Details

Time bar (total: 1.4m)

sample50.0ms

Algorithm
intervals
Results
11.0ms175×body80valid
10.0ms32×body1280valid
7.0ms256×pre80true
7.0ms23×body640valid
4.0ms20×body320valid
1.0ms6×body160valid

simplify129.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
129.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize41.0ms

Local error

Found 2 expressions with local error:

2.2b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite234.0ms

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
170.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
60.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series169.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
105.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
63.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify5.0s

Counts
104 → 108
Calls
104 calls:
Slowest
272.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
261.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
260.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
233.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))
227.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.4b

localize38.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))

rewrite1.2s

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
888.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
191.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
38.0ms
(/ alpha (+ (+ alpha beta) 2.0))
30.0ms
(/ beta (+ (+ alpha beta) 2.0))

series376.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
110.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
81.0ms
(/ beta (+ (+ alpha beta) 2.0))
63.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify21.3s

Counts
300 → 245
Calls
300 calls:
Slowest
561.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
471.0ms
(/ (cbrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 2.0)
358.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
340.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
338.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize62.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (/ 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))

rewrite254.0ms

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--
Counts
4 → 156
Calls
4 calls:
Slowest
222.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.0ms
(cbrt (+ (+ alpha beta) 2.0))
10.0ms
(cbrt (+ (+ alpha beta) 2.0))
9.0ms
(cbrt (+ (+ alpha beta) 2.0))

series591.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(cbrt (+ (+ alpha beta) 2.0))
150.0ms
(cbrt (+ (+ alpha beta) 2.0))
145.0ms
(cbrt (+ (+ alpha beta) 2.0))
133.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify14.9s

Counts
184 → 168
Calls
184 calls:
Slowest
321.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
314.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))
311.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
304.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
296.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize46.0ms

Local error

Found 4 expressions with local error:

9.3b
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
2.2b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
208×*-un-lft-identity
151×add-sqr-sqrt
134×times-frac
96×add-cube-cbrt
63×prod-diff
50×log-prod
36×distribute-lft-out
31×distribute-lft-out--
25×exp-sum
22×difference-of-squares
21×fma-neg
9×add-exp-log
8×associate-/r/
7×div-inv associate-/l*
6×pow1 add-cbrt-cube add-log-exp
4×expm1-log1p-u exp-prod flip3-+ flip-+ insert-posit16 log1p-expm1-u associate-/l/
3×associate-/r* flip3-- flip--
2×log-div div-exp rem-log-exp log-pow frac-sub
1×cbrt-undiv clear-num sub-neg frac-2neg exp-diff diff-log div-sub rem-exp-log
Counts
4 → 233
Calls
4 calls:
Slowest
1.1s
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
284.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
230.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
167.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series546.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
202.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
124.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
123.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
97.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))

simplify25.1s

Counts
277 → 245
Calls
277 calls:
Slowest
636.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ (cbrt alpha) (cbrt (+ (+ alpha beta) 2.0))) (- (* 1.0 1)))
525.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
351.0ms
(exp (* (cbrt (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))) (cbrt (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))))
313.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
309.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

regimes318.0ms

Accuracy

98.4% (0.2b remaining)

Error of 3.5b against oracle of 3.3b and baseline of 15.9b

bsearch11.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
879.0ms824×body1280valid
644.0ms5814×body80valid
375.0ms8000×pre80true
292.0ms756×body640valid
112.0ms430×body320valid
56.0ms176×body160valid