Details

Time bar (total: 14.8s)

sample48.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
7.0ms256×pre80true

simplify41.0ms

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: 53.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
39.7b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
46.4b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite328.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×add-cube-cbrt *-un-lft-identity
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
18×associate-*l/
16×pow1
14×associate-/l* difference-of-squares
9×associate-/l/
7×div-inv
6×associate-*r*
5×associate-/r*
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u add-log-exp
3×swap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×pow2 flip3-- pow-plus pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 208
Calls
4 calls:
74.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
53.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
119.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
73.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.1s

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
104.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
746.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
169.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify79.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012775707
150025130

prune737.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 39.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.0b
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
0.1b
(* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) (* 2.0 i)))))
44.1b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) (* 2.0 i))))

rewrite600.0ms

Algorithm
rewrite-expression-head
Rules
82×add-exp-log add-cbrt-cube
55×*-un-lft-identity
33×times-frac prod-exp cbrt-unprod
27×add-sqr-sqrt add-cube-cbrt
26×cbrt-undiv div-exp
18×associate-/r/
16×distribute-lft-out
15×associate-*r*
13×frac-times
11×associate-/l*
9×pow1 associate-*l/
8×flip3-+ associate-/r* flip-+
7×associate-*r/
6×flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×frac-2neg pow-prod-down clear-num
2×associate-/l/
1×associate-*l* *-commutative
Counts
4 → 170
Calls
4 calls:
65.0ms
(/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
35.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
415.0ms
(* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) (* 2.0 i)))))
78.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) (* 2.0 i))))

series3.1s

Counts
4 → 12
Calls
4 calls:
147.0ms
(/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
67.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
2.6s
(* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) (* 2.0 i)))))
326.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) (* 2.0 i))))

simplify54.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09123974
150022939

prune622.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 38.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
0.2b
(* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
39.8b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
39.8b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite561.0ms

Algorithm
rewrite-expression-head
Rules
146×add-exp-log add-cbrt-cube
94×add-sqr-sqrt
69×prod-exp cbrt-unprod
66×times-frac
50×*-un-lft-identity
45×sqrt-prod
44×cbrt-undiv div-exp
43×associate-*l*
38×add-cube-cbrt
25×associate-*r*
20×pow1
18×frac-times
12×associate-*r/ associate-*l/ difference-of-squares
9×pow-prod-down unswap-sqr
6×distribute-lft-out--
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative div-inv
1×flip3-- flip3-+ flip-- flip-+
Counts
4 → 208
Calls
4 calls:
343.0ms
(* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
205.0ms
(* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series3.2s

Counts
4 → 12
Calls
4 calls:
2.8s
(* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
335.0ms
(* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
62.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
56.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify85.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
011766960
150014659

prune662.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 38.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b
(* (/ (* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))) (+ beta (+ alpha (fma i 2.0 (sqrt 1.0))))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
39.8b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
39.8b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite440.0ms

Algorithm
rewrite-expression-head
Rules
90×add-exp-log add-cbrt-cube
80×add-sqr-sqrt
61×*-un-lft-identity times-frac
44×sqrt-prod
42×add-cube-cbrt
36×prod-exp cbrt-unprod
33×cbrt-undiv div-exp
24×associate-*r*
14×difference-of-squares
11×associate-*l*
8×pow1
7×distribute-lft-out--
6×associate-/r* associate-/r/ associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-inv distribute-lft-out unswap-sqr
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×frac-times flip3-- frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative flip--
Counts
4 → 178
Calls
4 calls:
66.0ms
(/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
361.0ms
(* (/ (* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))) (+ beta (+ alpha (fma i 2.0 (sqrt 1.0))))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series919.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
617.0ms
(* (/ (* (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))) (+ beta (+ alpha (fma i 2.0 (sqrt 1.0))))) (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
60.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
55.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify69.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010625358
150014295

prune698.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 38.0b

regimes135.0ms

Accuracy

33.5% (2.6b remaining)

Error of 36.3b against oracle of 33.8b and baseline of 37.6b

bsearch75.0ms

Steps
ItersRangePoint
8
1.6208653379945526e+193
4.0896974484002643e+197
1.6468702855116692e+193

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04233
14233

end0.0ms

sample1.1s

Algorithm
intervals
Results
751.0ms8000×body80valid
196.0ms8000×pre80true