Details

Time bar (total: 15.7s)

sample31.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
6.0ms256×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: 52.3b

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)))
0.0b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
41.5b
(/ (* (* (- (* (+ (+ 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))))
41.9b
(/ (* 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)))))

rewrite860.0ms

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:
265.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
190.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
227.0ms
(/ (* (* (- (* (+ (+ 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))))
174.0ms
(/ (* 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)))))

series3.6s

Counts
4 → 12
Calls
4 calls:
508.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
266.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
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))))
852.0ms
(/ (* 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)))))

simplify47.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07943237
150022435

prune448.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 47.0b

localize26.0ms

Local error

Found 4 expressions with local error:

5.4b
(/ (/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
7.7b
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)
32.8b
(/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i))
36.7b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
3226×times-frac
2239×*-un-lft-identity
1259×add-sqr-sqrt add-cube-cbrt
588×distribute-lft-out
165×div-inv
81×associate-/l*
34×add-exp-log add-cbrt-cube
32×associate-/r*
20×cbrt-undiv div-exp
16×associate-/r/
5×associate-/l/
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×flip3-+ div-sub distribute-rgt-neg-out flip-+
1×unsub-neg
Counts
4 → 1183
Calls
4 calls:
452.0ms
(/ (/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
636.0ms
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)
310.0ms
(/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i))
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.6s

Counts
4 → 12
Calls
4 calls:
452.0ms
(/ (/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
516.0ms
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)
512.0ms
(/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i))
98.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify455.0ms

Algorithm
egg-herbie
Counts
1195 → 1195
Iterations

Useful iterations: 1 (70.0ms)

IterNodesCost
0439047810
1500147622

prune3.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 39.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta))))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
0.2b
(* 12.0 (* i beta))
35.7b
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))
36.7b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
661×times-frac
519×*-un-lft-identity
289×add-sqr-sqrt add-cube-cbrt
138×distribute-lft-out
37×div-inv
27×associate-/l*
25×add-exp-log add-cbrt-cube
19×associate-/r*
10×cbrt-undiv div-exp
9×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*l* pow-prod-down prod-exp clear-num cbrt-unprod associate-/l/
1×flip3-+ associate-*r* associate-/r/ *-commutative flip-+
Counts
4 → 389
Calls
4 calls:
81.0ms
(/ (/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta))))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
17.0ms
(* 12.0 (* i beta))
70.0ms
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series483.0ms

Counts
4 → 12
Calls
4 calls:
254.0ms
(/ (/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta))))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
21.0ms
(* 12.0 (* i beta))
107.0ms
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))
101.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify133.0ms

Algorithm
egg-herbie
Counts
401 → 401
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0144911450
1500111125

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.7b

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify3.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 12.7b

regimes142.0ms

Accuracy

68.9% (2.1b remaining)

Error of 13.8b against oracle of 11.7b and baseline of 18.5b

bsearch98.0ms

Steps
ItersRangePoint
5
3.5264299813103045e+124
1.4001323433063586e+125
1.373853224073776e+125
8
3.373949676493062e+62
4.212139861465462e+66
1.2003341027076766e+64

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05232
15632
25732
35732

end0.0ms

sample709.0ms

Algorithm
intervals
Results
344.0ms8000×body80valid
117.0ms8000×pre80true