Details

Time bar (total: 4.7m)

sample130.0ms

Algorithm
intervals
Results
36.0ms204×body80valid
24.0ms10×body320valid
17.0ms256×pre80true
15.0ms20×body640valid
13.0ms14×body1280valid
3.0ms8×body160valid

simplify138.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
138.0ms
(/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize27.0ms

Local error

Found 3 expressions with local error:

20.5b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.7b
(+ (/ (/ (* (+ 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))

rewrite946.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
83×*-un-lft-identity
43×add-sqr-sqrt add-cube-cbrt
42×fma-def
24×associate-/r/
20×distribute-lft-out
17×add-cbrt-cube add-exp-log
16×flip3-+ flip-+
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp
5×add-log-exp
4×frac-times
3×expm1-log1p-u pow1 flip3-- insert-posit16 log1p-expm1-u flip--
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative sum-log
Counts
3 → 162
Calls
3 calls:
Slowest
663.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
197.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
81.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series910.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
406.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
379.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
125.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify33.1s

Counts
169 → 171
Calls
169 calls:
Slowest
789.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
747.0ms
(- (- (+ (log (+ alpha beta)) (log (- beta alpha))) (log (+ (+ alpha beta) (* 2 i)))) (log (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
723.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
687.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))
677.0ms
(/ (* (* (/ (* (+ 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)))

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

localize52.0ms

Local error

Found 4 expressions with local error:

6.6b
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
0.4b
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.2b
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
1015×times-frac
755×*-un-lft-identity
655×add-sqr-sqrt
413×add-cube-cbrt
333×sqrt-prod
153×associate-*r*
121×distribute-lft-out
118×associate-*l*
64×add-exp-log
50×add-cbrt-cube
45×distribute-lft-out-- difference-of-squares
38×associate-/r/
37×associate-/l*
35×div-exp unswap-sqr
34×div-inv
24×cbrt-undiv
20×flip3-+ flip-+
14×associate-/r*
12×prod-exp
9×cbrt-unprod
8×sqrt-div
6×pow1 add-log-exp
4×expm1-log1p-u 1-exp insert-posit16 log1p-expm1-u
2×clear-num frac-2neg div-sub associate-/l/
1×frac-times +-commutative sum-log fma-def pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 709
Calls
4 calls:
Slowest
723.0ms
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
131.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
111.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
110.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
424.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
352.0ms
(* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
323.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
173.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

simplify2.4m

Counts
963 → 721
Calls
963 calls:
Slowest
775.0ms
(* (/ (* (* (/ (+ alpha beta) 1) (/ (+ alpha beta) 1)) (/ (+ alpha beta) 1)) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
605.0ms
(/ (/ (- (sqrt beta) (sqrt alpha)) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
605.0ms
(/ (/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i)))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))
594.0ms
(* (* (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) (/ (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (* (* (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))
581.0ms
(/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (sqrt 1)) (* (cbrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (cbrt (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))))

prune11.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

localize101.0ms

Local error

Found 4 expressions with local error:

6.6b
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
6.6b
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
6.6b
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
0.4b
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

rewrite628.0ms

Algorithm
rewrite-expression-head
Rules
208×times-frac
184×*-un-lft-identity
102×add-sqr-sqrt add-cube-cbrt
68×sqrt-prod
41×distribute-lft-out
16×associate-/l*
11×add-exp-log
10×add-log-exp
9×add-cbrt-cube div-inv
7×associate-/r*
5×div-exp
4×expm1-log1p-u pow1 flip3-+ flip-+ insert-posit16 log1p-expm1-u
3×cbrt-undiv +-commutative sum-log fma-def
2×sqrt-div associate-/r/
1×clear-num frac-2neg 1-exp associate-/l/
Counts
4 → 201
Calls
4 calls:
Slowest
183.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
176.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
138.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
126.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
382.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
360.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
346.0ms
(+ (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))) 1.0)
143.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0)))

simplify29.3s

Counts
272 → 213
Calls
272 calls:
Slowest
449.0ms
(* (exp (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) (exp 1.0))
433.0ms
(* (exp (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) (exp 1.0))
430.0ms
(* (exp (* (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))))) (exp 1.0))
281.0ms
(- (+ (* (sqrt 0.5) beta) (* (sqrt 0.5) alpha)) (* 1/2 (* (sqrt 0.125) (pow alpha 2))))
227.0ms
(- (+ (* 2.0 (/ 1 alpha)) (* 8.0 (/ 1 (pow alpha 3)))) (* 4.0 (/ 1 (pow alpha 2))))

prune4.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

localize45.0ms

Local error

Found 3 expressions with local error:

12.1b
(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)))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
162×*-un-lft-identity
118×add-sqr-sqrt
80×add-cube-cbrt
26×associate-/l*
22×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
10×add-cbrt-cube add-exp-log
7×associate-/r* flip3-+ flip-+ div-inv
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 div-sub insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×clear-num frac-2neg
1×flip3-- fma-udef flip--
Counts
3 → 184
Calls
3 calls:
Slowest
178.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
30.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

series592.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
252.0ms
(fma (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
215.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
125.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify42.6s

Counts
252 → 193
Calls
252 calls:
Slowest
1.1s
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.0s
(/ (/ (* (* (- 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)))
803.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
783.0ms
(/ (/ (- (sqrt beta) (sqrt alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
755.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

regimes341.0ms

Accuracy

-3.9% (6.6b remaining)

Error of 12.5b against oracle of 5.9b and baseline of 12.2b

bsearch277.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s6376×body80valid
818.0ms489×body1280valid
426.0ms523×body640valid
382.0ms8000×pre80true
198.0ms396×body320valid
60.0ms216×body160valid