Details

Time bar (total: 24.5s)

sample84.0ms

Algorithm
intervals
Results
21.0ms209×body80valid
10.0ms19×body1280valid
9.0ms256×pre80true
7.0ms17×body640valid
2.0ms8×body320valid
1.0ms3×body160valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done5001
42483
3453
2102
131
015

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.3b

localize42.0ms

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))
1.1b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
23.4b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite990.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-cbrt-cube add-exp-log
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
248.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
668.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
70.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series894.0ms

Counts
3 → 9
Calls
3 calls:
369.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
399.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
126.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.0s

Counts
120 → 120
Iterations
IterNodes
done5001
24479
1697
0225

prune792.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha))
0.1b
(/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))
1.1b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))
2.3b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))) 1.0)

rewrite683.0ms

Algorithm
rewrite-expression-head
Rules
667×*-un-lft-identity
503×times-frac
287×add-sqr-sqrt
221×distribute-lft-out
180×add-cube-cbrt
140×associate-*r*
49×distribute-lft-out-- difference-of-squares
36×associate-/r/
31×associate-/l*
25×flip3-+ flip-+
20×add-cbrt-cube add-exp-log
14×div-inv
9×associate-/r*
8×frac-add
7×cbrt-undiv div-exp
6×pow1 add-log-exp
4×associate-*l*
3×div-sub prod-exp cbrt-unprod unswap-sqr associate-/l/
2×frac-times clear-num frac-2neg associate-*l/
1×+-commutative sum-log flip3-- pow-prod-down associate-*r/ *-commutative flip--
Counts
4 → 407
Calls
4 calls:
40.0ms
(/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha))
141.0ms
(/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))
328.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))
126.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha))
232.0ms
(/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))
341.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))
414.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))) 1.0)

simplify611.0ms

Counts
419 → 419
Iterations
IterNodes
done5001
11256
0416

prune2.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.3b

localize46.0ms

Local error

Found 4 expressions with local error:

4.6b
(cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha))))
4.6b
(cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha))))
4.6b
(cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha))))
6.5b
(+ (* (+ alpha beta) (* (/ (cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha)))) (/ (sqrt (+ alpha (+ beta (+ (* 2.0 i) 2.0)))) (cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha)))))) (/ (cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha)))) (sqrt (+ alpha (+ beta (+ (* 2.0 i) 2.0))))))) 1.0)

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
88×*-un-lft-identity
78×cbrt-prod
60×times-frac
58×add-sqr-sqrt
34×add-cube-cbrt
15×distribute-lft-out
12×distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
4×pow1 flip3-+ add-cbrt-cube add-exp-log flip-+
3×cbrt-div pow1/3 div-inv
1×+-commutative sum-log
Counts
4 → 116
Calls
4 calls:
17.0ms
(cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha))))
26.0ms
(cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha))))
30.0ms
(cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha))))
2.1s
(+ (* (+ alpha beta) (* (/ (cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha)))) (/ (sqrt (+ alpha (+ beta (+ (* 2.0 i) 2.0)))) (cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha)))))) (/ (cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha)))) (sqrt (+ alpha (+ beta (+ (* 2.0 i) 2.0))))))) 1.0)

series2.2s

Counts
4 → 12
Calls
4 calls:
493.0ms
(cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha))))
578.0ms
(cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha))))
619.0ms
(cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha))))
508.0ms
(+ (* (+ alpha beta) (* (/ (cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha)))) (/ (sqrt (+ alpha (+ beta (+ (* 2.0 i) 2.0)))) (cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha)))))) (/ (cbrt (/ (- beta alpha) (+ beta (+ (* 2.0 i) alpha)))) (sqrt (+ alpha (+ beta (+ (* 2.0 i) 2.0))))))) 1.0)

simplify655.0ms

Counts
128 → 128
Iterations
IterNodes
done5000
21217
1359
0159

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.3b

localize59.0ms

Local error

Found 4 expressions with local error:

4.6b
(cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta))))
4.6b
(cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta))))
4.6b
(cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta))))
6.5b
(+ 1.0 (* (* (/ (cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))) (/ (sqrt (+ (+ (+ beta alpha) (* i 2.0)) 2.0)) (cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))))) (/ (cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))) (sqrt (+ (+ (+ beta alpha) (* i 2.0)) 2.0)))) (+ beta alpha)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
88×*-un-lft-identity
78×cbrt-prod
60×times-frac
58×add-sqr-sqrt
34×add-cube-cbrt
15×distribute-lft-out
12×distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
4×pow1 flip3-+ add-cbrt-cube add-exp-log flip-+
3×cbrt-div pow1/3 div-inv
2×associate-+r+
1×distribute-rgt-in +-commutative sum-log distribute-lft-in
Counts
4 → 118
Calls
4 calls:
31.0ms
(cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta))))
30.0ms
(cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta))))
27.0ms
(cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta))))
14.0ms
(+ 1.0 (* (* (/ (cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))) (/ (sqrt (+ (+ (+ beta alpha) (* i 2.0)) 2.0)) (cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))))) (/ (cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))) (sqrt (+ (+ (+ beta alpha) (* i 2.0)) 2.0)))) (+ beta alpha)))

series1.9s

Counts
4 → 12
Calls
4 calls:
586.0ms
(cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta))))
521.0ms
(cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta))))
538.0ms
(cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta))))
293.0ms
(+ 1.0 (* (* (/ (cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))) (/ (sqrt (+ (+ (+ beta alpha) (* i 2.0)) 2.0)) (cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))))) (/ (cbrt (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))) (sqrt (+ (+ (+ beta alpha) (* i 2.0)) 2.0)))) (+ beta alpha)))

simplify701.0ms

Counts
130 → 130
Iterations
IterNodes
done5001
21371
1361
0158

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

regimes487.0ms

Accuracy

13.9% (5.8b remaining)

Error of 11.6b against oracle of 5.9b and baseline of 12.6b

bsearch419.0ms

Steps
ItersRangePoint
9
4.6934296581421965e+201
4.887025533313191e+207
3.039415483981533e+202
5
3.050881520042425e+157
1.1514695753805634e+158
8.090655368014929e+157
10
2.886473143426602e+94
3.6643778747462423e+109
3.8513886774320383e+108

simplify15.0ms

Iterations
IterNodes
done78
178
059

end0.0ms

sample2.1s

Algorithm
intervals
Results
794.0ms6329×body80valid
252.0ms8000×pre80true
247.0ms606×body640valid
212.0ms501×body1280valid
86.0ms350×body320valid
76.0ms214×body160valid