Details

Time bar (total: 3.4m)

sample85.0ms

Algorithm
intervals
Results
23.0ms197×body80valid
15.0ms24×body1280valid
13.0ms256×pre80true
8.0ms17×body640valid
4.0ms12×body320valid
2.0ms6×body160valid

simplify153.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
150.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize16.0ms

Local error

Found 2 expressions with local error:

2.1b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite202.0ms

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-cbrt-cube add-exp-log associate-/r/ add-log-exp
3×flip3-+ flip-+
2×expm1-log1p-u pow1 div-sub insert-posit16 log1p-expm1-u div-inv associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-- div-exp associate-+l- flip--
Counts
2 → 102
Calls
2 calls:
Slowest
149.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
50.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series192.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
109.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
83.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify5.0s

Counts
104 → 108
Calls
104 calls:
Slowest
312.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
256.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
236.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
232.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
230.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))

prune937.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.2b

localize33.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
215×*-un-lft-identity
118×add-sqr-sqrt
116×times-frac
93×add-cube-cbrt
63×prod-diff
60×distribute-lft-out
21×fma-neg
13×associate-/r* associate-/l* distribute-lft-out--
12×associate-/r/
10×add-cbrt-cube add-exp-log difference-of-squares
7×div-inv
6×flip3-+ flip-+ add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l/
3×cbrt-undiv clear-num frac-2neg flip3-- div-exp flip--
2×frac-sub
1×sub-neg diff-log div-sub
Counts
4 → 233
Calls
4 calls:
Slowest
997.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
186.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
46.0ms
(/ beta (+ (+ alpha beta) 2.0))
45.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series370.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
93.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
85.0ms
(/ beta (+ (+ alpha beta) 2.0))
79.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify20.9s

Counts
300 → 245
Calls
300 calls:
Slowest
499.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
361.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
349.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
334.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
317.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize59.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
0.1b
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.0b
(/ (- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
0.0b
(- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))

rewrite868.0ms

Algorithm
rewrite-expression-head
Rules
186×*-un-lft-identity
103×times-frac
72×distribute-lft-out
66×add-sqr-sqrt
54×add-cube-cbrt
51×associate-*r/
39×swap-sqr
38×flip3-+ flip-+
32×frac-sub
25×add-cbrt-cube add-exp-log
21×frac-times associate-*r* associate-*l*
18×associate-/l/
16×associate-/r/
15×flip3-- flip--
11×pow1 associate-*l/
8×add-log-exp
7×cbrt-undiv div-exp prod-exp cbrt-unprod
6×associate--r+
5×div-inv
4×distribute-rgt-in expm1-log1p-u sub-neg distribute-lft-in prod-diff insert-posit16 log1p-expm1-u unswap-sqr
3×associate-/l*
2×fma-neg diff-log associate--l+
1×pow2 clear-num associate-/r* frac-2neg pow-plus div-sub pow-prod-down pow-sqr *-commutative pow-prod-up difference-of-squares
Counts
4 → 224
Calls
4 calls:
Slowest
532.0ms
(/ (- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
177.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
115.0ms
(- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))
39.0ms
(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series742.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
334.0ms
(/ (- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
192.0ms
(- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))
127.0ms
(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
88.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))

simplify46.8s

Counts
247 → 236
Calls
247 calls:
Slowest
1.1s
(- (* (* beta (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))) (* (- (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))) (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (* (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0)) (- (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* 1.0 1.0) (* 1.0 1.0))))))
990.0ms
(- (* (* beta (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))) (* (- (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))) (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (* (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0)) (- (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* 1.0 1.0) (* 1.0 1.0))))))
909.0ms
(* (fma (- 1.0) 1.0 (* 1.0 1.0)) (+ (+ alpha beta) 2.0))
848.0ms
(- (* (* beta (+ (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))) (- (+ alpha beta) 2.0)) (* (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (- (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (* (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0)) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))))
836.0ms
(- (* (* beta (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))) (+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))) (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (* (+ (pow (+ alpha beta) 3) (pow 2.0 3)) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))))

prune3.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.8b

localize105.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (* 1.0 1.0) 3))
0.1b
(pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3)
0.1b
(* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))
0.1b
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))

rewrite502.0ms

Algorithm
rewrite-expression-head
Rules
204×*-un-lft-identity
159×add-cbrt-cube add-exp-log
130×pow1
100×times-frac
90×add-sqr-sqrt
73×prod-exp cbrt-unprod
72×distribute-lft-out
70×add-cube-cbrt
64×prod-diff
48×cbrt-undiv div-exp
40×swap-sqr
38×pow-prod-up
26×unpow-prod-down cube-prod sqr-pow
25×pow-prod-down
24×pow-sqr
22×associate-*r* associate-*l*
20×pow-plus
19×frac-times
18×cube-mult unpow3
16×difference-of-squares
15×pow2
13×associate-*l/ associate-*r/
8×fma-neg associate-/r/
6×pow-pow add-log-exp
5×pow-exp rem-cube-cbrt unswap-sqr
4×expm1-log1p-u flip3-+ flip-+ insert-posit16 log1p-expm1-u div-inv
3×cube-div pow-unpow
2×*-commutative
1×pow-to-exp difference-cubes sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 378
Calls
4 calls:
Slowest
266.0ms
(* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))
146.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
54.0ms
(pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3)
27.0ms
(- (pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (* 1.0 1.0) 3))

series464.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(- (pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (* 1.0 1.0) 3))
121.0ms
(pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3)
119.0ms
(* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))
80.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))

simplify1.9m

Counts
507 → 390
Calls
507 calls:
Slowest
969.0ms
(* (* (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))) (/ (* (* alpha alpha) alpha) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))) (* (/ (* (* alpha alpha) alpha) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0))) (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0)))))
918.0ms
(* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))
839.0ms
(* (* (/ (* (* alpha alpha) alpha) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0))) (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))) (/ (* (* alpha alpha) alpha) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))))
777.0ms
(* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0))
768.0ms
(* (* (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))) (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))) (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0)))))

prune7.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.8b

regimes201.0ms

Accuracy

64.1% (4.5b remaining)

Error of 7.6b against oracle of 3.1b and baseline of 15.6b

bsearch327.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
677.0ms5860×body80valid
498.0ms858×body1280valid
337.0ms8000×pre80true
250.0ms690×body640valid
130.0ms386×body320valid
37.0ms206×body160valid