Details

Time bar (total: 14.0s)

sample41.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
6.0ms256×pre80true

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 49.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
0.1b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
37.8b
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
39.2b
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite416.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log add-cbrt-cube
17×cbrt-undiv div-exp prod-exp cbrt-unprod
16×add-sqr-sqrt times-frac
13×add-cube-cbrt *-un-lft-identity
11×pow1
10×associate-*l/ associate-/r*
6×associate-*r*
5×associate-*l*
4×expm1-log1p-u pow-prod-down fma-udef log1p-expm1-u div-inv associate-/l/ add-log-exp
3×flip3-- flip--
2×distribute-rgt-in frac-2neg distribute-lft-in associate-*r/ clear-num *-commutative associate-/l*
1×flip3-+ associate-/r/ flip-+ difference-of-squares unswap-sqr
Counts
4 → 122
Calls
4 calls:
121.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
93.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
90.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
106.0ms
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series3.4s

Counts
4 → 12
Calls
4 calls:
501.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
261.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
749.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
1.9s
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify49.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
07943237
150022435

prune508.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 40.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
6.9b
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
33.4b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
37.8b
(/ (* i (+ (+ alpha beta) i)) (/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
61×add-exp-log add-cbrt-cube
47×add-sqr-sqrt
44×add-cube-cbrt *-un-lft-identity
34×associate-/r*
29×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
9×div-inv
6×pow1
5×associate-/l*
4×expm1-log1p-u associate-*l* associate-*l/ associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg associate-*r* clear-num
2×flip3-- associate-*r/ flip-- fma-udef
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down *-commutative flip-+ difference-of-squares unswap-sqr
Counts
4 → 176
Calls
4 calls:
92.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
41.0ms
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
2.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
42.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))

series3.2s

Counts
4 → 12
Calls
4 calls:
265.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
2.0s
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
119.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
776.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09814480
150013634

prune636.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 33.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))))
0.2b
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
0.3b
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
38.7b
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite343.0ms

Algorithm
rewrite-expression-head
Rules
348×times-frac
292×*-un-lft-identity
216×add-sqr-sqrt
167×add-cube-cbrt
75×distribute-lft-out
61×associate-*r*
53×associate-*l*
49×add-exp-log add-cbrt-cube
28×associate-/l*
23×cbrt-undiv div-exp
15×div-inv
13×difference-of-squares
9×prod-exp associate-/r* cbrt-unprod unswap-sqr
6×pow1
5×associate-/l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×frac-times flip3-- flip3-+ div-sub associate-*r/ pow-prod-down associate-*l/ associate-/r/ *-commutative flip-- flip-+
Counts
4 → 326
Calls
4 calls:
180.0ms
(* (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))))
39.0ms
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
36.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
66.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.2s

Counts
4 → 12
Calls
4 calls:
767.0ms
(* (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))))
97.0ms
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
75.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
254.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify97.0ms

Algorithm
egg-herbie
Counts
338 → 338
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013617039
150026324

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ i 4.0) (/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))))
0.2b
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
0.3b
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
248×*-un-lft-identity
144×add-sqr-sqrt
123×add-cube-cbrt
75×distribute-lft-out
61×associate-*r*
31×add-exp-log add-cbrt-cube
24×associate-/l*
13×cbrt-undiv div-exp associate-*l*
11×div-inv
6×prod-exp associate-/r* cbrt-unprod unswap-sqr
5×pow1
3×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
2×frac-2neg clear-num
1×frac-times flip3-+ associate-*r/ pow-prod-down associate-*l/ *-commutative flip-+
Counts
3 → 241
Calls
3 calls:
75.0ms
(* (/ i 4.0) (/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))))
39.0ms
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
38.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))

series294.0ms

Counts
3 → 9
Calls
3 calls:
121.0ms
(* (/ i 4.0) (/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))))
98.0ms
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
74.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))

simplify99.0ms

Algorithm
egg-herbie
Counts
250 → 250
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
08133279
138692950
250012941

prune522.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.4b

regimes238.0ms

Accuracy

56.7% (5.1b remaining)

Error of 12.2b against oracle of 7.1b and baseline of 18.8b

bsearch184.0ms

Steps
ItersRangePoint
7
4.614439106502894e+145
1.1963549483378118e+147
1.4988189954877084e+146
7
1.05606416635184e+81
3.7954374245748784e+82
1.684205502803454e+81
6
1.4077139984351696e+42
1.523107952296189e+43
1.4938731981295666e+43

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05183
15183

end0.0ms

sample1.1s

Algorithm
intervals
Results
696.0ms8000×body80valid
187.0ms8000×pre80true