Details

Time bar (total: 19.2s)

sample34.0ms

Algorithm
intervals
Results
8.0ms212×body80valid
4.0ms256×pre80true
4.0ms19×body1280valid
2.0ms15×body640valid
1.0ms8×body320valid
0.0ms2×body160valid

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize13.0ms

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))
1.0b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.4b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite857.0ms

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:
175.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
618.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
57.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series563.0ms

Counts
3 → 9
Calls
3 calls:
218.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
266.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
79.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify96.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07011971
137401800
250011782

prune536.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
10.4b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
162×*-un-lft-identity
118×add-sqr-sqrt
80×add-cube-cbrt
26×associate-/l*
22×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
10×add-exp-log add-cbrt-cube
7×flip3-+ associate-/r* flip-+ div-inv
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/ add-log-exp
2×frac-2neg clear-num
1×flip3-- flip-- fma-udef
Counts
3 → 181
Calls
3 calls:
43.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
177.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series485.0ms

Counts
3 → 9
Calls
3 calls:
69.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
157.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
258.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify103.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
07273112
132592892
250022876

prune614.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- beta alpha))
0.5b
(cbrt (- beta alpha))
0.5b
(cbrt (- beta alpha))
10.4b
(fma (/ (/ (+ alpha beta) 1) 1) (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (/ (cbrt (- beta alpha)) (+ alpha (+ beta (fma i 2.0 2.0)))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) 1.0)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
1×fma-udef
Counts
4 → 61
Calls
4 calls:
4.0ms
(cbrt (- beta alpha))
4.0ms
(cbrt (- beta alpha))
8.0ms
(cbrt (- beta alpha))
0.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (/ (cbrt (- beta alpha)) (+ alpha (+ beta (fma i 2.0 2.0)))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) 1.0)

series702.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(cbrt (- beta alpha))
145.0ms
(cbrt (- beta alpha))
139.0ms
(cbrt (- beta alpha))
278.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (/ (cbrt (- beta alpha)) (+ alpha (+ beta (fma i 2.0 2.0)))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) 1.0)

simplify92.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0247778
1752690
23403659
35002645

prune414.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
0.5b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
0.5b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
7.3b
(+ (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
7204×times-frac
4206×*-un-lft-identity
2754×add-sqr-sqrt
2389×fma-def
1986×add-cube-cbrt
1922×cbrt-div
1337×associate-/r/
969×cbrt-prod
962×flip3-+ flip-+
726×distribute-lft-out
596×frac-times
384×distribute-lft-out-- difference-of-squares
298×associate-*r/ associate-*l/
230×div-inv
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow1/3
1×+-commutative sum-log
Counts
4 → 2448
Calls
4 calls:
15.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
15.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
15.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
2.1s
(+ (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

series733.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
146.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
145.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
298.0ms
(+ (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

simplify53.0ms

Algorithm
egg-herbie
Counts
2460 → 2460
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0307988
1994897
25001860

prune9.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

regimes239.0ms

Accuracy

16.9% (5.4b remaining)

Error of 11.1b against oracle of 5.6b and baseline of 12.2b

bsearch81.0ms

Steps
ItersRangePoint
9
3.6722806727149755e+159
5.762254725775896e+165
2.956513572083282e+162

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04341
14341

end0.0ms

sample852.0ms

Algorithm
intervals
Results
260.0ms6404×body80valid
119.0ms8000×pre80true
94.0ms487×body1280valid
90.0ms590×body640valid
38.0ms337×body320valid
14.0ms182×body160valid