Details

Time bar (total: 2.2m)

sample64.0ms

Algorithm
intervals
Results
17.0ms187×body80valid
14.0ms31×body1280valid
10.0ms256×pre80true
9.0ms24×body640valid
2.0ms9×body320valid
1.0ms5×body160valid

simplify105.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize32.0ms

Local error

Found 2 expressions with local error:

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

rewrite156.0ms

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
123.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
30.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series143.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
80.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
62.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify4.7s

Counts
104 → 108
Calls
104 calls:
Slowest
294.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
262.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
234.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
210.0ms
(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3)))
207.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))

prune994.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.7b

localize29.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (/ 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))

rewrite627.0ms

Algorithm
rewrite-expression-head
Rules
512×*-un-lft-identity
328×add-sqr-sqrt
263×times-frac
252×prod-diff
213×add-cube-cbrt
150×distribute-lft-out
65×associate--r+
46×difference-of-squares
42×fma-neg
32×associate-/r/
25×distribute-lft-out--
16×flip3-+ flip-+ div-inv
11×add-log-exp
10×associate-/r*
8×add-cbrt-cube add-exp-log
6×associate-/l*
4×expm1-log1p-u pow1 diff-log insert-posit16 log1p-expm1-u
3×sub-neg flip3-- flip--
2×cbrt-undiv clear-num frac-2neg div-exp frac-sub
1×associate--r-
Counts
4 → 417
Calls
4 calls:
Slowest
412.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
159.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
23.0ms
(/ beta (+ (+ alpha beta) 2.0))
23.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series318.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
77.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
64.0ms
(/ alpha (+ (+ alpha beta) 2.0))
63.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify1.2m

Counts
593 → 429
Calls
593 calls:
Slowest
827.0ms
(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))))))
516.0ms
(fma (- (- (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0))) (+ (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (* (- (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (+ (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0))))
458.0ms
(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))))))
458.0ms
(fma (/ (sqrt beta) (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ (sqrt beta) (cbrt (+ (+ alpha beta) 2.0))) (- (* (- (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (+ (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)))))
441.0ms
(fma (/ (sqrt beta) (sqrt (+ (+ alpha beta) 2.0))) (/ (sqrt beta) (sqrt (+ (+ alpha beta) 2.0))) (- (* (- (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)) (+ (sqrt (/ alpha (+ (+ alpha beta) 2.0))) (sqrt 1.0)))))

prune4.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.6b

localize25.0ms

Local error

Found 4 expressions with local error:

10.2b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
0.0b
(/ beta (+ (+ alpha beta) 2.0))

rewrite887.0ms

Algorithm
rewrite-expression-head
Rules
166×*-un-lft-identity
89×add-sqr-sqrt
78×times-frac
74×add-cube-cbrt
63×prod-diff
48×distribute-lft-out
21×fma-neg
14×log-prod
10×associate-/r/
8×log-div
7×exp-sum add-exp-log distribute-lft-out--
6×pow1 add-cbrt-cube add-log-exp difference-of-squares
5×associate-/r* flip3-+ flip3-- flip-+ div-inv flip--
4×expm1-log1p-u exp-prod exp-diff frac-sub insert-posit16 log1p-expm1-u
3×associate-/l*
2×log-pow
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp rem-log-exp rem-exp-log
Counts
4 → 191
Calls
4 calls:
Slowest
366.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
274.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
217.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
23.0ms
(/ beta (+ (+ alpha beta) 2.0))

series447.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
203.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
108.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
72.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
63.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify17.5s

Counts
232 → 203
Calls
232 calls:
Slowest
593.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
552.0ms
(exp (log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))))
491.0ms
(fma (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
387.0ms
(exp (log (- (* 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))))))
356.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

localize50.0ms

Local error

Found 4 expressions with local error:

10.2b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
10.2b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
10.2b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
141×*-un-lft-identity
84×add-sqr-sqrt
64×times-frac add-cube-cbrt
63×prod-diff
36×distribute-lft-out
21×log-prod fma-neg
12×log-div
10×distribute-lft-out--
8×associate-/r/ difference-of-squares
7×pow1 flip3-- add-exp-log flip--
6×frac-sub add-log-exp
4×expm1-log1p-u flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u div-inv
3×rem-log-exp log-pow
1×sub-neg diff-log
Counts
4 → 171
Calls
4 calls:
Slowest
413.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
390.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
365.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
166.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series636.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
191.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
174.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
168.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
102.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify17.5s

Counts
199 → 183
Calls
199 calls:
Slowest
507.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
490.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
482.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
365.0ms
(log (- (* 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)))))
318.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))

prune2.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.6b

regimes190.0ms

Accuracy

76.9% (3.0b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 16.2b

bsearch127.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
617.0ms752×body640valid
617.0ms5777×body80valid
496.0ms915×body1280valid
306.0ms8000×pre80true
85.0ms359×body320valid
32.0ms197×body160valid