Details

Time bar (total: 18.6s)

sample76.0ms

Algorithm
intervals
Results
23.0ms199×body80valid
12.0ms256×pre80true
11.0ms20×body1280valid
8.0ms17×body640valid
6.0ms17×body320valid
1.0ms3×body160valid

simplify154.0ms

Calls
1 calls:
Slowest
154.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize37.0ms

Local error

Found 2 expressions with local error:

1.1b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×pow1 flip3-+ div-sub associate-/r/ flip-+ insert-posit16 add-log-exp associate-/l/
1×cbrt-undiv +-commutative clear-num frac-2neg flip3-- div-exp associate-+l- div-inv flip--
Calls
2 calls:
Slowest
35.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
12.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series79.0ms

Calls
2 calls:
Slowest
45.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
34.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify2.1s

Calls
37 calls:
Slowest
287.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
215.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
196.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
165.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
161.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))

prune510.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.9b

localize29.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (/ 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)

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×associate-/r*
5×associate-/l*
4×pow1 add-cbrt-cube add-exp-log associate-/r/ insert-posit16 add-log-exp associate-/l/
3×clear-num frac-2neg flip3-- div-inv flip--
2×flip3-+ frac-sub flip-+
1×sub-neg div-sub distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
54.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
13.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.0ms
(/ beta (+ (+ alpha beta) 2.0))
2.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series156.0ms

Calls
4 calls:
Slowest
54.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
51.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
28.0ms
(/ beta (+ (+ alpha beta) 2.0))
23.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify3.4s

Calls
30 calls:
Slowest
349.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
305.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
287.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
287.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
258.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune828.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.3b

localize11.0ms

Local error

Found 4 expressions with local error:

1.1b
(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.1b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×associate-/r*
5×pow1 log-prod
4×add-cbrt-cube add-exp-log associate-/r/ log-pow insert-posit16 add-log-exp
3×exp-prod
2×clear-num sub-neg frac-2neg flip3-+ exp-sum flip-+ div-inv
1×log-div flip3-- exp-diff rem-log-exp flip--
Calls
4 calls:
Slowest
19.0ms
(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
7.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.0ms
(/ beta (+ (+ alpha beta) 2.0))
2.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series171.0ms

Calls
4 calls:
Slowest
63.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
50.0ms
(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
35.0ms
(/ beta (+ (+ alpha beta) 2.0))
23.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify3.2s

Calls
32 calls:
Slowest
374.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
338.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
337.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
290.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
279.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune882.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.3b

localize38.0ms

Local error

Found 4 expressions with local error:

1.1b
(log (exp (- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)))
1.1b
(- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)
0.4b
(/ 1 (/ (+ (+ alpha beta) 2.0) alpha))
0.0b
(/ (+ (+ alpha beta) 2.0) alpha)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1
5×log-prod add-exp-log
4×associate-/r* add-cbrt-cube log-pow insert-posit16 add-log-exp
3×exp-prod div-inv associate-/l*
2×clear-num sub-neg frac-2neg exp-sum associate-/l/
1×log-div rec-exp flip3-+ flip3-- exp-diff rem-log-exp associate-/r/ flip-+ pow-flip flip-- inv-pow
Calls
4 calls:
Slowest
19.0ms
(log (exp (- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)))
18.0ms
(/ (+ (+ alpha beta) 2.0) alpha)
13.0ms
(- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)
6.0ms
(/ 1 (/ (+ (+ alpha beta) 2.0) alpha))

series161.0ms

Calls
4 calls:
Slowest
54.0ms
(- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)
45.0ms
(log (exp (- (/ 1 (/ (+ (+ alpha beta) 2.0) alpha)) 1.0)))
40.0ms
(/ 1 (/ (+ (+ alpha beta) 2.0) alpha))
22.0ms
(/ (+ (+ alpha beta) 2.0) alpha)

simplify3.0s

Calls
31 calls:
Slowest
483.0ms
(+ (pow (+ alpha beta) 3) (pow 2.0 3))
312.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
264.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))
263.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
262.0ms
(- (* 4.0 (/ 1 (pow alpha 2))) (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))))

prune856.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.3b

regimes165.0ms

Accuracy

75.4% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 15.5b

bsearch92.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
628.0ms5868×body80valid
423.0ms204×body160valid
400.0ms802×body1280valid
319.0ms8000×pre80true
306.0ms724×body640valid
131.0ms402×body320valid