Details

Time bar (total: 14.2s)

sample28.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 49.6b

localize20.0ms

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))) (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)))
36.7b
(/ (* 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)))))
39.7b
(/ (* (* (- (* (+ (+ 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))))

rewrite401.0ms

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:
119.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
89.0ms
(* (- (* (+ (+ 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)))))
101.0ms
(/ (* (* (- (* (+ (+ 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)))
268.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
759.0ms
(/ (* 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))))

simplify50.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
07943237
150022435

prune457.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 43.8b

localize24.0ms

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)))))
9.0b
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)
28.0b
(/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i))
32.7b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite803.0ms

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:
254.0ms
(/ (/ (+ (+ 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)))))
259.0ms
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)
166.0ms
(/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i))
2.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.5s

Counts
4 → 12
Calls
4 calls:
419.0ms
(/ (/ (+ (+ 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)))))
523.0ms
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)
484.0ms
(/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i))
113.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify478.0ms

Algorithm
egg-herbie
Counts
1195 → 1195
Iterations

Useful iterations: 1 (69.0ms)

IterNodesCost
0439047810
1500147622

prune3.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 34.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma 12.0 (* alpha i) (* 12.0 (* i beta)))
0.3b
(* 12.0 (* i beta))
32.2b
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))
32.7b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
24×times-frac
23×add-sqr-sqrt add-cube-cbrt
13×add-exp-log add-cbrt-cube
12×distribute-lft-out
9×pow1
8×associate-/l*
6×associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×cbrt-undiv frac-2neg div-exp clear-num div-inv associate-/l/
1×flip3-+ associate-*r* *-commutative flip-+ fma-udef
Counts
4 → 98
Calls
4 calls:
0.0ms
(fma 12.0 (* alpha i) (* 12.0 (* i beta)))
6.0ms
(* 12.0 (* i beta))
35.0ms
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))
2.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series261.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(fma 12.0 (* alpha i) (* 12.0 (* i beta)))
19.0ms
(* 12.0 (* i beta))
96.0ms
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))
94.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify48.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03471095
11277999
25001998

prune386.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 34.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma 12.0 (* alpha i) (* 12.0 (* i beta)))
0.2b
(/ (/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta))))) (/ 2.0 i))
0.3b
(* 12.0 (* i beta))
32.2b
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
652×times-frac
511×*-un-lft-identity
281×add-sqr-sqrt add-cube-cbrt
138×distribute-lft-out
36×div-inv
24×associate-/l*
23×add-exp-log add-cbrt-cube
16×associate-/r*
9×pow1 cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l/
2×frac-2neg clear-num
1×flip3-+ associate-*r* associate-/r/ *-commutative flip-+ fma-udef
Counts
4 → 370
Calls
4 calls:
0.0ms
(fma 12.0 (* alpha i) (* 12.0 (* i beta)))
46.0ms
(/ (/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta))))) (/ 2.0 i))
6.0ms
(* 12.0 (* i beta))
36.0ms
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(fma 12.0 (* alpha i) (* 12.0 (* i beta)))
110.0ms
(/ (/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta))))) (/ 2.0 i))
19.0ms
(* 12.0 (* i beta))
101.0ms
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))

simplify109.0ms

Algorithm
egg-herbie
Counts
382 → 382
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014437937
150027685

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.4b

regimes152.0ms

Accuracy

54.3% (3.1b remaining)

Error of 15.1b against oracle of 12.0b and baseline of 18.7b

bsearch35.0ms

Steps
ItersRangePoint
5
1.0898743726317437e+89
3.38348899766463e+89
1.1059547689128916e+89

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03421
13821
23921
33921

end0.0ms

sample653.0ms

Algorithm
intervals
Results
357.0ms8000×body80valid
115.0ms8000×pre80true