Details

Time bar (total: 14.4s)

sample29.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
4.0ms256×pre80true

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune10.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 50.9b

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)))
39.4b
(/ (* (* (- (* (+ (+ 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
(/ (* 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)))))

rewrite415.0ms

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:
120.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
92.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
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))))
93.0ms
(/ (* 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)))))

series3.5s

Counts
4 → 12
Calls
4 calls:
514.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
275.0ms
(* (- (* (+ (+ 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 i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
771.0ms
(/ (* 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)))))

simplify54.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07943237
150022435

prune482.0ms

Filtered
134 candidates to 97 candidates (72.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 46.7b

localize32.0ms

Local error

Found 4 expressions with local error:

5.8b
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
35.0b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
35.0b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
44.7b
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

rewrite518.0ms

Algorithm
rewrite-expression-head
Rules
211×times-frac
208×*-un-lft-identity
115×associate-*r*
113×add-sqr-sqrt
98×add-cube-cbrt
66×distribute-lft-out
52×sqrt-prod
45×add-exp-log add-cbrt-cube
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
9×associate-*l*
8×pow1 div-inv
5×associate-/r/
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 215
Calls
4 calls:
364.0ms
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (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))))
137.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
61.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
57.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
500.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

simplify80.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
011075952
150025104

prune712.0ms

Filtered
227 candidates to 126 candidates (55.5%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 46.7b

localize35.0ms

Local error

Found 4 expressions with local error:

5.8b
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
35.0b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
35.0b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
44.7b
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

rewrite670.0ms

Algorithm
rewrite-expression-head
Rules
211×times-frac
208×*-un-lft-identity
115×associate-*r*
113×add-sqr-sqrt
98×add-cube-cbrt
66×distribute-lft-out
52×sqrt-prod
45×add-exp-log add-cbrt-cube
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
9×associate-*l*
8×pow1 div-inv
5×associate-/r/
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 215
Calls
4 calls:
372.0ms
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (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))))
281.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

series1.6s

Counts
4 → 12
Calls
4 calls:
1.0s
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
60.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
60.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
495.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

simplify84.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
011075952
150025104

prune805.0ms

Filtered
227 candidates to 127 candidates (55.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 46.7b

localize35.0ms

Local error

Found 4 expressions with local error:

35.0b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
44.7b
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
44.7b
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
44.7b
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

rewrite415.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×times-frac associate-/r*
6×cbrt-undiv div-exp associate-/r/
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ prod-exp clear-num sqrt-prod cbrt-unprod flip-+ div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 90
Calls
4 calls:
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
137.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
137.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
137.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

series1.6s

Counts
4 → 12
Calls
4 calls:
62.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
500.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
553.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
498.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

simplify54.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03071819
113971523
250021469

prune534.0ms

Filtered
102 candidates to 80 candidates (78.4%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 46.7b

regimes194.0ms

Accuracy

35% (3.0b remaining)

Error of 47.5b against oracle of 44.5b and baseline of 49.1b

bsearch28.0ms

Steps
ItersRangePoint
3
4.932253681127649e+104
5.938859855373114e+104
4.9887567759118044e+104

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04030
14430
24530
34530

end0.0ms

sample766.0ms

Algorithm
intervals
Results
423.0ms8000×body80valid
142.0ms8000×pre80true