Details

Time bar (total: 18.1s)

sample38.0ms

Algorithm
intervals
Results
9.0ms202×body80valid
6.0ms256×pre80true
4.0ms22×body640valid
4.0ms15×body1280valid
2.0ms11×body320valid
1.0ms6×body160valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 22.7b

Counts
2 → 1

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.0b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.7b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite72.0ms

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:
19.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
15.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series575.0ms

Counts
3 → 9
Calls
3 calls:
227.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
270.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
78.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify101.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07011971
137401800
250011782

prune484.0ms

Filtered
168 candidates to 131 candidates (78.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1599168
Fresh000
Picked101
Done000
Total1609169

Merged error: 6.0b

Counts
169 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
0.0b
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.8b
(+ (log (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
2.3b
(log (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
61×*-un-lft-identity
39×add-sqr-sqrt
32×times-frac
29×add-cube-cbrt
14×log-prod
11×distribute-lft-out
9×add-exp-log associate-/l*
8×add-cbrt-cube
7×associate-+l+ associate-/r*
6×unpow-prod-down
5×distribute-lft-out-- add-log-exp difference-of-squares
4×pow1 expm1-log1p-u fma-def log1p-expm1-u associate-/l/
3×flip3-+ div-sub rem-log-exp flip-+
2×cbrt-undiv log-div frac-2neg div-exp clear-num associate-/r/ log-pow div-inv pow-sub sqr-pow
1×+-commutative pow-to-exp associate-+l- flip3-- pow-exp sum-log flip--
Counts
4 → 130
Calls
4 calls:
6.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
12.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
10.0ms
(+ (log (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
6.0ms
(log (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

series729.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
85.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
317.0ms
(+ (log (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
258.0ms
(log (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

simplify64.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05631601
120941451
250011431

prune479.0ms

Filtered
142 candidates to 108 candidates (76.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1375142
Fresh268
Picked101
Done000
Total14011151

Merged error: 6.0b

Counts
151 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.6b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
4.0b
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite950.0ms

Algorithm
rewrite-expression-head
Rules
10036×times-frac
6754×*-un-lft-identity
4612×add-sqr-sqrt
3458×add-cube-cbrt
1178×fma-def
1071×distribute-lft-out
577×distribute-lft-out-- difference-of-squares
400×associate-/r/
314×associate-/l*
205×div-inv
164×flip3-+ flip-+
105×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 → 3236
Calls
4 calls:
84.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
15.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
25.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
394.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series831.0ms

Counts
4 → 12
Calls
4 calls:
281.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
66.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
146.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
337.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify495.0ms

Algorithm
egg-herbie
Counts
3248 → 3248
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
0500147178

prune8.0s

Filtered
3248 candidates to 1754 candidates (54.0%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New3236123248
Fresh8210
Picked101
Done000
Total3245143259

Merged error: 6.0b

Counts
3259 → 14

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
4.2b
(fma (/ (/ 1 (/ 1 (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (cbrt (- beta alpha)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite27.0ms

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:
11.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
7.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.0ms
(fma (/ (/ 1 (/ 1 (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (cbrt (- beta alpha)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series3.1s

Counts
4 → 12
Calls
4 calls:
181.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
175.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
176.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.6s
(fma (/ (/ 1 (/ 1 (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (cbrt (- beta alpha)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify115.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
02781061
1903949
24732919
35001919

prune359.0ms

Filtered
70 candidates to 66 candidates (94.3%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New68270
Fresh11213
Picked101
Done000
Total701484

Merged error: 6.0b

Counts
84 → 14

regimes395.0ms

Accuracy

9.1% (5.9b remaining)

Error of 11.7b against oracle of 5.8b and baseline of 12.3b

bsearch86.0ms

Steps
ItersRangePoint
10
6.708564941018832e+66
1.4668071073409935e+78
1.449803413031472e+78

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04324
14324

end0.0ms

sample1.0s

Algorithm
intervals
Results
316.0ms6387×body80valid
176.0ms8000×pre80true
128.0ms527×body1280valid
110.0ms562×body640valid
51.0ms346×body320valid
17.0ms178×body160valid