Details

Time bar (total: 10.6s)

sample22.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
3.0ms256×pre80true

simplify86.0ms

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: 2.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
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))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite621.0ms

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
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 expm1-log1p-u fma-def log1p-expm1-u associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 475
Calls
4 calls:
15.0ms
(+ (+ alpha beta) (* beta alpha))
170.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
254.0ms
(/ (/ (/ (+ (+ (+ 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))
144.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series373.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (+ alpha beta) (* beta alpha))
137.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
148.0ms
(/ (/ (/ (+ (+ (+ 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))
73.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify155.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0153413079
1500112129

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.0b
(* (/ (/ (/ (+ (+ (+ 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)))
2.7b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
964×times-frac
575×*-un-lft-identity
459×add-sqr-sqrt
427×add-cube-cbrt
166×associate-*l*
74×distribute-lft-out
61×associate-/l*
49×add-exp-log add-cbrt-cube
33×div-inv
24×cbrt-undiv div-exp
18×associate-*r* associate-/r/
10×associate-/r*
8×flip3-- prod-exp flip-- cbrt-unprod unswap-sqr
6×pow1
5×associate-/l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ clear-num flip-+
1×frac-times div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 533
Calls
4 calls:
100.0ms
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
568.0ms
(* (/ (/ (/ (+ (+ (+ 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)))
174.0ms
(/ (/ (/ (+ (+ (+ 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)))
130.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
153.0ms
(* (/ (/ (/ (+ (+ (+ 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)))
156.0ms
(/ (/ (/ (+ (+ (+ 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)))
84.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify172.0ms

Algorithm
egg-herbie
Counts
545 → 545
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0232013529
1500112956

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ beta (+ alpha (fma 1.0 2.0 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))))
2.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite343.0ms

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:
88.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
111.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
69.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
68.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series420.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
103.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
50.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
47.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify78.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05412716
119602543
250012472

prune594.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
0.7b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
2.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite498.0ms

Algorithm
rewrite-expression-head
Rules
1740×sqrt-prod
1314×times-frac
864×*-un-lft-identity
666×add-sqr-sqrt
660×add-cube-cbrt
102×distribute-lft-out
76×associate-/l*
54×sqrt-div
24×associate-/r/
18×associate-/r*
15×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×sqrt-undiv associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num hypot-def
Counts
4 → 855
Calls
4 calls:
166.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
114.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
69.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
70.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series371.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
158.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
48.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
55.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify261.0ms

Algorithm
egg-herbie
Counts
867 → 867
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0157726396
1500124056

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.8b

regimes86.0ms

Accuracy

52.6% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.6b

bsearch56.0ms

Steps
ItersRangePoint
7
2.928539913264705e+160
1.678957329733711e+162
1.4537693536698273e+162

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03232
13232

end0.0ms

sample548.0ms

Algorithm
intervals
Results
300.0ms8000×body80valid
104.0ms8000×pre80true