Details

Time bar (total: 3.7m)

sample74.0ms

Algorithm
intervals
Results
27.0ms208×body80valid
10.0ms256×pre80true
9.0ms14×body1280valid
9.0ms17×body640valid
4.0ms11×body320valid
1.0ms6×body160valid

simplify133.0ms

Calls
1 calls:
Slowest
132.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.9b

localize48.0ms

Local error

Found 3 expressions with local error:

19.2b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.2b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
39×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
33×fma-def
20×associate-/r/
17×add-cbrt-cube add-exp-log
14×flip3-+ flip-+
10×div-inv associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp
6×associate-/r*
4×frac-times
3×expm1-log1p-u pow1 flip3-- insert-posit16 log1p-expm1-u flip-- add-log-exp
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative
Calls
3 calls:
Slowest
104.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
42.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
12.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series431.0ms

Calls
3 calls:
Slowest
232.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
150.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
49.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify27.7s

Calls
139 calls:
Slowest
1.1s
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
724.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
627.0ms
(/ (* (* (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
584.0ms
(* (+ (pow alpha 3) (pow beta 3)) (- (pow beta 3) (pow alpha 3)))
530.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))
0.1b
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b
(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
894×times-frac
417×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
156×fma-def
64×associate-/r/
56×associate-/l*
36×div-inv
26×flip3-- flip--
21×associate-/r*
20×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
5×flip3-+ flip-+ associate-/l/
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×+-commutative
Calls
4 calls:
Slowest
121.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
46.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
14.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))
13.0ms
(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))

series605.0ms

Calls
4 calls:
Slowest
222.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
221.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
97.0ms
(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))
65.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))

simplify2.1m

Calls
671 calls:
Slowest
889.0ms
(/ (/ (cbrt (+ alpha beta)) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
781.0ms
(/ (/ (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)) (* (* (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
771.0ms
(/ (/ (+ alpha beta) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
769.0ms
(/ (/ (sqrt (+ alpha beta)) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
743.0ms
(/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) (sqrt (- beta alpha)))) 1)

prune7.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize27.0ms

Local error

Found 4 expressions with local error:

3.9b
(+ (/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.4b
(/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta)))
0.1b
(/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))
0.1b
(/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
183×times-frac
104×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
57×associate-/r*
30×associate-/r/
26×add-exp-log
21×fma-def
20×associate-/l*
19×div-inv
13×div-exp
11×add-cbrt-cube
7×flip3-- flip--
6×rec-exp
5×pow1 flip3-+ flip-+
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×associate-/l/
1×+-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
114.0ms
(+ (/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
19.0ms
(/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
16.0ms
(/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))
4.0ms
(/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta)))

series603.0ms

Calls
4 calls:
Slowest
261.0ms
(+ (/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
163.0ms
(/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
103.0ms
(/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))
76.0ms
(/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta)))

simplify27.8s

Calls
242 calls:
Slowest
1.0s
(/ (* (* (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta)))) (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta)))) (* (* (+ (+ (+ alpha beta) (* 2 i)) 2.0) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
484.0ms
(/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
457.0ms
(/ (/ (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))) (* (* (- beta alpha) (- beta alpha)) (- beta alpha))) (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)))
422.0ms
(/ (/ 1 (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) 1)
419.0ms
(/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune3.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize11.0ms

Local error

Found 4 expressions with local error:

11.3b
(fma (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.4b
(/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta)))
0.1b
(/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))
0.0b
(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
93×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
57×associate-/r*
21×associate-/r/
18×associate-/l*
17×add-exp-log
11×add-cbrt-cube div-inv
8×flip3-- flip--
7×div-exp
5×pow1
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp clear-num frac-2neg flip3-+ flip-+ associate-/l/
1×fma-udef pow-flip inv-pow
Calls
4 calls:
Slowest
26.0ms
(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))
16.0ms
(/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))
4.0ms
(/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta)))
0.0ms
(fma (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

series441.0ms

Calls
4 calls:
Slowest
206.0ms
(fma (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
89.0ms
(/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))
75.0ms
(/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta)))
72.0ms
(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))

simplify16.0s

Calls
208 calls:
Slowest
444.0ms
(/ (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) (* (cbrt (- beta alpha)) (cbrt (- beta alpha)))) (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))))
403.0ms
(/ (/ (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))) (* (* (- beta alpha) (- beta alpha)) (- beta alpha))) (* (* (+ alpha beta) (+ alpha beta)) (+ alpha beta)))
352.0ms
(/ (/ (+ (+ alpha beta) (* 2 i)) (- (* beta beta) (* alpha alpha))) (sqrt (+ alpha beta)))
336.0ms
(/ (/ (+ (+ alpha beta) (* 2 i)) (- (pow beta 3) (pow alpha 3))) (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))))
309.0ms
(/ (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))) (* (* (- beta alpha) (- beta alpha)) (- beta alpha)))

prune2.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

regimes397.0ms

Accuracy

17.2% (5.1b remaining)

Error of 11.1b against oracle of 6.0b and baseline of 12.1b

bsearch124.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.6s6402×body80valid
464.0ms470×body1280valid
433.0ms8000×pre80true
409.0ms591×body640valid
161.0ms349×body320valid
85.0ms188×body160valid