Details

Time bar (total: 12.9s)

sample28.0ms

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

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.6b

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)))
40.4b
(/ (* 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)))))
42.4b
(/ (* (* (- (* (+ (+ 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))))

rewrite78.0ms

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:
16.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
16.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
20.0ms
(/ (* 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)))))
21.0ms
(/ (* (* (- (* (+ (+ 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:
510.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
265.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
769.0ms
(/ (* 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))))

simplify48.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
07943237
150022435

prune465.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 47.2b

localize18.0ms

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)))
9.3b
(/ (* (- (* (+ (+ 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))))
35.3b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
40.4b
(/ (* 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)))))

rewrite68.0ms

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:
19.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
18.0ms
(/ (* (- (* (+ (+ 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))))
3.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
22.0ms
(/ (* 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))))
120.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
762.0ms
(/ (* 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)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09814480
150013634

prune617.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 36.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (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))))
40.2b
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
429×times-frac
311×*-un-lft-identity
267×add-sqr-sqrt
206×add-cube-cbrt
63×distribute-lft-out
61×associate-*r*
53×associate-*l*
52×add-exp-log add-cbrt-cube
26×associate-/l*
25×cbrt-undiv div-exp difference-of-squares
22×associate-/r*
19×div-inv
9×prod-exp cbrt-unprod unswap-sqr
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/l/
2×associate-/r/
1×frac-times flip3-- div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 371
Calls
4 calls:
11.0ms
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
18.0ms
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))))
70.0ms
(* (/ 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))))
17.0ms
(/ (- (* (+ (+ 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:
95.0ms
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
188.0ms
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i)))))
772.0ms
(* (/ 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))))
259.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify110.0ms

Algorithm
egg-herbie
Counts
383 → 383
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015188781
150018011

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
0.0b
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (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))))

rewrite67.0ms

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:
8.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
11.0ms
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
35.0ms
(* (/ i 4.0) (/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))))

series284.0ms

Counts
3 → 9
Calls
3 calls:
67.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
95.0ms
(/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
123.0ms
(* (/ i 4.0) (/ (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))))

simplify99.0ms

Algorithm
egg-herbie
Counts
250 → 250
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
08133279
138692950
250022934

prune655.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.3b

regimes212.0ms

Accuracy

65.3% (4.1b remaining)

Error of 10.9b against oracle of 6.8b and baseline of 18.6b

bsearch47.0ms

Steps
ItersRangePoint
6
4.080437872243752e+131
4.708326762322658e+132
4.0079005132304603e+132

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04340
14340

end0.0ms

sample666.0ms

Algorithm
intervals
Results
358.0ms8000×body80valid
125.0ms8000×pre80true