Details

Time bar (total: 3.0m)

sample82.0ms

Algorithm
intervals
Results
22.0ms256×pre80true
19.0ms183×body80valid
15.0ms30×body1280valid
11.0ms26×body640valid
3.0ms9×body320valid
2.0ms8×body160valid

simplify141.0ms

Calls
1 calls:
Slowest
141.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize19.0ms

Local error

Found 2 expressions with local error:

1.9b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite191.0ms

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--
Calls
2 calls:
Slowest
125.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
63.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series183.0ms

Calls
2 calls:
Slowest
101.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
83.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify4.8s

Calls
104 calls:
Slowest
277.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
273.0ms
(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
268.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
254.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
239.0ms
(/ (- beta alpha) (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0)))

prune917.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.4b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
635×*-un-lft-identity
406×add-sqr-sqrt
318×times-frac
315×prod-diff
271×add-cube-cbrt
177×distribute-lft-out
130×associate--r+
66×div-sub
54×difference-of-squares
44×frac-sub
42×fma-neg
37×distribute-lft-out--
36×associate-/r/
28×associate-/r*
25×flip3-- flip--
24×associate-/l/
22×associate-/l*
19×div-inv
18×flip3-+ flip-+
11×add-log-exp
8×add-cbrt-cube add-exp-log
6×clear-num frac-2neg
4×expm1-log1p-u pow1 sub-neg diff-log insert-posit16 log1p-expm1-u
2×cbrt-undiv div-exp
1×associate--r-
Calls
4 calls:
Slowest
1.3s
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
610.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
235.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
27.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series386.0ms

Calls
4 calls:
Slowest
112.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
105.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
90.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
79.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify1.8m

Calls
732 calls:
Slowest
707.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (fma (/ (* (cbrt alpha) (cbrt alpha)) (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ (cbrt alpha) (cbrt (+ (+ alpha beta) 2.0))) (- (* (sqrt 1.0) (sqrt 1.0))))) 2.0)
579.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
552.0ms
(fma (/ (* (cbrt beta) (cbrt beta)) 1) (/ (cbrt beta) (+ (+ alpha beta) 2.0)) (- (* (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))))
550.0ms
(fma (/ 1 1) (/ beta (+ (+ alpha beta) 2.0)) (- (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 1)))
522.0ms
(fma (/ (* (cbrt beta) (cbrt beta)) (sqrt (+ (+ alpha beta) 2.0))) (/ (cbrt beta) (sqrt (+ (+ alpha beta) 2.0))) (- (* (sqrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (sqrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))

prune5.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize33.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(cbrt (+ (+ alpha beta) 2.0))
0.7b
(cbrt (+ (+ alpha beta) 2.0))
0.7b
(cbrt (+ (+ alpha beta) 2.0))

rewrite277.0ms

Algorithm
rewrite-expression-head
Rules
141×*-un-lft-identity
69×add-sqr-sqrt
64×add-cube-cbrt
63×prod-diff
61×times-frac
45×distribute-lft-out
21×fma-neg
15×cbrt-prod
8×associate-/r/
7×flip3-+ flip-+
6×cbrt-div add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u div-inv
3×pow1/3
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Calls
4 calls:
Slowest
213.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
20.0ms
(cbrt (+ (+ alpha beta) 2.0))
20.0ms
(cbrt (+ (+ alpha beta) 2.0))
19.0ms
(cbrt (+ (+ alpha beta) 2.0))

series535.0ms

Calls
4 calls:
Slowest
146.0ms
(cbrt (+ (+ alpha beta) 2.0))
146.0ms
(cbrt (+ (+ alpha beta) 2.0))
131.0ms
(cbrt (+ (+ alpha beta) 2.0))
111.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify15.3s

Calls
184 calls:
Slowest
644.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))
355.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
286.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
286.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* 1.0 1)))
282.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

localize17.0ms

Local error

Found 4 expressions with local error:

1.9b
(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(cbrt (+ (+ alpha beta) 2.0))
0.7b
(cbrt (+ (+ alpha beta) 2.0))

rewrite562.0ms

Algorithm
rewrite-expression-head
Rules
232×*-un-lft-identity
126×prod-diff
123×add-sqr-sqrt
113×add-cube-cbrt
107×times-frac
69×distribute-lft-out
68×log-prod
65×exp-sum
21×fma-neg
14×associate-/r/
10×cbrt-prod
9×flip3-+ flip-+
7×log-pow div-inv
6×exp-prod add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u cbrt-div add-cbrt-cube insert-posit16 log1p-expm1-u difference-of-squares
2×sub-neg pow1/3 rem-log-exp distribute-lft-out--
1×log-div flip3-- exp-diff diff-log flip--
Calls
4 calls:
Slowest
355.0ms
(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
180.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.0ms
(cbrt (+ (+ alpha beta) 2.0))
10.0ms
(cbrt (+ (+ alpha beta) 2.0))

series475.0ms

Calls
4 calls:
Slowest
145.0ms
(cbrt (+ (+ alpha beta) 2.0))
112.0ms
(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
110.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
107.0ms
(cbrt (+ (+ alpha beta) 2.0))

simplify31.7s

Calls
254 calls:
Slowest
516.0ms
(log (exp (fma (/ (* (cbrt alpha) (cbrt alpha)) (sqrt (+ (+ alpha beta) 2.0))) (/ (cbrt alpha) (sqrt (+ (+ alpha beta) 2.0))) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))))
515.0ms
(log (exp (fma (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))))
476.0ms
(log (exp (fma (/ (sqrt alpha) 1) (/ (sqrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))))
474.0ms
(log (exp (fma (* (cbrt (/ alpha (+ (+ alpha beta) 2.0))) (cbrt (/ alpha (+ (+ alpha beta) 2.0)))) (cbrt (/ alpha (+ (+ alpha beta) 2.0))) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))))
464.0ms
(fma (* (cbrt (/ alpha (+ (+ alpha beta) 2.0))) (cbrt (/ alpha (+ (+ alpha beta) 2.0)))) (cbrt (/ alpha (+ (+ alpha beta) 2.0))) (- (* (sqrt 1.0) (sqrt 1.0))))

prune3.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.7b

regimes220.0ms

Accuracy

75.5% (3.1b remaining)

Error of 6.0b against oracle of 2.9b and baseline of 15.6b

bsearch83.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.0s5851×body80valid
402.0ms899×body1280valid
312.0ms8000×pre80true
217.0ms678×body640valid
143.0ms367×body320valid
55.0ms205×body160valid