Details

Time bar (total: 24.6s)

sample36.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
5.0ms256×pre80true

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.1b

localize21.0ms

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)))
0.0b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
38.8b
(/ (* 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)))))
40.0b
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite389.0ms

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:
113.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
87.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
85.0ms
(/ (* 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)))))
100.0ms
(/ (* (* (- (* (+ (+ 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:
500.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
269.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
761.0ms
(/ (* 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

prune485.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 44.9b

localize23.0ms

Local error

Found 4 expressions with local error:

8.3b
(/ (+ (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))))
38.8b
(/ (* 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:
257.0ms
(/ (+ (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)))))
55.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
61.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
963.0ms
(/ (* 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)))))))

simplify103.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07023115
139102417
250032384

prune453.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 44.9b

localize28.0ms

Local error

Found 4 expressions with local error:

8.3b
(/ (+ (- (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))))
38.8b
(/ (- (* 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))))))

rewrite655.0ms

Algorithm
rewrite-expression-head
Rules
120×times-frac
55×add-sqr-sqrt
53×add-cube-cbrt *-un-lft-identity
39×sqrt-prod
20×add-exp-log add-cbrt-cube
16×associate-/r*
11×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in
9×cbrt-undiv div-exp div-inv associate-/l*
6×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
2×neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 div-sub associate-*r/ prod-exp clear-num cbrt-unprod flip-+ distribute-neg-frac
1×associate-+l- distribute-frac-neg associate-/r/
Counts
4 → 175
Calls
4 calls:
509.0ms
(/ (+ (- (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))))
138.0ms
(/ (- (* 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))))))

series5.4s

Counts
4 → 12
Calls
4 calls:
4.0s
(/ (+ (- (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))))
62.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.2s
(/ (- (* 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))))))

simplify137.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
09065461
145874995
250014988

prune846.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 44.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
8.2b
(/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
34.2b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
39.6b
(* (/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))

rewrite511.0ms

Algorithm
rewrite-expression-head
Rules
256×*-un-lft-identity
247×times-frac
130×add-sqr-sqrt
121×add-cube-cbrt
81×distribute-lft-out
70×associate-*r*
66×add-exp-log
52×add-cbrt-cube
28×div-exp
21×cbrt-undiv
20×prod-exp
19×associate-/r*
16×div-inv
13×cbrt-unprod
9×associate-*l* associate-/l*
6×pow1 associate-/r/
4×expm1-log1p-u 1-exp log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ clear-num flip-+ unswap-sqr
2×associate-/l/
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 274
Calls
4 calls:
37.0ms
(/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
130.0ms
(/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
2.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
328.0ms
(* (/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
281.0ms
(/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
94.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
946.0ms
(* (/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))

simplify76.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011065824
150024977

prune913.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 44.9b

regimes212.0ms

Accuracy

41.3% (2.6b remaining)

Error of 47.4b against oracle of 44.7b and baseline of 49.2b

bsearch58.0ms

Steps
ItersRangePoint
6
5.136045203612384e+98
2.8306216217683757e+99
6.558263200049806e+98

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05252
16052
26452
36452

end0.0ms

sample701.0ms

Algorithm
intervals
Results
370.0ms8000×body80valid
135.0ms8000×pre80true