Details

Time bar (total: 1.3m)

sample58.0ms

Algorithm
intervals
Results
15.0ms185×body80valid
11.0ms29×body1280valid
9.0ms256×pre80true
8.0ms24×body640valid
4.0ms15×body320valid
0.0ms3×body160valid

simplify139.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
138.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize39.0ms

Local error

Found 2 expressions with local error:

1.4b
(+ (/ (- 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
192.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
40.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series169.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
91.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
78.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify5.3s

Counts
104 → 108
Calls
104 calls:
Slowest
623.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
267.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
259.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
256.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
254.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.0b

localize34.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (/ 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
950.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
200.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
44.0ms
(/ alpha (+ (+ alpha beta) 2.0))
44.0ms
(/ beta (+ (+ alpha beta) 2.0))

series364.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
102.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
71.0ms
(/ alpha (+ (+ alpha beta) 2.0))
58.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify20.4s

Counts
300 → 245
Calls
300 calls:
Slowest
518.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
334.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
329.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
301.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
294.0ms
(- (* 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))))

prune2.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize54.0ms

Local error

Found 4 expressions with local error:

6.3b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.3b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.3b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
1.4b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite268.0ms

Algorithm
rewrite-expression-head
Rules
195×*-un-lft-identity
106×times-frac
93×add-sqr-sqrt
88×add-cube-cbrt
63×cbrt-prod prod-diff distribute-lft-out
21×fma-neg
14×associate-/r/
7×flip3-+ flip-+ div-inv
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cbrt-div pow1/3
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 201
Calls
4 calls:
Slowest
190.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
29.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
21.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
21.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series716.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
213.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
206.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
183.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
113.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify15.9s

Counts
229 → 213
Calls
229 calls:
Slowest
473.0ms
(fma (/ alpha (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0))) (- (+ alpha beta) 2.0) (- (* 1.0 1)))
336.0ms
(- (exp (* 1/3 (+ (log beta) (log 0.5)))) (+ (* 0.16666666666666666 (* beta (exp (* 1/3 (+ (log beta) (log 0.5)))))) (* 0.16666666666666666 (* (exp (* 1/3 (+ (log beta) (log 0.5)))) alpha))))
315.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* 1.0 1)))
303.0ms
(- (exp (* 1/3 (+ (log beta) (log 0.5)))) (+ (* 0.16666666666666666 (* beta (exp (* 1/3 (+ (log beta) (log 0.5)))))) (* 0.16666666666666666 (* (exp (* 1/3 (+ (log beta) (log 0.5)))) alpha))))
295.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* 1.0 1)))

prune2.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.4b

localize24.0ms

Local error

Found 4 expressions with local error:

8.1b
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
1.4b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.8b
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
0.0b
(/ beta (+ (+ alpha beta) 2.0))

rewrite721.0ms

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
259.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
250.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
166.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
42.0ms
(/ beta (+ (+ alpha beta) 2.0))

series432.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
109.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
93.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
62.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify19.3s

Counts
263 → 234
Calls
263 calls:
Slowest
330.0ms
(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)))))
327.0ms
(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)))))
317.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
304.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
290.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))

prune2.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.3b

regimes238.0ms

Accuracy

73.9% (3.2b remaining)

Error of 6.3b against oracle of 3.0b and baseline of 15.5b

bsearch78.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
647.0ms730×body640valid
492.0ms785×body1280valid
472.0ms5875×body80valid
265.0ms8000×pre80true
146.0ms400×body320valid
33.0ms210×body160valid