Details

Time bar (total: 51.3s)

sample36.0ms

Algorithm
intervals
Results
8.0ms204×body80valid
7.0ms256×pre80true
5.0ms26×body1280valid
2.0ms13×body320valid
1.0ms9×body640valid
0.0ms4×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.3b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite488.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
83×*-un-lft-identity
43×add-sqr-sqrt add-cube-cbrt
42×fma-def
24×associate-/r/
20×distribute-lft-out
17×add-exp-log add-cbrt-cube
16×flip3-+ flip-+
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r*
5×add-log-exp
4×frac-times
3×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 159
Calls
3 calls:
96.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
356.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
28.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series590.0ms

Counts
3 → 9
Calls
3 calls:
232.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
277.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
80.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify94.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07011971
137401800
250011782

prune571.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
0.1b
(/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
1.3b
(+ (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite772.0ms

Algorithm
rewrite-expression-head
Rules
2182×times-frac
1819×*-un-lft-identity
1037×add-sqr-sqrt
783×add-cube-cbrt
391×distribute-lft-out
362×fma-def
127×distribute-lft-out-- difference-of-squares
98×associate-/r/
96×associate-/l*
54×div-inv
42×flip3-- flip--
30×associate-/r*
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
6×add-log-exp
4×pow1 expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×frac-2neg clear-num associate-/l/
1×+-commutative sum-log
Counts
4 → 1013
Calls
4 calls:
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
104.0ms
(/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
16.0ms
(/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
542.0ms
(+ (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series682.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
239.0ms
(/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
87.0ms
(/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
285.0ms
(+ (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify159.0ms

Algorithm
egg-herbie
Counts
1025 → 1025
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0176912717
1500112362

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize19.0ms

Local error

Found 4 expressions with local error:

1.3b
(fma (* (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
14.2b
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
14.2b
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
14.2b
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite342.0ms

Algorithm
rewrite-expression-head
Rules
2796×times-frac
2296×*-un-lft-identity
1258×add-sqr-sqrt
1086×cbrt-prod
970×add-cube-cbrt
519×distribute-lft-out
144×distribute-lft-out-- difference-of-squares
114×associate-/r/
63×div-inv
48×flip3-- flip--
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div flip3-+ pow1/3 flip-+
1×fma-udef
Counts
4 → 1129
Calls
4 calls:
0.0ms
(fma (* (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
68.0ms
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
68.0ms
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
68.0ms
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series15.1s

Counts
4 → 12
Calls
4 calls:
13.9s
(fma (* (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
366.0ms
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
371.0ms
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
379.0ms
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify309.0ms

Algorithm
egg-herbie
Counts
1141 → 1141
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0182431674
1500131433

prune4.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 4 expressions with local error:

2.3b
(log (fma (* (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
14.2b
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
14.2b
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
14.2b
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite340.0ms

Algorithm
rewrite-expression-head
Rules
2796×times-frac
2297×*-un-lft-identity
1259×add-sqr-sqrt
1086×cbrt-prod
971×add-cube-cbrt
519×distribute-lft-out
144×distribute-lft-out-- difference-of-squares
114×associate-/r/
63×div-inv
48×flip3-- flip--
5×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div log-prod flip3-+ pow1/3 flip-+
1×rem-log-exp log-pow
Counts
4 → 1133
Calls
4 calls:
1.0ms
(log (fma (* (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
67.0ms
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
67.0ms
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
67.0ms
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series18.9s

Counts
4 → 12
Calls
4 calls:
17.7s
(log (fma (* (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
373.0ms
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
376.0ms
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
373.0ms
(cbrt (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify308.0ms

Algorithm
egg-herbie
Counts
1145 → 1145
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0187831944
1500131684

prune4.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

regimes242.0ms

Accuracy

18.5% (5.5b remaining)

Error of 11.6b against oracle of 6.1b and baseline of 12.8b

bsearch19.0ms

Steps
ItersRangePoint
2
5.061669446582593e+189
5.947606409351588e+189
5.615380048313215e+189

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04651
14651

end0.0ms

sample849.0ms

Algorithm
intervals
Results
257.0ms6302×body80valid
135.0ms8000×pre80true
111.0ms540×body1280valid
94.0ms577×body640valid
48.0ms395×body320valid
15.0ms186×body160valid