Details

Time bar (total: 1.4m)

sample88.0ms

Algorithm
intervals
Results
20.0ms185×body80valid
18.0ms256×pre80true
17.0ms31×body1280valid
11.0ms23×body640valid
3.0ms9×body320valid
2.0ms8×body160valid

simplify167.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
167.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize26.0ms

Local error

Found 2 expressions with local error:

1.9b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite213.0ms

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
163.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
47.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series162.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
85.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
77.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify5.1s

Counts
104 → 108
Calls
104 calls:
Slowest
283.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
252.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
243.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
238.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
231.0ms
(/ (- beta alpha) (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0)))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.9b

localize24.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (/ 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
1.1s
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
198.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
33.0ms
(/ beta (+ (+ alpha beta) 2.0))
30.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series329.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
98.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
67.0ms
(/ beta (+ (+ alpha beta) 2.0))
52.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify20.7s

Counts
300 → 245
Calls
300 calls:
Slowest
509.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
357.0ms
(- (* 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))))
346.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
343.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
335.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* 1.0 1)))

prune2.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize56.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(cbrt (+ (+ alpha beta) 2.0))
0.7b
(cbrt (+ (+ alpha beta) 2.0))
0.7b
(cbrt (+ (+ alpha beta) 2.0))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
141×*-un-lft-identity
69×add-sqr-sqrt
64×add-cube-cbrt
63×prod-diff
61×times-frac
45×distribute-lft-out
21×fma-neg
15×cbrt-prod
8×associate-/r/
7×flip3-+ flip-+
6×cbrt-div add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u div-inv
3×pow1/3
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 156
Calls
4 calls:
Slowest
208.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
21.0ms
(cbrt (+ (+ alpha beta) 2.0))
20.0ms
(cbrt (+ (+ alpha beta) 2.0))
20.0ms
(cbrt (+ (+ alpha beta) 2.0))

series493.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(cbrt (+ (+ alpha beta) 2.0))
129.0ms
(cbrt (+ (+ alpha beta) 2.0))
117.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
115.0ms
(cbrt (+ (+ alpha beta) 2.0))

simplify15.5s

Counts
184 → 168
Calls
184 calls:
Slowest
704.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
308.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (cbrt 1.0) (* (cbrt 1.0) (cbrt 1.0)))))
301.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
300.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))
300.0ms
(fma (/ (* (cbrt alpha) (cbrt alpha)) 1) (/ (cbrt alpha) (+ (+ alpha beta) 2.0)) (- (* (sqrt 1.0) (sqrt 1.0))))

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize41.0ms

Local error

Found 4 expressions with local error:

11.1b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.7b
(- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0))
0.6b
(exp (- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
168×*-un-lft-identity
107×add-sqr-sqrt
95×prod-diff
83×add-cube-cbrt
64×times-frac
36×distribute-lft-out
30×pow1
26×log-pow
25×fma-neg exp-sum
24×log-prod
18×distribute-lft-out--
14×associate--l+
10×difference-of-squares
8×log-div exp-prod associate-/r/
7×add-log-exp
6×flip3-- flip--
5×add-exp-log
4×associate--l- expm1-log1p-u flip3-+ add-cbrt-cube frac-sub flip-+ insert-posit16 log1p-expm1-u div-inv
3×sub-neg diff-log associate--r+
2×rem-exp-log
1×exp-diff rem-log-exp
Counts
4 → 225
Calls
4 calls:
Slowest
319.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
268.0ms
(- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0))
241.0ms
(exp (- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0)))
181.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series931.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
423.0ms
(- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0))
247.0ms
(exp (- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0)))
167.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
94.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify28.1s

Counts
266 → 237
Calls
266 calls:
Slowest
598.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
576.0ms
(exp (fma 1 (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (- (* (sqrt (log 2.0)) (sqrt (log 2.0))))))
520.0ms
(exp (fma (* (cbrt (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (cbrt (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))) (cbrt (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (- (* (log 2.0) 1))))
518.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
457.0ms
(exp (fma 1 (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (- (* (sqrt (log 2.0)) (sqrt (log 2.0))))))

prune3.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.4b

regimes184.0ms

Accuracy

72.4% (3.5b remaining)

Error of 6.7b against oracle of 3.2b and baseline of 15.8b

bsearch32.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
634.0ms5835×body80valid
405.0ms843×body1280valid
368.0ms8000×pre80true
271.0ms736×body640valid
124.0ms379×body320valid
35.0ms207×body160valid