)))

rewrite3.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
4×log-prod_binary64
4×log-pow_binary64
3×*-un-lft-identity_binary64
3×add-sqr-sqrt_binary64
3×exp-prod_binary64
Counts
1 → 18
Calls

1 calls:

2.0ms
(log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)))

simplify131.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
895×fma-def_binary64
445×associate-*l/_binary64
266×+-commutative_binary64
242×*-commutative_binary64
229×associate-+r+_binary64
Counts
54 → 77
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07969496
130559078
253749078

prune1.1s (8.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3673370
Fresh246
Picked011
Done000
Total3698377
Error
0.2b
Counts
377 → 8
Alt Table
StatusErrorProgram
12.2b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)))) (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1))))) (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1))))) 2)
50.1b
(/.f64 (/.f64 (fma.f64 beta 2 (fma.f64 i 4 2)) alpha) 2)
12.3b
(/.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)))))) 2)
54.3b
(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i i) (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i beta) (pow.f64 alpha 3)) (*.f64 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 240 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (*.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 (*.f64 beta beta) (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (*.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (*.f64 beta beta) (pow.f64 alpha 4)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha)))))))))))))))))))))))) 2)
20.9b
(/.f64 (+.f64 1 (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 2 alpha)))) 2)
12.3b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))) 1)) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))) 1))) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))) 1))) 2)
✓11.9b
(/.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1))) 2)
▶12.2b
(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
Compiler

Compiled 44086 to 28413 computations (35.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
✓0.5b
(*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha)))
✓0.6b
(cbrt.f64 (-.f64 beta alpha))
✓11.9b
(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

series873.0ms (6.2%)

Counts
4 → 120
Calls

4 calls:

504.0ms
(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
299.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
38.0ms
(*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha)))
31.0ms
(cbrt.f64 (-.f64 beta alpha))

rewrite55.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
74×add-sqr-sqrt_binary64
72×*-un-lft-identity_binary64
55×cbrt-prod_binary64
46×associate-*r*_binary64
42×times-frac_binary64
Counts
4 → 162
Calls

4 calls:

23.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
9.0ms
(*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha)))
2.0ms
(cbrt.f64 (-.f64 beta alpha))
0.0ms
(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

simplify518.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
465×fma-def_binary64
444×associate-+r+_binary64
331×associate-*r/_binary64
166×associate-/l*_binary64
156×associate-/r*_binary64
Counts
282 → 335
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0159323468
1498323468

prune1.1s (7.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New4470447
Fresh066
Picked011
Done011
Total4478455
Error
0.2b
Counts
455 → 8
Alt Table
StatusErrorProgram
12.2b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)))) (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1))))) (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1))))) 2)
50.1b
(/.f64 (/.f64 (fma.f64 beta 2 (fma.f64 i 4 2)) alpha) 2)
12.3b
(/.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)))))) 2)
54.3b
(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i i) (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (*.f64 i beta) (pow.f64 alpha 3)) (*.f64 (/.f64 (*.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 240 (/.f64 (*.f64 beta (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (*.f64 alpha alpha)) (+.f64 (/.f64 4 (*.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (*.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 (*.f64 beta beta) (*.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (*.f64 i (*.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (*.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i i) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (*.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (*.f64 i beta) (*.f64 alpha alpha)) (fma.f64 160 (/.f64 (*.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (*.f64 beta beta) (pow.f64 alpha 4)) (*.f64 2 (/.f64 (*.f64 beta beta) (*.f64 alpha alpha)))))))))))))))))))))))) 2)
20.9b
(/.f64 (+.f64 1 (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 2 alpha)))) 2)
12.3b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))) 1)) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))) 1))) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))) 1))) 2)
✓11.9b
(/.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1))) 2)
✓12.2b
(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 beta alpha)) (cbrt.f64 (-.f64 beta alpha))) (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (cbrt.f64 (-.f64 beta alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
Compiler

Compiled 39652 to 22804 computations (42.5% saved)

regimes3.1s (22.1%)

Accuracy

Total 1.4b remaining (92.3%)

Threshold costs 0b (0%)

Counts
255 → 2
Compiler

Compiled 79938 to 49157 computations (38.5% saved)

bsearch18.0ms (0.1%)

Compiler

Compiled 28 to 16 computations (42.9% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Rules
7×+-commutative_binary64
4×*-commutative_binary64
2×sub-neg_binary64
1×neg-sub0_binary64
1×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
032100
144100
248100
350100
451100
550100

end1.0ms (0%)

Compiler

Compiled 71 to 42 computations (40.8% saved)

sample1.8s (12.6%)

Algorithm
1×intervals
Results
507.0ms6446×body128valid
212.0ms691×body1024valid
199.0ms8000×pre128true
113.0ms498×body512valid
45.0ms311×body256valid
19.0ms54×body2048valid
Compiler

Compiled 780 to 466 computations (40.3% saved)

Profiling

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