Details

Time bar (total: 22.8s)

sample69.0ms

Algorithm
intervals
Results
19.0ms205×body80valid
7.0ms256×pre80true
7.0ms19×body640valid
6.0ms13×body1280valid
4.0ms13×body320valid
1.0ms6×body160valid

simplify897.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.7b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-exp-log add-cbrt-cube
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
227.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
798.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
123.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series851.0ms

Counts
3 → 9
Calls
3 calls:
350.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
406.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
95.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify1.4s

Counts
120 → 120

prune380.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
3.2b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
3.3b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite978.0ms

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-exp-log add-cbrt-cube
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv div-exp associate-/r*
6×pow1 add-log-exp
4×associate-*l*
3×div-sub prod-exp cbrt-unprod associate-/l/ unswap-sqr
2×frac-times frac-2neg associate-*l/ clear-num
1×+-commutative flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 295
Calls
4 calls:
63.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
243.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
161.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
492.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
236.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
396.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
280.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify720.0ms

Counts
307 → 307

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
3.2b
(+ (* (+ alpha beta) (/ (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
3.3b
(* (+ alpha beta) (/ (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
355×times-frac
323×*-un-lft-identity
233×add-sqr-sqrt
191×unpow-prod-down
157×add-cube-cbrt
106×associate-*r*
52×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
30×associate-/l*
28×add-exp-log
24×associate-/r/
15×flip3-+ flip-+
13×add-cbrt-cube
12×div-inv
11×div-exp
10×sqr-pow
7×associate-/r*
6×pow1 add-log-exp
5×prod-exp unswap-sqr
4×associate-*l* pow-exp
3×cbrt-undiv
2×frac-times pow-to-exp frac-2neg associate-*l/ clear-num cbrt-unprod associate-/l/
1×+-commutative flip3-- div-sub associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 333
Calls
4 calls:
46.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
428.0ms
(/ (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
152.0ms
(+ (* (+ alpha beta) (/ (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
764.0ms
(* (+ alpha beta) (/ (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
243.0ms
(/ (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
448.0ms
(+ (* (+ alpha beta) (/ (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
380.0ms
(* (+ alpha beta) (/ (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify716.0ms

Counts
345 → 345

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* (pow (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) 2) (+ alpha beta)) (/ (cbrt (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.2b
(+ (* (* (pow (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) 2) (+ alpha beta)) (/ (cbrt (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
4.1b
(cbrt (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1))
4.1b
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
202×times-frac
188×*-un-lft-identity
146×cbrt-prod
132×add-sqr-sqrt
118×associate-*r*
105×unpow-prod-down
96×add-cube-cbrt
28×add-exp-log distribute-lft-out
18×distribute-lft-out-- difference-of-squares
14×prod-exp associate-/r/ add-cbrt-cube
10×flip3-+ flip-+
7×div-inv
6×pow1 cbrt-unprod add-log-exp
5×associate-*r/ sqr-pow
4×div-exp
2×cbrt-undiv frac-times pow-to-exp pow1/3 associate-*l/ pow-exp
1×+-commutative cbrt-div associate-*l* pow-prod-down sum-log *-commutative
Counts
4 → 219
Calls
4 calls:
739.0ms
(* (* (pow (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) 2) (+ alpha beta)) (/ (cbrt (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
397.0ms
(+ (* (* (pow (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) 2) (+ alpha beta)) (/ (cbrt (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
69.0ms
(cbrt (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1))
23.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))

series1.9s

Counts
4 → 12
Calls
4 calls:
400.0ms
(* (* (pow (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) 2) (+ alpha beta)) (/ (cbrt (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
307.0ms
(+ (* (* (pow (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) 2) (+ alpha beta)) (/ (cbrt (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
591.0ms
(cbrt (pow (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) 1))
609.0ms
(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))

simplify738.0ms

Counts
231 → 231

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

regimes332.0ms

Accuracy

4.5% (6.3b remaining)

Error of 12.4b against oracle of 6.1b and baseline of 12.7b

bsearch306.0ms

Steps
ItersRangePoint
7
1.6312164156823986e+262
2.953454065783771e+263
2.831345554250201e+263
9
2.3348036620988474e+142
1.1037931664225405e+150
1.0834670219855457e+150

simplify767.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.1s6297×body80valid
350.0ms8000×pre80true
294.0ms585×body640valid
238.0ms508×body1280valid
133.0ms391×body320valid
36.0ms219×body160valid