Details

Time bar (total: 22.0s)

sample33.0ms

Algorithm
intervals
Results
8.0ms201×body80valid
4.0ms256×pre80true
4.0ms20×body1280valid
3.0ms20×body640valid
1.0ms10×body320valid
0.0ms5×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: 24.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* 2.0 i))
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.5b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite490.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
87×*-un-lft-identity
46×fma-def
45×add-sqr-sqrt add-cube-cbrt
24×associate-/r/
21×distribute-lft-out
18×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
12×div-inv
11×add-log-exp
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r*
4×pow1 expm1-log1p-u frac-times sum-log log1p-expm1-u
3×flip3-- flip--
2×+-commutative frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×associate-+l+
Counts
4 → 178
Calls
4 calls:
15.0ms
(+ (+ alpha beta) (* 2.0 i))
93.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
348.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
27.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series590.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (+ alpha beta) (* 2.0 i))
225.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
269.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
77.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify105.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
07242051
141011860
250011852

prune594.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))
0.3b
(/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha)))
3.4b
(+ (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
12400×times-frac
9469×*-un-lft-identity
5477×add-sqr-sqrt
4067×add-cube-cbrt
1996×distribute-lft-out
1418×fma-def
705×distribute-lft-out-- difference-of-squares
400×associate-/r/
378×associate-/l*
205×div-inv
164×flip3-+ flip-+
125×associate-/r*
62×add-exp-log
43×div-exp
32×flip3-- add-cbrt-cube flip--
19×cbrt-undiv
6×rec-exp 1-exp add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num
2×associate-/l/
1×+-commutative pow-flip sum-log inv-pow
Counts
4 → 3880
Calls
4 calls:
193.0ms
(/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
22.0ms
(/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))
40.0ms
(/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha)))
1.4s
(+ (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series606.0ms

Counts
4 → 12
Calls
4 calls:
278.0ms
(/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
67.0ms
(/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))
143.0ms
(/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha)))
119.0ms
(+ (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify583.0ms

Algorithm
egg-herbie
Counts
3892 → 3892
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500155520

prune9.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.7b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.7b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
4.7b
(fma (/ (/ 1 (/ (/ 1 (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta)))) 1)) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (cbrt (+ alpha beta))) (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt 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
1×fma-udef
Counts
4 → 58
Calls
4 calls:
32.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
30.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
33.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0ms
(fma (/ (/ 1 (/ (/ 1 (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta)))) 1)) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (cbrt (+ alpha beta))) (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series2.3s

Counts
4 → 12
Calls
4 calls:
175.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
173.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
173.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.8s
(fma (/ (/ 1 (/ (/ 1 (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta)))) 1)) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (cbrt (+ alpha beta))) (- beta alpha))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify43.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03151077
11015966
25002950

prune492.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.7b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.7b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
6.9b
(fma (/ (/ 1 (/ (/ 1 (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta)))) 1)) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (cbrt (+ alpha beta))) (- beta alpha))) (* (cbrt (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (cbrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt 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
1×fma-udef
Counts
4 → 58
Calls
4 calls:
31.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
32.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0ms
(fma (/ (/ 1 (/ (/ 1 (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta)))) 1)) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (cbrt (+ alpha beta))) (- beta alpha))) (* (cbrt (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (cbrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

series2.3s

Counts
4 → 12
Calls
4 calls:
178.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
181.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
172.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.8s
(fma (/ (/ 1 (/ (/ 1 (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta)))) 1)) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (cbrt (+ alpha beta))) (- beta alpha))) (* (cbrt (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (cbrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) 1.0)

simplify44.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03191259
110491120
250011104

prune489.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 7.2b

regimes405.0ms

Accuracy

20.3% (5.3b remaining)

Error of 11.0b against oracle of 5.7b and baseline of 12.4b

bsearch39.0ms

Steps
ItersRangePoint
4
1.3922232554522014e+156
2.2830781917720807e+156
1.6389858218069558e+156

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04931
14931

end0.0ms

sample840.0ms

Algorithm
intervals
Results
252.0ms6359×body80valid
133.0ms8000×pre80true
117.0ms555×body1280valid
88.0ms559×body640valid
39.0ms316×body320valid
16.0ms211×body160valid