Details

Time bar (total: 12.8s)

sample27.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
3.0ms256×pre80true

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.5b

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)))
40.4b
(/ (* 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)))))
40.8b
(/ (* (* (- (* (+ (+ 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))))

rewrite828.0ms

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:
254.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
183.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
165.0ms
(/ (* 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)))))
221.0ms
(/ (* (* (- (* (+ (+ 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))))

series3.2s

Counts
4 → 12
Calls
4 calls:
444.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
244.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
735.0ms
(/ (* 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))))

simplify49.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
07943237
150022435

prune485.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 44.6b

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)))
7.2b
(/ (* (- (* (+ (+ 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))))
35.0b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
40.4b
(/ (* 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)))))

rewrite357.0ms

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:
183.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
86.0ms
(/ (* (- (* (+ (+ 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))))
5.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
77.0ms
(/ (* 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)))))

series3.0s

Counts
4 → 12
Calls
4 calls:
381.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
1.8s
(/ (* (- (* (+ (+ 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))))
111.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
742.0ms
(/ (* 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)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09814480
150013634

prune589.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 36.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
0.5b
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i)))
35.0b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
39.0b
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
262×times-frac
237×*-un-lft-identity
158×add-sqr-sqrt
132×add-cube-cbrt
63×distribute-lft-out
47×associate-/r*
26×difference-of-squares
18×add-exp-log add-cbrt-cube
13×associate-/l*
12×associate-/r/ div-inv
8×cbrt-undiv div-exp
5×flip3-+ flip-+
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×associate-/l/
1×flip3-- div-sub flip--
Counts
4 → 273
Calls
4 calls:
9.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
100.0ms
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i)))
5.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
147.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

series488.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
122.0ms
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i)))
107.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
133.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

simplify71.0ms

Algorithm
egg-herbie
Counts
285 → 285
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09775178
150014779

prune924.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 33.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.5b
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
34.1b
(/ (* i (+ (+ alpha beta) i)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
35.0b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
77×*-un-lft-identity
73×add-sqr-sqrt
65×add-cube-cbrt
26×associate-/r*
20×add-exp-log
18×add-cbrt-cube
10×associate-/l*
8×div-exp div-inv
7×cbrt-undiv
5×pow1 associate-/r/
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u distribute-lft-out add-log-exp difference-of-squares
2×flip3-+ associate-*r/ sqrt-prod flip-+ associate-/l/ distribute-lft-out--
1×rec-exp flip3-- pow-flip 1-exp prod-exp flip-- cbrt-unprod inv-pow
Counts
4 → 173
Calls
4 calls:
122.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
10.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
46.0ms
(/ (* i (+ (+ alpha beta) i)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
5.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
122.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
168.0ms
(/ (* i (+ (+ alpha beta) i)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0)))
109.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

simplify111.0ms

Algorithm
egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
07322496
138102275
250012251

prune611.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 33.5b

regimes168.0ms

Accuracy

38.7% (2.3b remaining)

Error of 36.4b against oracle of 34.2b and baseline of 37.9b

bsearch48.0ms

Steps
ItersRangePoint
6
5.239843939584887e+224
2.3275081152992616e+225
5.302202607558163e+224

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04645
14645

end0.0ms

sample694.0ms

Algorithm
intervals
Results
350.0ms8000×body80valid
108.0ms8000×pre80true