Details

Time bar (total: 7.0s)

sample26.0ms

Algorithm
intervals
Results
5.0ms176×body80valid
4.0ms33×body1280valid
3.0ms256×pre80true
3.0ms27×body640valid
1.0ms13×body320valid
0.0ms7×body160valid

simplify76.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0206
1346
2526
3736
41236
51846
62506
72876
83496
94376
105746
116546
127126
137856
1410756
1511506
1611936
1712136
1812216
1912216

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.0b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
104×*-un-lft-identity
50×times-frac
47×add-sqr-sqrt
34×distribute-lft-out
31×fma-def
25×add-cube-cbrt
11×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log associate-/r/ add-cbrt-cube add-log-exp
3×flip3-+ flip-+
2×pow1 expm1-log1p-u div-sub log1p-expm1-u div-inv associate-/l/
1×cbrt-undiv +-commutative associate-+l- flip3-- frac-2neg div-exp clear-num sum-log flip--
Counts
2 → 100
Calls
2 calls:
24.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
94.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series105.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
59.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0335555
11087529
25002525

prune223.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite473.0ms

Algorithm
rewrite-expression-head
Rules
512×*-un-lft-identity
328×add-sqr-sqrt
263×times-frac
252×prod-diff
213×add-cube-cbrt
150×distribute-lft-out
65×associate--r+
46×difference-of-squares
42×fma-neg
32×associate-/r/
25×distribute-lft-out--
16×flip3-+ flip-+ div-inv
11×add-log-exp
10×associate-/r*
8×add-exp-log add-cbrt-cube
6×associate-/l*
4×pow1 expm1-log1p-u diff-log log1p-expm1-u
3×sub-neg flip3-- flip--
2×cbrt-undiv frac-2neg div-exp clear-num frac-sub
1×associate--r-
Counts
4 → 413
Calls
4 calls:
293.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
17.0ms
(/ beta (+ (+ alpha beta) 2.0))
17.0ms
(/ alpha (+ (+ alpha beta) 2.0))
115.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series228.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
47.0ms
(/ beta (+ (+ alpha beta) 2.0))
43.0ms
(/ alpha (+ (+ alpha beta) 2.0))
77.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify128.0ms

Algorithm
egg-herbie
Counts
425 → 425
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
09778429
131436259
250026131

prune787.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0))
0.1b
(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b
(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
2.0b
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite426.0ms

Algorithm
rewrite-expression-head
Rules
853×*-un-lft-identity
576×prod-diff
466×add-sqr-sqrt
456×unpow-prod-down cube-prod
431×times-frac
418×add-cube-cbrt
255×distribute-lft-out
72×sqr-pow
62×cube-mult unpow3
58×associate-/r/
48×fma-neg
30×flip3-+ flip-+
29×div-inv
24×difference-of-squares
14×add-exp-log add-cbrt-cube
7×pow1
6×add-log-exp
5×associate-*r* distribute-lft-out--
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×cbrt-undiv pow-unpow div-exp associate-*l* associate-/l*
2×pow-exp prod-exp cbrt-unprod rem-cube-cbrt
1×difference-cubes cube-div distribute-rgt-in pow-to-exp sub-neg flip3-- pow-pow frac-2neg distribute-lft-in diff-log pow-prod-down clear-num associate-/r* *-commutative flip-- unswap-sqr
Counts
4 → 783
Calls
4 calls:
36.0ms
(* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0))
20.0ms
(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
13.0ms
(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
283.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series727.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0))
70.0ms
(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
399.0ms
(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
102.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify290.0ms

Algorithm
egg-herbie
Counts
795 → 795
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
0124514117
1480010117
2500110117

prune763.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0))
0.1b
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b
(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (- (* (+ (+ alpha beta) 2.0) (fma (/ alpha (+ (+ alpha beta) 2.0)) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (- (pow 1.0 3)))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
2.0b
(fma (/ alpha (+ (+ alpha beta) 2.0)) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (- (pow 1.0 3)))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
193×*-un-lft-identity
103×times-frac
75×distribute-lft-out
70×add-sqr-sqrt
56×add-cube-cbrt
39×swap-sqr
26×associate-*r*
24×associate-*l*
23×add-exp-log add-cbrt-cube
13×pow1
10×associate-/r/
6×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+
5×associate-*r/ div-inv unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/l*
2×pow-prod-down *-commutative
1×pow2 distribute-rgt-in frac-times frac-2neg distribute-lft-in pow-plus associate-*l/ clear-num associate-/r* pow-sqr pow-prod-up fma-udef
Counts
4 → 172
Calls
4 calls:
38.0ms
(* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0))
83.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
11.0ms
(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (- (* (+ (+ alpha beta) 2.0) (fma (/ alpha (+ (+ alpha beta) 2.0)) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (- (pow 1.0 3)))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
0.0ms
(fma (/ alpha (+ (+ alpha beta) 2.0)) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (- (pow 1.0 3)))

series842.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0))
57.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
472.0ms
(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (- (* (+ (+ alpha beta) 2.0) (fma (/ alpha (+ (+ alpha beta) 2.0)) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (- (pow 1.0 3)))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
155.0ms
(fma (/ alpha (+ (+ alpha beta) 2.0)) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (- (pow 1.0 3)))

simplify124.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
07563446
136302925
250012877

prune605.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.7b

regimes114.0ms

Accuracy

74.8% (3.2b remaining)

Error of 6.2b against oracle of 3.1b and baseline of 15.6b

bsearch61.0ms

Steps
ItersRangePoint
8
55.701487215568164
44831.15638062826
44214.99850275348

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05355
16355
26755
36755

end0.0ms

sample636.0ms

Algorithm
intervals
Results
160.0ms5858×body80valid
118.0ms870×body1280valid
100.0ms8000×pre80true
68.0ms671×body640valid
29.0ms375×body320valid
12.0ms226×body160valid