Details

Time bar (total: 1.5m)

sample44.0ms

Algorithm
intervals
Results
11.0ms192×body80valid
7.0ms256×pre80true
6.0ms20×body1280valid
4.0ms19×body640valid
3.0ms18×body320valid
1.0ms7×body160valid

simplify105.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
105.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize25.0ms

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))

rewrite212.0ms

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
147.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
61.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series156.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
86.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
70.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify4.8s

Counts
104 → 108
Calls
104 calls:
Slowest
464.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
275.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
235.0ms
(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
221.0ms
(/ (- beta alpha) (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0)))
213.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.4b

localize26.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 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
916.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
203.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
41.0ms
(/ alpha (+ (+ alpha beta) 2.0))
23.0ms
(/ beta (+ (+ alpha beta) 2.0))

series316.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
86.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
72.0ms
(/ alpha (+ (+ alpha beta) 2.0))
60.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify20.3s

Counts
300 → 245
Calls
300 calls:
Slowest
520.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
381.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
364.0ms
(- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))
343.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
294.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.0b

localize56.0ms

Local error

Found 4 expressions with local error:

7.0b
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
2.3b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.6b
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
0.0b
(/ beta (+ (+ alpha beta) 2.0))

rewrite828.0ms

Algorithm
rewrite-expression-head
Rules
206×*-un-lft-identity
129×add-sqr-sqrt
124×times-frac
94×add-cube-cbrt
63×prod-diff
50×log-prod
48×distribute-lft-out
25×exp-sum
21×fma-neg
19×distribute-lft-out--
14×difference-of-squares
10×associate-/r/
9×add-exp-log
7×div-inv
6×pow1 add-cbrt-cube add-log-exp
5×associate-/r* flip3-+ flip-+
4×expm1-log1p-u exp-prod insert-posit16 log1p-expm1-u
3×associate-/l*
2×log-div div-exp rem-log-exp log-pow
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-- exp-diff diff-log flip-- rem-exp-log
Counts
4 → 222
Calls
4 calls:
Slowest
293.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
270.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
211.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
45.0ms
(/ beta (+ (+ alpha beta) 2.0))

series399.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
113.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
81.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
52.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify20.5s

Counts
263 → 234
Calls
263 calls:
Slowest
783.0ms
(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)))))
350.0ms
(exp (log (/ (* (cbrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (cbrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (cbrt 2.0) (cbrt 2.0)))))
302.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
295.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* 1.0 1)))
290.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.0b

localize61.0ms

Local error

Found 4 expressions with local error:

26.6b
(cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0))))
7.0b
(log (/ (- (cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
2.3b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.6b
(exp (log (/ (- (cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))

rewrite712.0ms

Algorithm
rewrite-expression-head
Rules
174×*-un-lft-identity
99×add-sqr-sqrt
97×times-frac
82×add-cube-cbrt
63×prod-diff
44×log-prod
36×distribute-lft-out
22×exp-sum
21×fma-neg
19×distribute-lft-out--
8×associate-/r/ difference-of-squares
7×cbrt-div add-exp-log
6×pow1 div-inv add-log-exp
5×frac-times associate-*l/
4×expm1-log1p-u exp-prod flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u
3×associate-*r/
2×log-div rem-log-exp log-pow
1×cbrt-prod sub-neg flip3-- exp-diff pow1/3 diff-log div-exp pow3 rem-cbrt-cube flip-- rem-exp-log
Counts
4 → 196
Calls
4 calls:
Slowest
222.0ms
(log (/ (- (cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
186.0ms
(exp (log (/ (- (cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
171.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
126.0ms
(cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
999.0ms
(log (/ (- (cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
161.0ms
(exp (log (/ (- (cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
117.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
109.0ms
(cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0))))

simplify25.8s

Counts
224 → 208
Calls
224 calls:
Slowest
589.0ms
(- (* 0.5 alpha) (+ 1.0 (* 0.25 (pow alpha 2))))
549.0ms
(cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) beta))
460.0ms
(cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) beta) (/ beta (+ (+ alpha beta) 2.0))))
438.0ms
(- (+ (* 1.0 (/ (cbrt -1) beta)) 0.5) (+ (* 2.0 (/ (cbrt -1) (pow beta 2))) (* 0.5 (cbrt -1))))
423.0ms
(log (/ (* (cbrt (- (cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (cbrt (- (cbrt (* (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (/ beta (+ (+ alpha beta) 2.0)))) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (cbrt 2.0) (cbrt 2.0))))

prune2.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.0b

regimes216.0ms

Accuracy

73.7% (3.4b remaining)

Error of 6.5b against oracle of 3.1b and baseline of 16.0b

bsearch86.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
612.0ms5828×body80valid
510.0ms855×body1280valid
341.0ms8000×pre80true
321.0ms724×body640valid
102.0ms380×body320valid
38.0ms213×body160valid