Details

Time bar (total: 7.5s)

sample38.0ms

Algorithm
intervals
Results
10.0ms206×body80valid
6.0ms256×pre80true
4.0ms16×body1280valid
3.0ms16×body640valid
1.0ms10×body320valid
1.0ms8×body160valid

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune3.0ms

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: 21.9b

Counts
2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.5b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.9b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite78.0ms

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:
20.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
37.0ms
(+ (/ (/ (* (+ 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)))

series731.0ms

Counts
3 → 9
Calls
3 calls:
223.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
425.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
83.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify99.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
07011971
137401800
250011782

prune481.0ms

Filtered
168 candidates to 131 candidates (78.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New15810168
Fresh000
Picked101
Done000
Total15910169

Merged error: 5.6b

Counts
169 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
0.3b
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.5b
(+ (log (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)
3.1b
(log (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

rewrite40.0ms

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)))
13.0ms
(/ (- 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)
7.0ms
(log (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))

series722.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
83.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
315.0ms
(+ (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))))

simplify65.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05631601
120941451
250011431

prune462.0ms

Filtered
142 candidates to 108 candidates (76.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1393142
Fresh279
Picked101
Done000
Total14210152

Merged error: 5.6b

Counts
152 → 10

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.3b
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.0b
(fma (- 1.0) (/ (* (- beta alpha) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (+ alpha (+ beta (fma i 2.0 2.0)))) (* 1.0 1.0))
2.5b
(fma (pow (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) 3) (pow 1.0 3))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
46×add-sqr-sqrt
40×times-frac
26×add-cube-cbrt
12×distribute-lft-out
10×associate-/l* distribute-lft-out-- difference-of-squares
8×add-exp-log associate-/r* add-cbrt-cube
4×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-sub div-exp clear-num flip-- flip-+ fma-udef div-inv
Counts
4 → 116
Calls
4 calls:
13.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
16.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.0ms
(fma (- 1.0) (/ (* (- beta alpha) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (+ alpha (+ beta (fma i 2.0 2.0)))) (* 1.0 1.0))
1.0ms
(fma (pow (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) 3) (pow 1.0 3))

series652.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
83.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
284.0ms
(fma (- 1.0) (/ (* (- beta alpha) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (+ alpha (+ beta (fma i 2.0 2.0)))) (* 1.0 1.0))
204.0ms
(fma (pow (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) 3) (pow 1.0 3))

simplify54.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03751405
114731290
250021276

prune710.0ms

Filtered
128 candidates to 96 candidates (75.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1271128
Fresh099
Picked101
Done000
Total12810138

Merged error: 5.6b

Counts
138 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.5b
(+ (+ (log (sqrt (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (log (sqrt (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))) 1.0)
3.2b
(log (sqrt (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
3.2b
(log (sqrt (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
36×add-sqr-sqrt
28×log-pow
26×add-cube-cbrt
24×fma-def
23×distribute-lft-out
20×pow1 log-prod times-frac
14×sqrt-prod
8×add-exp-log distribute-rgt-out
7×add-log-exp
6×unpow-prod-down sqrt-pow1 pow1/2 add-cbrt-cube
5×div-sub associate-/l* distribute-lft-out-- difference-of-squares
4×expm1-log1p-u log-div sqrt-div associate-/r* log1p-expm1-u pow-sub
3×associate-+l- sum-log
2×distribute-lft1-in flip3-+ rem-log-exp distribute-rgt1-in associate-/r/ flip-+ associate-/l/ sqr-pow
1×cbrt-undiv +-commutative associate-+r- associate-+l+ flip3-- frac-2neg count-2 div-exp clear-num flip-- div-inv
Counts
4 → 142
Calls
4 calls:
13.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
18.0ms
(+ (+ (log (sqrt (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (log (sqrt (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))) 1.0)
7.0ms
(log (sqrt (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
7.0ms
(log (sqrt (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
329.0ms
(+ (+ (log (sqrt (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (log (sqrt (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))) 1.0)
399.0ms
(log (sqrt (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
403.0ms
(log (sqrt (pow (exp (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04922369
117052059
250021993

prune548.0ms

Filtered
154 candidates to 106 candidates (68.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1522154
Fresh189
Picked101
Done000
Total15410164

Merged error: 5.6b

Counts
164 → 10

regimes263.0ms

Accuracy

19.9% (5.1b remaining)

Error of 11.2b against oracle of 6.1b and baseline of 12.5b

bsearch82.0ms

Steps
ItersRangePoint
9
1.9757578440146217e+183
9.146270359262107e+189
4.1803409020900765e+186

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04225
14425
24425

end0.0ms

sample956.0ms

Algorithm
intervals
Results
290.0ms6348×body80valid
168.0ms8000×pre80true
128.0ms519×body1280valid
117.0ms613×body640valid
46.0ms338×body320valid
17.0ms182×body160valid