Details

Time bar (total: 13.5s)

sample27.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune9.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 48.2b

localize20.0ms

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))) (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)))
36.7b
(/ (* 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)))))
38.7b
(/ (* (* (- (* (+ (+ 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))))

rewrite398.0ms

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:
116.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
89.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
87.0ms
(/ (* 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)))))
101.0ms
(/ (* (* (- (* (+ (+ 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))))

series3.5s

Counts
4 → 12
Calls
4 calls:
502.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
262.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
742.0ms
(/ (* 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)))))
2.0s
(/ (* (* (- (* (+ (+ 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))))

simplify47.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07943237
150022435

prune473.0ms

Filtered
134 candidates to 97 candidates (72.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 40.5b

localize17.0ms

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)))
7.5b
(/ (* (- (* (+ (+ 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))))
32.2b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
36.7b
(/ (* 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)))))

rewrite178.0ms

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:
89.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
40.0ms
(/ (* (- (* (+ (+ 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)))
40.0ms
(/ (* 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)))))

series3.1s

Counts
4 → 12
Calls
4 calls:
269.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
1.9s
(/ (* (- (* (+ (+ 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))))
124.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
781.0ms
(/ (* 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)))))

simplify68.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09814480
150013634

prune617.0ms

Filtered
188 candidates to 139 candidates (73.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 32.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
0.1b
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))))
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))))
36.6b
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
327×times-frac
225×*-un-lft-identity
221×add-sqr-sqrt
160×add-cube-cbrt
61×associate-*r*
53×associate-*l*
49×add-exp-log add-cbrt-cube
39×distribute-lft-out
25×difference-of-squares
23×cbrt-undiv div-exp
22×associate-/r*
15×div-inv
12×associate-/l*
9×prod-exp cbrt-unprod unswap-sqr
6×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg clear-num
2×associate-/r/
1×frac-times flip3-- flip3-+ div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- flip-+
Counts
4 → 314
Calls
4 calls:
33.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
39.0ms
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))))
173.0ms
(* (/ 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))))
60.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.3s

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
187.0ms
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))))
761.0ms
(* (/ 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))))
252.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify100.0ms

Algorithm
egg-herbie
Counts
326 → 326
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014587630
150026934

prune1.2s

Filtered
326 candidates to 249 candidates (76.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
0.0b
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
0.2b
(* (/ i 4.0) (/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))))

rewrite156.0ms

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:
39.0ms
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
33.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
71.0ms
(* (/ i 4.0) (/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))))

series281.0ms

Counts
3 → 9
Calls
3 calls:
95.0ms
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
73.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
114.0ms
(* (/ i 4.0) (/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))))

simplify95.0ms

Algorithm
egg-herbie
Counts
250 → 250
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
08133279
138692950
250022934

prune495.0ms

Filtered
250 candidates to 151 candidates (60.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

regimes220.0ms

Accuracy

54.2% (4.8b remaining)

Error of 11.3b against oracle of 6.5b and baseline of 16.9b

bsearch161.0ms

Steps
ItersRangePoint
7
7.66782313461503e+136
1.0404348873744127e+139
8.918316156529291e+138
6
1.3310576141320075e+77
1.1338344132292419e+78
1.3588700991282888e+77
6
1.065914080559615e+54
8.678793905475049e+54
8.533939001167322e+54

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04974
14974

end0.0ms

sample668.0ms

Algorithm
intervals
Results
357.0ms8000×body80valid
124.0ms8000×pre80true