Details

Time bar (total: 24.6s)

sample65.0ms

Algorithm
intervals
Results
23.0ms208×body80valid
6.0ms256×pre80true
5.0ms15×body1280valid
4.0ms15×body640valid
3.0ms13×body320valid
1.0ms5×body160valid

simplify1.2s

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize21.0ms

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))
2.3b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.2b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite970.0ms

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:
187.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
716.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
58.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series896.0ms

Counts
3 → 9
Calls
3 calls:
336.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
417.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
142.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify1.8s

Counts
120 → 120
Iterations
IterNodes
done5001
24479
1697
0225

prune817.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha))
0.0b
(/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))
1.7b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))
3.5b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))) 1.0)

rewrite692.0ms

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:
54.0ms
(/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha))
186.0ms
(/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))
315.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))
99.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))) 1.0)

series1.2s

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha))
299.0ms
(/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))
356.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))
387.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))) 1.0)

simplify642.0ms

Counts
419 → 419
Iterations
IterNodes
done5001
11256
0416

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (+ alpha beta) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))))
0.3b
(/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))
7.4b
(+ (* (/ (+ alpha beta) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))) 1.0)

rewrite998.0ms

Algorithm
rewrite-expression-head
Rules
967×*-un-lft-identity
848×times-frac
511×add-sqr-sqrt
321×sqrt-prod
317×add-cube-cbrt
288×distribute-lft-out
218×associate-*r*
68×distribute-lft-out-- difference-of-squares
58×associate-/r/
42×associate-*l*
39×flip3-+ flip-+
32×add-cbrt-cube add-exp-log
30×associate-/l*
24×sqrt-div
21×div-inv
16×associate-/r* frac-add
15×unswap-sqr
13×cbrt-undiv div-exp
6×pow1 prod-exp cbrt-unprod add-log-exp
3×associate-/l/
2×clear-num frac-2neg div-sub
1×frac-times +-commutative sum-log pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 638
Calls
4 calls:
602.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))))
145.0ms
(/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))
75.0ms
(/ (+ alpha beta) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))
130.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))) 1.0)

series1.3s

Counts
4 → 12
Calls
4 calls:
366.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))))
339.0ms
(/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))
192.0ms
(/ (+ alpha beta) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))
395.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0)))) (/ (/ (- beta alpha) (+ (+ (* 2.0 i) beta) alpha)) (sqrt (+ (+ alpha beta) (+ (* 2.0 i) 2.0))))) 1.0)

simplify846.0ms

Counts
650 → 650
Iterations
IterNodes
done5001
12034
0622

prune3.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

localize88.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (- beta alpha) (+ (+ beta (* 2.0 i)) alpha)) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i)))))
0.4b
(/ (+ beta alpha) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i)))))
7.4b
(+ (cbrt (pow (* (/ (/ (- beta alpha) (+ (+ beta (* 2.0 i)) alpha)) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i))))) (/ (+ beta alpha) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i)))))) 3)) 1.0)
11.5b
(cbrt (pow (* (/ (/ (- beta alpha) (+ (+ beta (* 2.0 i)) alpha)) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i))))) (/ (+ beta alpha) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i)))))) 3))

rewrite297.0ms

Algorithm
rewrite-expression-head
Rules
510×*-un-lft-identity
420×times-frac
240×add-sqr-sqrt
168×add-cube-cbrt
160×sqrt-prod
151×distribute-lft-out
36×distribute-lft-out-- difference-of-squares
30×associate-/r/ associate-/l*
21×flip3-+ flip-+
16×associate-/r*
12×sqrt-div
11×add-cbrt-cube add-exp-log div-inv
8×cbrt-prod frac-add
6×add-log-exp
4×pow1 cbrt-undiv div-exp
3×cube-div cbrt-div associate-/l/
2×clear-num frac-2neg div-sub
1×cube-mult frac-times +-commutative sum-log unpow-prod-down pow1/3 unpow3 cube-prod associate-*l/ associate-*r/ rem-cbrt-cube sqr-pow
Counts
4 → 360
Calls
4 calls:
146.0ms
(/ (/ (- beta alpha) (+ (+ beta (* 2.0 i)) alpha)) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i)))))
95.0ms
(/ (+ beta alpha) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i)))))
31.0ms
(+ (cbrt (pow (* (/ (/ (- beta alpha) (+ (+ beta (* 2.0 i)) alpha)) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i))))) (/ (+ beta alpha) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i)))))) 3)) 1.0)
4.0ms
(cbrt (pow (* (/ (/ (- beta alpha) (+ (+ beta (* 2.0 i)) alpha)) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i))))) (/ (+ beta alpha) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i)))))) 3))

series1.2s

Counts
4 → 12
Calls
4 calls:
315.0ms
(/ (/ (- beta alpha) (+ (+ beta (* 2.0 i)) alpha)) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i)))))
200.0ms
(/ (+ beta alpha) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i)))))
311.0ms
(+ (cbrt (pow (* (/ (/ (- beta alpha) (+ (+ beta (* 2.0 i)) alpha)) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i))))) (/ (+ beta alpha) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i)))))) 3)) 1.0)
383.0ms
(cbrt (pow (* (/ (/ (- beta alpha) (+ (+ beta (* 2.0 i)) alpha)) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i))))) (/ (+ beta alpha) (sqrt (+ (+ alpha beta) (+ 2.0 (* 2.0 i)))))) 3))

simplify721.0ms

Counts
372 → 372
Iterations
IterNodes
done5001
11355
0499

prune2.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.6b

regimes618.0ms

Accuracy

12.9% (5.9b remaining)

Error of 11.8b against oracle of 5.9b and baseline of 12.7b

bsearch156.0ms

Steps
ItersRangePoint
9
2.5571677378596085e+141
6.851744006698495e+147
3.5065776138048876e+145

simplify6.0ms

Iterations
IterNodes
done58
258
156
045

end0.0ms

sample2.0s

Algorithm
intervals
Results
616.0ms6316×body80valid
333.0ms519×body1280valid
294.0ms8000×pre80true
197.0ms385×body320valid
184.0ms582×body640valid
32.0ms198×body160valid