Details

Time bar (total: 1.4m)

sample57.0ms

Algorithm
intervals
Results
14.0ms183×body80valid
10.0ms29×body1280valid
9.0ms256×pre80true
7.0ms22×body640valid
2.0ms14×body160valid
2.0ms8×body320valid

simplify160.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
160.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize20.0ms

Local error

Found 2 expressions with local error:

2.9b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite166.0ms

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
113.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
49.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series128.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
72.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
56.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify4.8s

Counts
104 → 108
Calls
104 calls:
Slowest
294.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
273.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
245.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
236.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
230.0ms
(/ (- beta alpha) (+ (pow (+ alpha beta) 3) (pow 2.0 3)))

prune964.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.2b

localize28.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)

rewrite1.3s

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
993.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
195.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
44.0ms
(/ alpha (+ (+ alpha beta) 2.0))
22.0ms
(/ beta (+ (+ alpha beta) 2.0))

series314.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
80.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
63.0ms
(/ beta (+ (+ alpha beta) 2.0))
61.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify20.7s

Counts
300 → 245
Calls
300 calls:
Slowest
443.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
349.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
327.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
312.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
303.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize37.0ms

Local error

Found 4 expressions with local error:

9.8b
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
2.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.5b
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))

rewrite699.0ms

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
265.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
223.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
185.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
22.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series423.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
115.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
84.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
61.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify20.0s

Counts
263 → 234
Calls
263 calls:
Slowest
579.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) (* (cbrt (+ (+ alpha beta) 2.0)) (cbrt (+ (+ alpha beta) 2.0)))) (/ (cbrt alpha) (cbrt (+ (+ alpha beta) 2.0))) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
373.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
332.0ms
(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)))))
326.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* 1.0 1)))
324.0ms
(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)))))

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize37.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)

rewrite1.4s

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
1.1s
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
228.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
29.0ms
(/ beta (+ (+ alpha beta) 2.0))
24.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series334.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
91.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
83.0ms
(/ beta (+ (+ alpha beta) 2.0))
61.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify20.5s

Counts
300 → 245
Calls
300 calls:
Slowest
493.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
333.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
304.0ms
(- (* 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))))
296.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))
292.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* 1.0 1)))

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.0b

regimes173.0ms

Accuracy

77.6% (2.9b remaining)

Error of 6.1b against oracle of 3.3b and baseline of 16.0b

bsearch91.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
912.0ms837×body1280valid
612.0ms5792×body80valid
360.0ms8000×pre80true
304.0ms738×body640valid
110.0ms420×body320valid
62.0ms213×body160valid