Details

Time bar (total: 5.6m)

sample61.0ms

Algorithm
intervals
Results
19.0ms198×body80valid
8.0ms256×pre80true
8.0ms22×body640valid
8.0ms17×body1280valid
3.0ms11×body320valid
1.0ms8×body160valid

simplify139.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
139.0ms
(/ (+ (/ (/ (* (+ 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: 27.2b

localize53.0ms

Local error

Found 3 expressions with local error:

23.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))
2.5b
(+ (/ (/ (* (+ 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))

rewrite871.0ms

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
607.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
202.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
58.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series854.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
388.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
319.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
147.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify33.1s

Counts
169 → 171
Calls
169 calls:
Slowest
848.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
787.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
747.0ms
(/ (/ 1 (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
714.0ms
(/ (* (* (/ (* (+ 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)))
683.0ms
(/ (* (* (* (+ alpha beta) (- beta alpha)) (* (+ alpha beta) (- beta alpha))) (* (+ alpha beta) (- beta alpha))) (* (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) (+ (+ alpha beta) (* 2 i))))

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize35.0ms

Local error

Found 4 expressions with local error:

2.5b
(+ (/ (/ (+ 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))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
2182×times-frac
1819×*-un-lft-identity
1037×add-sqr-sqrt
783×add-cube-cbrt
391×distribute-lft-out
362×fma-def
127×distribute-lft-out-- difference-of-squares
98×associate-/r/
96×associate-/l*
54×div-inv
42×flip3-- flip--
30×associate-/r*
20×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
6×add-log-exp
5×flip3-+ flip-+ associate-/l/
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×clear-num frac-2neg
1×+-commutative sum-log
Counts
4 → 1019
Calls
4 calls:
Slowest
755.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
183.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
67.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))
64.0ms
(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
411.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
321.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
176.0ms
(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))
107.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))

simplify4.4m

Counts
1429 → 1031
Calls
1429 calls:
Slowest
1.2s
(/ (/ (cbrt (+ alpha beta)) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
946.0ms
(/ (/ (+ alpha beta) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
886.0ms
(/ (/ (cbrt (+ alpha beta)) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
835.0ms
(/ (/ (sqrt (+ alpha beta)) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
827.0ms
(/ (/ (+ alpha beta) (+ (* beta beta) (+ (* alpha alpha) (* beta alpha)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

prune13.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize69.0ms

Local error

Found 4 expressions with local error:

13.3b
(fma (/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) 1)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (cbrt (+ alpha beta)) (/ (cbrt (+ (+ alpha beta) (* 2 i))) (- beta alpha))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
0.5b
(cbrt (+ (+ alpha beta) (* 2 i)))
0.5b
(cbrt (+ (+ alpha beta) (* 2 i)))
0.5b
(cbrt (+ (+ alpha beta) (* 2 i)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity 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-+
1×fma-udef
Counts
4 → 59
Calls
4 calls:
Slowest
10.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
10.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
10.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
0.0ms
(fma (/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) 1)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (cbrt (+ alpha beta)) (/ (cbrt (+ (+ alpha beta) (* 2 i))) (- beta alpha))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
919.0ms
(fma (/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) 1)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (cbrt (+ alpha beta)) (/ (cbrt (+ (+ alpha beta) (* 2 i))) (- beta alpha))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
246.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
243.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
243.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))

simplify2.9s

Counts
27 → 71
Calls
27 calls:
Slowest
269.0ms
(cbrt (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)))
266.0ms
(+ (* 1/3 (* (exp (* 1/3 (- (log 1/4) (* 2 (log i))))) alpha)) (+ (* 1/6 (* (exp (* 1/3 (- (log 2) (* 2 (log i))))) beta)) (exp (* 1/3 (+ (log 2) (log i))))))
261.0ms
(+ (* 1/3 (* (exp (* 1/3 (- (log 1/4) (* 2 (log i))))) alpha)) (+ (* 1/6 (* (exp (* 1/3 (- (log 2) (* 2 (log i))))) beta)) (exp (* 1/3 (+ (log 2) (log i))))))
245.0ms
(cbrt (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))
235.0ms
(cbrt (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize97.0ms

Local error

Found 4 expressions with local error:

13.3b
(fma (/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) 1)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (cbrt (+ alpha beta)) (/ (cbrt (* (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) (cbrt (+ (+ alpha beta) (* 2 i))))) (- beta alpha))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
0.5b
(cbrt (+ (+ alpha beta) (* 2 i)))
0.5b
(cbrt (+ (+ alpha beta) (* 2 i)))
0.5b
(cbrt (+ (+ alpha beta) (* 2 i)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity 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-+
1×fma-udef
Counts
4 → 59
Calls
4 calls:
Slowest
10.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
10.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
10.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
0.0ms
(fma (/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) 1)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (cbrt (+ alpha beta)) (/ (cbrt (* (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) (cbrt (+ (+ alpha beta) (* 2 i))))) (- beta alpha))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
872.0ms
(fma (/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) 1)) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) (/ (/ (cbrt (+ alpha beta)) (/ (cbrt (* (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) (cbrt (+ (+ alpha beta) (* 2 i))))) (- beta alpha))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
250.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
224.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))
200.0ms
(cbrt (+ (+ alpha beta) (* 2 i)))

simplify3.5s

Counts
27 → 71
Calls
27 calls:
Slowest
471.0ms
(* (pow (* alpha -1) 1/3) (cbrt -1))
296.0ms
(+ (* 1/3 (* (exp (* 1/3 (- (log 1/4) (* 2 (log i))))) alpha)) (+ (* 1/6 (* (exp (* 1/3 (- (log 2) (* 2 (log i))))) beta)) (exp (* 1/3 (+ (log 2) (log i))))))
284.0ms
(cbrt (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)))
266.0ms
(cbrt (+ (pow (+ alpha beta) 3) (pow (* 2 i) 3)))
242.0ms
(cbrt (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 i) (* 2 i))))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

regimes498.0ms

Accuracy

12.7% (5.8b remaining)

Error of 11.8b against oracle of 6.0b and baseline of 12.6b

bsearch351.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.1s6334×body80valid
470.0ms519×body1280valid
418.0ms564×body640valid
346.0ms8000×pre80true
186.0ms352×body320valid
66.0ms231×body160valid