Details

Time bar (total: 9.7s)

sample27.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×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: 54.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.0b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
40.8b
(/ (* 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)))))
43.0b
(/ (* (* (- (* (+ (+ 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))))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log add-cbrt-cube
21×add-sqr-sqrt
17×cbrt-undiv div-exp
16×add-cube-cbrt *-un-lft-identity times-frac
15×prod-exp cbrt-unprod
13×pow1
10×associate-/r*
8×associate-*l/
7×flip3-+ associate-*l* flip-+
6×associate-*r*
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u div-inv associate-/l/ add-log-exp
3×swap-sqr
2×distribute-rgt-in flip3-- frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative flip-- fma-udef associate-/l* unswap-sqr
1×pow2 pow-plus associate-/r/ pow-sqr pow-prod-up difference-of-squares
Counts
4 → 135
Calls
4 calls:
72.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
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)))))
102.0ms
(/ (* (* (- (* (+ (+ 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))))

series2.9s

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
258.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
739.0ms
(/ (* 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
147 → 147
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09113106
150022350

prune467.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 35.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
4.4b
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
30.1b
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
36.2b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
77×times-frac
65×*-un-lft-identity
62×add-sqr-sqrt
61×add-exp-log add-cbrt-cube
50×add-cube-cbrt
29×cbrt-undiv div-exp
19×associate-*r* associate-/r*
13×associate-*l*
12×prod-exp cbrt-unprod
9×distribute-lft-out
7×div-inv associate-/l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×frac-2neg clear-num associate-/l/
2×frac-times associate-*r/ associate-*l/
1×pow-prod-down associate-/r/ *-commutative
Counts
4 → 179
Calls
4 calls:
51.0ms
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
24.0ms
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
2.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
2.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.3s

Counts
4 → 12
Calls
4 calls:
336.0ms
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
741.0ms
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
164.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
93.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify122.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08383659
148932981
250012981

prune577.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 35.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))
0.0b
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
3.5b
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ 2.0 i))
30.1b
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
68×times-frac
59×add-exp-log add-cbrt-cube
57×*-un-lft-identity
54×add-sqr-sqrt
42×add-cube-cbrt
28×cbrt-undiv div-exp
19×associate-*r*
16×associate-/r*
13×associate-*l*
12×prod-exp cbrt-unprod
9×distribute-lft-out
6×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp unswap-sqr
3×associate-/l/
2×frac-times frac-2neg associate-*r/ associate-*l/ clear-num
1×pow-prod-down associate-/r/ *-commutative fma-udef
Counts
4 → 160
Calls
4 calls:
0.0ms
(fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))
49.0ms
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
163.0ms
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ 2.0 i))
2.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))

series916.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))
334.0ms
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
329.0ms
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ 2.0 i))
158.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))

simplify47.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08702825
150012305

prune490.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 35.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))
9.5b
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (+ (+ alpha beta) i))
30.1b
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
36.2b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
41×*-un-lft-identity
38×times-frac
36×add-cube-cbrt
26×associate-*l*
18×add-exp-log add-cbrt-cube
8×pow1 associate-*r*
6×associate-/r* associate-/l*
4×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp unswap-sqr
3×distribute-lft-out
2×distribute-rgt-in frac-times frac-2neg distribute-lft-in flip3-+ associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative flip-+ fma-udef
Counts
4 → 136
Calls
4 calls:
8.0ms
(* (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))
45.0ms
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (+ (+ alpha beta) i))
2.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
2.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series528.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(* (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))) (fma i 2.0 (+ alpha beta)))
132.0ms
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (+ (+ alpha beta) i))
162.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
93.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify81.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06271795
131331597
250011595

prune479.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 35.7b

regimes136.0ms

Accuracy

35.2% (2.4b remaining)

Error of 38.5b against oracle of 36.1b and baseline of 39.8b

bsearch68.0ms

Steps
ItersRangePoint
9
1.5047751988170833e+141
2.1668113938075237e+147
1.7873990429441248e+144

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03835
13835

end0.0ms

sample655.0ms

Algorithm
intervals
Results
357.0ms8000×body80valid
121.0ms8000×pre80true