Details

Time bar (total: 1.8m)

sample111.0ms

Algorithm
intervals
Results
36.0ms199×body80valid
15.0ms256×pre80true
15.0ms20×body640valid
15.0ms17×body1280valid
8.0ms15×body320valid
2.0ms5×body160valid

simplify119.0ms

Calls
1 calls:
Slowest
119.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize40.0ms

Local error

Found 4 expressions with local error:

20.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
1.4b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(+ (+ (+ alpha beta) (* 2 i)) 2.0)

rewrite892.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
87×*-un-lft-identity
45×add-sqr-sqrt fma-def add-cube-cbrt
24×associate-/r/
21×distribute-lft-out
18×add-cbrt-cube add-exp-log
17×flip3-+ flip-+
15×add-log-exp
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* sum-log div-exp
4×expm1-log1p-u frac-times pow1 insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×+-commutative clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×associate-+l+
Calls
4 calls:
Slowest
591.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
149.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
102.0ms
(+ (+ (+ alpha beta) (* 2 i)) 2.0)
48.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series876.0ms

Calls
4 calls:
Slowest
364.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
360.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
123.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
29.0ms
(+ (+ (+ alpha beta) (* 2 i)) 2.0)

simplify34.9s

Calls
179 calls:
Slowest
733.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
688.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
686.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
686.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
671.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize45.0ms

Local error

Found 4 expressions with local error:

13.6b
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.0b
(+ (+ (+ alpha beta) (* 2 i)) 2.0)

rewrite341.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
166×*-un-lft-identity
120×add-sqr-sqrt
82×add-cube-cbrt
26×associate-/l*
23×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
13×add-log-exp
11×add-cbrt-cube add-exp-log
8×flip3-+ flip-+
7×associate-/r* div-inv
6×sum-log
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u
3×fma-def div-sub associate-/l/
2×clear-num frac-2neg
1×+-commutative associate-+l+ flip3-- fma-udef flip--
Calls
4 calls:
Slowest
175.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
128.0ms
(+ (+ (+ alpha beta) (* 2 i)) 2.0)
33.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
1.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

series608.0ms

Calls
4 calls:
Slowest
236.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
198.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
144.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
30.0ms
(+ (+ (+ alpha beta) (* 2 i)) 2.0)

simplify44.2s

Calls
262 calls:
Slowest
1.1s
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
858.0ms
(/ (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
848.0ms
(/ (/ (- (sqrt beta) (sqrt alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
793.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
764.0ms
(/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize69.0ms

Local error

Found 4 expressions with local error:

13.5b
(fma (+ beta alpha) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×fma-udef
Calls
4 calls:
Slowest
77.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
39.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
38.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.0ms
(fma (+ beta alpha) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

series985.0ms

Calls
4 calls:
Slowest
268.0ms
(fma (+ beta alpha) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
247.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
243.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
227.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))

simplify4.1s

Calls
30 calls:
Slowest
313.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
274.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
260.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
251.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
235.0ms
(+ (* 1/3 (* (pow 0.25 1/3) beta)) (+ (pow 2.0 1/3) (* 1/3 (* (pow 0.25 1/3) alpha))))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.5b

localize79.0ms

Local error

Found 4 expressions with local error:

13.5b
(fma (+ beta alpha) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (* (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))) 1.0)
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×fma-udef
Calls
4 calls:
Slowest
57.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
47.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
40.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0ms
(fma (+ beta alpha) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (* (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))) 1.0)

series995.0ms

Calls
4 calls:
Slowest
257.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
256.0ms
(fma (+ beta alpha) (* (/ (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) 1) (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (cbrt (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (cbrt (* (* (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))) 1.0)
247.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))
236.0ms
(cbrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))

simplify4.8s

Calls
30 calls:
Slowest
670.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
313.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
290.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
269.0ms
(+ (* 1/3 (* (pow 0.25 1/3) beta)) (+ (pow 2.0 1/3) (* 1/3 (* (pow 0.25 1/3) alpha))))
268.0ms
(+ (* 1/3 (* (pow 0.25 1/3) beta)) (+ (pow 2.0 1/3) (* 1/3 (* (pow 0.25 1/3) alpha))))

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.5b

regimes588.0ms

Accuracy

74.8% (1.7b remaining)

Error of 7.6b against oracle of 5.9b and baseline of 12.6b

bsearch10.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
982.0ms6339×body80valid
638.0ms359×body320valid
510.0ms540×body1280valid
406.0ms8000×pre80true
404.0ms576×body640valid
79.0ms186×body160valid