Details

Time bar (total: 22.0s)

analyze103.0ms (0.5%)

Algorithm
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)

sample53.0ms (0.2%)

Algorithm
intervals
Results
26.0ms256×body128valid
6.0ms256×pre128true
Compiler

Compiled 126 to 65 computations (48.4% saved)

simplify42.0ms (0.2%)

Algorithm
egg-herbie
Rules
705×associate-+l+_binary64
492×associate-*l*_binary64
422×associate-*r*_binary64
369×times-frac_binary64
336×associate-/l*_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01875
16767
229367
3161267
4497967
5503567

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
55.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
55.5b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
Compiler

Compiled 203 to 89 computations (56.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 i (+.f64 i (+.f64 alpha beta)))
0.1b
(*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
39.7b
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
47.3b
(/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))

series3.4s (15.6%)

Counts
4 → 144
Calls

4 calls:

3.1s
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
284.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
47.0ms
(*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
9.0ms
(*.f64 i (+.f64 i (+.f64 alpha beta)))

rewrite55.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube_binary64
61×add-exp-log_binary64
22×*-un-lft-identity_binary64
22×cbrt-unprod_binary64
22×prod-exp_binary64
Counts
4 → 129
Calls

4 calls:

11.0ms
(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
9.0ms
(/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
7.0ms
(*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
6.0ms
(*.f64 i (+.f64 i (+.f64 alpha beta)))

simplify437.0ms (2%)

Algorithm
egg-herbie
Rules
731×fma-def_binary64
507×associate-/l*_binary64
344×times-frac_binary64
54×sqr-pow_binary64
54×sub-neg_binary64
Counts
273 → 274
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0254448017
1513648017

prune995.0ms (4.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2686274
Fresh000
Picked101
Done000
Total2696275
Error
12.9b
Counts
275 → 6
Alt Table
StatusErrorProgram
44.0b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (*.f64 (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
43.6b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
60.6b
(/.f64 (/.f64 (*.f64 i (*.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
59.4b
(-.f64 (+.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) (/.f64 (*.f64 i alpha) (*.f64 beta beta))) (fma.f64 3 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (*.f64 (*.f64 i i) alpha) (pow.f64 beta 3)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))
57.9b
(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
18.6b
1/16
Compiler

Compiled 62146 to 36187 computations (41.8% saved)

localize0.0ms (0%)

prune9.0ms (0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New000
Fresh055
Picked011
Done000
Total066
Error
12.9b
Counts
6 → 6
Alt Table
StatusErrorProgram
44.0b
(*.f64 (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (*.f64 (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
43.6b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
60.6b
(/.f64 (/.f64 (*.f64 i (*.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
59.4b
(-.f64 (+.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) (/.f64 (*.f64 i alpha) (*.f64 beta beta))) (fma.f64 3 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (*.f64 (*.f64 i i) alpha) (pow.f64 beta 3)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))
57.9b
(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
18.6b
1/16
Compiler

Compiled 476 to 246 computations (48.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
6.4b
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
38.7b
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
39.7b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

series3.9s (17.6%)

Counts
4 → 144
Calls

4 calls:

2.8s
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
492.0ms
(/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
480.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
63.0ms
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite375.0ms (1.7%)

Algorithm
rewrite-expression-head
Rules
847×times-frac_binary64
318×*-un-lft-identity_binary64
318×add-sqr-sqrt_binary64
318×add-cube-cbrt_binary64
63×associate-/r*_binary64
Counts
4 → 443
Calls

4 calls:

35.0ms
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
26.0ms
(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
9.0ms
(/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
4.0ms
(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

simplify1.6s (7.3%)

Algorithm
egg-herbie
Rules
867×fma-def_binary64
371×times-frac_binary64
13×cube-mult_binary64
13×unpow2_binary64
13×unpow3_binary64
Counts
587 → 634
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0368686910
1529286910

prune4.2s (18.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New6322634
Fresh224
Picked011
Done011
Total6346640
Error
12.9b
Counts
640 → 6
Alt Table
StatusErrorProgram
42.8b
(/.f64 (*.f64 1/4 (*.f64 i i)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
43.6b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
60.6b
(/.f64 (/.f64 (*.f64 i (*.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
59.4b
(-.f64 (+.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) (/.f64 (*.f64 i alpha) (*.f64 beta beta))) (fma.f64 3 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (*.f64 (*.f64 i i) alpha) (pow.f64 beta 3)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))
43.6b
(*.f64 (/.f64 (/.f64 i 1) 1) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
18.6b
1/16
Compiler

Compiled 99188 to 51307 computations (48.3% saved)

localize18.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)
39.2b
(/.f64 (*.f64 1/4 (*.f64 i i)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

series452.0ms (2.1%)

Counts
2 → 72
Calls

2 calls:

410.0ms
(/.f64 (*.f64 1/4 (*.f64 i i)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
41.0ms
(fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)

rewrite17.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
2 → 35
Calls

2 calls:

11.0ms
(/.f64 (*.f64 1/4 (*.f64 i i)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
1.0ms
(fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)

simplify200.0ms (0.9%)

Algorithm
egg-herbie
Rules
563×times-frac_binary64
446×associate-/l*_binary64
435×fma-def_binary64
326×associate-/r*_binary64
288×associate-*r*_binary64
Counts
107 → 118
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04397066
114206322
252506322

prune330.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1162118
Fresh123
Picked101
Done022
Total1186124
Error
12.8b
Counts
124 → 6
Alt Table
StatusErrorProgram
43.3b
(exp.f64 (-.f64 (+.f64 (log.f64 1/4) (+.f64 (log.f64 i) (log.f64 i))) (log.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
43.6b
(/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
59.4b
(-.f64 (+.f64 (/.f64 (*.f64 i i) (*.f64 beta beta)) (/.f64 (*.f64 i alpha) (*.f64 beta beta))) (fma.f64 3 (/.f64 (*.f64 i (*.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (*.f64 (*.f64 i i) alpha) (pow.f64 beta 3)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))
43.9b
(/.f64 (*.f64 1/4 (*.f64 i i)) (*.f64 4 (+.f64 (*.f64 i (+.f64 i beta)) (*.f64 i alpha))))
43.6b
(*.f64 (/.f64 (/.f64 i 1) 1) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
18.6b
1/16
Compiler

Compiled 7278 to 4345 computations (40.3% saved)

regimes2.1s (9.7%)

Accuracy

Total 3.1b remaining (24.2%)

Threshold costs 0b (0%)

Counts
152 → 3
Compiler

Compiled 31100 to 16909 computations (45.6% saved)

bsearch108.0ms (0.5%)

Steps
ItersRangePoint
7
8.543962667643894e+124
3.6263556368995286e+126
8.934596183311938e+125
7
2.6292161326185564e+36
1.5380136720765097e+38
2.660517665891581e+36
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033100
141100
241100

end20.0ms (0.1%)

Compiler

Compiled 216 to 123 computations (43.1% saved)

sample3.6s (16.2%)

Algorithm
intervals
Results
1.8s8000×body128valid
349.0ms8000×pre128true
Compiler

Compiled 348 to 192 computations (44.8% saved)

Profiling

Loading profile data...