Details

Time bar (total: 36.5s)

sample29.0ms

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: 52.8b

localize21.0ms

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)))
40.6b
(/ (* 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)))))
42.0b
(/ (* (* (- (* (+ (+ 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))))

rewrite400.0ms

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:
118.0ms
(* (* (- (* (+ (+ 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)))))
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))))

series3.4s

Counts
4 → 12
Calls
4 calls:
500.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
263.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (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 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))))

simplify51.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07943237
150022435

prune484.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 45.8b

localize19.0ms

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)))
7.4b
(/ (* (- (* (+ (+ 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))))
36.3b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
40.6b
(/ (* 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)))))

rewrite178.0ms

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:
89.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
40.0ms
(/ (* (- (* (+ (+ 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))))
2.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
40.0ms
(/ (* 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)))))

series3.2s

Counts
4 → 12
Calls
4 calls:
267.0ms
(* (- (* (+ (+ 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 beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
125.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (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 beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))

simplify74.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09814480
150013634

prune600.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 37.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
0.1b
(/ (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
36.3b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
39.1b
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

rewrite831.0ms

Algorithm
rewrite-expression-head
Rules
15510×times-frac
8295×*-un-lft-identity
6251×add-sqr-sqrt
5570×add-cube-cbrt
1635×distribute-lft-out
681×difference-of-squares
524×div-inv
403×associate-/r/
136×flip3-+ flip-+
93×associate-/l*
65×associate-/r*
49×add-exp-log add-cbrt-cube
32×cbrt-undiv div-exp
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×associate-/l/
1×flip3-- div-sub flip--
Counts
4 → 3960
Calls
4 calls:
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
177.0ms
(/ (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
2.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
77.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

series1.2s

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
761.0ms
(/ (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
119.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
152.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

simplify2.0s

Algorithm
egg-herbie
Counts
3972 → 3972
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
05297194379

prune16.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 35.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))
0.0b
(* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))
0.1b
(/ (/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
36.3b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

rewrite670.0ms

Algorithm
rewrite-expression-head
Rules
1389×times-frac
615×*-un-lft-identity
581×add-sqr-sqrt
520×add-cube-cbrt
151×add-exp-log associate-/r/
113×add-cbrt-cube
99×div-exp
94×div-inv
69×cbrt-undiv
52×associate-/r*
46×frac-times associate-*r/ associate-*l/
42×distribute-lft-out
36×associate-*r*
24×prod-exp
22×difference-of-squares
19×associate-/l*
16×associate-*l* cbrt-unprod
11×sqrt-prod distribute-lft-out--
8×1-exp
6×pow1 unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/l/
2×flip3-+ flip-+
1×flip3-- div-sub pow-prod-down *-commutative flip--
Counts
4 → 721
Calls
4 calls:
166.0ms
(/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))
350.0ms
(* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))
97.0ms
(/ (/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
2.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

series2.8s

Counts
4 → 12
Calls
4 calls:
172.0ms
(/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))
241.0ms
(* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))
2.2s
(/ (/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
128.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

simplify523.0ms

Algorithm
egg-herbie
Counts
733 → 733
Iterations

Useful iterations: 1 (63.0ms)

IterNodesCost
0398626974
1500126191

prune2.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.6b

regimes134.0ms

Accuracy

44.8% (9.0b remaining)

Error of 10.9b against oracle of 2.0b and baseline of 18.2b

bsearch46.0ms

Steps
ItersRangePoint
5
6.117946709845316e+117
2.1025380462941185e+118
2.0448798463430746e+118

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04350
14350

end0.0ms

sample667.0ms

Algorithm
intervals
Results
360.0ms8000×body80valid
123.0ms8000×pre80true