Details

Time bar (total: 21.1s)

sample22.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify82.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite647.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
587×*-un-lft-identity
341×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
13×add-log-exp
10×cbrt-undiv div-exp associate-/r*
6×sum-log
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×fma-def frac-2neg clear-num
1×+-commutative associate-+l+
Counts
4 → 476
Calls
4 calls:
61.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
166.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
248.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
141.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
136.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
146.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify137.0ms

Algorithm
egg-herbie
Counts
488 → 488
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0151312983
1500212137

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
15.1b
(* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

rewrite778.0ms

Algorithm
rewrite-expression-head
Rules
934×times-frac
557×*-un-lft-identity
429×add-sqr-sqrt
415×add-cube-cbrt
166×associate-*l*
71×distribute-lft-out
59×associate-/l*
49×add-exp-log add-cbrt-cube
32×div-inv
24×cbrt-undiv div-exp
16×associate-/r/
11×flip3-- flip--
10×associate-/r*
8×prod-diff prod-exp cbrt-unprod associate-/l/
7×distribute-rgt-in distribute-lft-in
6×pow1
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u add-log-exp unswap-sqr
3×frac-2neg associate-*r* clear-num
2×sub-neg flip3-+ associate-*l/ associate--l+ flip-+
1×pow-prod-down *-commutative
Counts
4 → 522
Calls
4 calls:
171.0ms
(/ (* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
166.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
125.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
279.0ms
(* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

series548.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(/ (* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
157.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta)))
81.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
151.0ms
(* (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0))) (fma 1.0 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 1.0)))

simplify151.0ms

Algorithm
egg-herbie
Counts
534 → 534
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0205412731
1500212127

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite340.0ms

Algorithm
rewrite-expression-head
Rules
126×*-un-lft-identity
84×sqrt-prod
77×times-frac
62×add-sqr-sqrt
56×add-cube-cbrt
39×distribute-lft-out
13×associate-/r*
12×associate-/l*
10×sqrt-div
8×add-exp-log add-cbrt-cube
6×pow1 flip3-+ flip-+
4×expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
1×sqrt-undiv
Counts
4 → 177
Calls
4 calls:
93.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
107.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
66.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
67.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series416.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
104.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
45.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
51.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify69.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05272718
119402545
250012473

prune595.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.2b
(/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.9b
(/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
3.5b
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
14328×times-frac
10257×*-un-lft-identity
5414×add-sqr-sqrt add-cube-cbrt
3762×sqrt-prod
2770×distribute-lft-out
831×associate-/l*
246×associate-/r/
244×sqrt-div
161×div-inv
124×flip3-+ flip-+
34×add-exp-log add-cbrt-cube
20×cbrt-undiv div-exp
19×associate-/r*
5×associate-/l/
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
Counts
4 → 4451
Calls
4 calls:
327.0ms
(/ (/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
103.0ms
(/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
55.0ms
(/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
42.0ms
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series627.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(/ (/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
150.0ms
(/ (/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
191.0ms
(/ (/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (fma 1.0 2.0 (+ alpha beta)))
115.0ms
(/ (+ beta (+ alpha (fma alpha beta 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify1.8s

Algorithm
egg-herbie
Counts
4463 → 4463
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
05001173358

prune9.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.7b

regimes104.0ms

Accuracy

43.4% (1.5b remaining)

Error of 2.6b against oracle of 1.1b and baseline of 3.7b

bsearch165.0ms

Steps
ItersRangePoint
8
8.87684895593605e+202
1.112373966613911e+206
9.033818313421002e+202
7
3.0378422936948995e+125
1.866677400288751e+127
6.921240179554494e+125
5
9.28359310650799e+76
2.4961067465364225e+77
2.442757479764143e+77

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06479
16479

end0.0ms

sample507.0ms

Algorithm
intervals
Results
280.0ms8000×body80valid
94.0ms8000×pre80true