Details

Time bar (total: 26.5s)

sample28.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 50.4b

localize17.0ms

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)))
38.1b
(/ (* 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)))))
40.2b
(/ (* (* (- (* (+ (+ 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))))

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)))
88.0ms
(* (- (* (+ (+ 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)))))
104.0ms
(/ (* (* (- (* (+ (+ 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:
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)))
755.0ms
(/ (* 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)))))
1.8s
(/ (* (* (- (* (+ (+ 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))))

simplify48.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
07943237
150022435

prune459.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 43.2b

localize24.0ms

Local error

Found 4 expressions with local error:

7.8b
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
34.0b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
34.0b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
38.1b
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
47×add-exp-log add-cbrt-cube
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
19×cbrt-undiv times-frac div-exp
18×sqrt-prod
13×prod-exp cbrt-unprod
7×associate-/r*
6×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l/ associate-/l* add-log-exp
3×associate-*r/ associate-/r/
2×rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 div-sub clear-num distribute-rgt-neg-out flip-+ div-inv
1×frac-times unsub-neg associate-*l/
Counts
4 → 115
Calls
4 calls:
259.0ms
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
89.0ms
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))

series8.2s

Counts
4 → 12
Calls
4 calls:
7.1s
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
55.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
59.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
948.0ms
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))

simplify99.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07023117
139022417
250012384

prune453.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 43.2b

localize28.0ms

Local error

Found 4 expressions with local error:

34.0b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
34.0b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
38.1b
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
38.1b
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log add-cbrt-cube
36×cbrt-undiv div-exp
26×prod-exp cbrt-unprod
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity associate-*r/ sqrt-prod associate-/r/
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
2×frac-times rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ times-frac pow1/2 associate-*l/ clear-num associate-/r* flip-+ div-inv associate-/l*
Counts
4 → 110
Calls
4 calls:
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
88.0ms
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
88.0ms
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))

series2.0s

Counts
4 → 12
Calls
4 calls:
55.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
61.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
958.0ms
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
958.0ms
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))

simplify88.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
05243688
131082486
250022458

prune489.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 43.2b

localize31.0ms

Local error

Found 4 expressions with local error:

7.8b
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
34.0b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
34.0b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
38.1b
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))

rewrite351.0ms

Algorithm
rewrite-expression-head
Rules
47×add-exp-log add-cbrt-cube
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
19×cbrt-undiv times-frac div-exp
18×sqrt-prod
13×prod-exp cbrt-unprod
7×associate-/r*
6×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l/ associate-/l* add-log-exp
3×associate-*r/ associate-/r/
2×rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 div-sub clear-num distribute-rgt-neg-out flip-+ div-inv
1×frac-times unsub-neg associate-*l/
Counts
4 → 115
Calls
4 calls:
256.0ms
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
88.0ms
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))

series8.3s

Counts
4 → 12
Calls
4 calls:
7.3s
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
56.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
61.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
953.0ms
(/ (* i (+ (+ alpha beta) i)) (* (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))

simplify98.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07023115
139102417
250032384

prune488.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 43.2b

regimes182.0ms

Accuracy

42.4% (2.2b remaining)

Error of 46.9b against oracle of 44.7b and baseline of 48.6b

bsearch38.0ms

Steps
ItersRangePoint
5
8.681072426445148e+90
3.1860324300925774e+91
9.402817752821194e+90

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03859
14259
24359
34359

end0.0ms

sample656.0ms

Algorithm
intervals
Results
349.0ms8000×body80valid
123.0ms8000×pre80true