Details

Time bar (total: 42.7s)

sample58.0ms

Algorithm
intervals
Results
15.0ms256×pre80true
11.0ms207×body80valid
5.0ms24×body640valid
3.0ms13×body1280valid
1.0ms6×body320valid
1.0ms6×body160valid

simplify1.2s

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* 2.0 i))
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)
19.4b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
54×times-frac
48×*-un-lft-identity
26×add-sqr-sqrt add-cube-cbrt
18×add-cbrt-cube add-exp-log
14×associate-/r/
12×flip3-+ flip-+
11×distribute-lft-out add-log-exp
10×associate-/l*
9×associate-/l/
7×cbrt-undiv associate-/r* div-exp div-inv
4×frac-times pow1 sum-log
3×flip3-- flip--
2×+-commutative clear-num frac-2neg associate-*l/ prod-exp associate-*r/ cbrt-unprod
1×associate-+l+
Counts
4 → 124
Calls
4 calls:
30.0ms
(+ (+ alpha beta) (* 2.0 i))
215.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
728.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
63.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series842.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (+ alpha beta) (* 2.0 i))
361.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
347.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
109.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify1.7s

Counts
136 → 136
Iterations
IterNodes
done5002
24533
1716
0235

prune904.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite916.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
51×add-sqr-sqrt
45×times-frac
28×add-cube-cbrt
26×associate-*r*
20×add-cbrt-cube add-exp-log
15×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
8×associate-/r* flip3-+ flip-+
7×associate-/l/
6×pow1 cbrt-undiv div-exp associate-/r/ associate-/l* add-log-exp
4×frac-times associate-*l* associate-*l/ prod-exp cbrt-unprod
3×div-inv
2×clear-num frac-2neg associate-*r/ unswap-sqr
1×+-commutative sum-log flip3-- div-sub pow-prod-down *-commutative flip--
Counts
4 → 140
Calls
4 calls:
52.0ms
(/ (- beta alpha) (+ (+ (* i 2.0) beta) alpha))
160.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ (* i 2.0) beta) alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
152.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ (* i 2.0) beta) alpha)))
547.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ (* i 2.0) beta) alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series1.0s

Counts
4 → 12
Calls
4 calls:
123.0ms
(/ (- beta alpha) (+ (+ (* i 2.0) beta) alpha))
327.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ (* i 2.0) beta) alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
132.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ (* i 2.0) beta) alpha)))
423.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ (* i 2.0) beta) alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify2.1s

Counts
152 → 152
Iterations
IterNodes
done5001
24679
1692
0230

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha (* i 2.0)) beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha (* i 2.0)) beta))))
0.2b
(* (- beta alpha) (/ 1 (+ (+ alpha (* i 2.0)) beta)))
2.6b
(+ (/ (* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha (* i 2.0)) beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite931.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log
38×frac-times
33×*-un-lft-identity
32×add-cbrt-cube
25×add-sqr-sqrt
22×prod-exp
20×associate-/l/
19×associate-*r* associate-*r/
18×times-frac associate-*l/
17×flip3-+ flip-+
16×add-cube-cbrt
14×flip3-- flip--
12×div-exp cbrt-unprod
11×pow1
9×associate-*l*
7×cbrt-undiv un-div-inv distribute-lft-out
6×add-log-exp
4×associate-/r* pow-prod-down associate-/r/
3×rec-exp 1-exp unswap-sqr
2×*-commutative div-inv
1×+-commutative clear-num sum-log frac-2neg associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 153
Calls
4 calls:
182.0ms
(/ (* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha (* i 2.0)) beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
89.0ms
(* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha (* i 2.0)) beta))))
87.0ms
(* (- beta alpha) (/ 1 (+ (+ alpha (* i 2.0)) beta)))
566.0ms
(+ (/ (* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha (* i 2.0)) beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
386.0ms
(/ (* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha (* i 2.0)) beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
143.0ms
(* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha (* i 2.0)) beta))))
133.0ms
(* (- beta alpha) (/ 1 (+ (+ alpha (* i 2.0)) beta)))
411.0ms
(+ (/ (* (+ alpha beta) (* (- beta alpha) (/ 1 (+ (+ alpha (* i 2.0)) beta)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify508.0ms

Counts
165 → 165
Iterations
IterNodes
done5001
1886
0275

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize105.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ (+ alpha beta) (/ (+ (+ 2.0 (+ alpha beta)) (* i 2.0)) (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))))
1.1b
(/ (+ alpha beta) (/ (+ (+ 2.0 (+ alpha beta)) (* i 2.0)) (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))))
1.1b
(/ (+ alpha beta) (/ (+ (+ 2.0 (+ alpha beta)) (* i 2.0)) (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))))
1.1b
(+ (pow (/ (+ alpha beta) (/ (+ (+ 2.0 (+ alpha beta)) (* i 2.0)) (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta))))) 3) (pow 1.0 3))

rewrite3.3s

Algorithm
rewrite-expression-head
Rules
3066×times-frac
2435×*-un-lft-identity
1471×add-sqr-sqrt
1111×add-cube-cbrt
482×distribute-lft-out
249×associate-/r*
180×distribute-lft-out-- difference-of-squares
108×associate-/r/
63×div-inv
49×flip3-+ flip-+
31×add-cbrt-cube add-exp-log
18×cbrt-undiv div-exp
12×associate-/l*
6×add-log-exp associate-/l/
4×pow1 unpow-prod-down cube-prod
3×clear-num frac-2neg
1×+-commutative sum-log sum-cubes
Counts
4 → 1331
Calls
4 calls:
228.0ms
(/ (+ alpha beta) (/ (+ (+ 2.0 (+ alpha beta)) (* i 2.0)) (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))))
243.0ms
(/ (+ alpha beta) (/ (+ (+ 2.0 (+ alpha beta)) (* i 2.0)) (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))))
244.0ms
(/ (+ alpha beta) (/ (+ (+ 2.0 (+ alpha beta)) (* i 2.0)) (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))))
2.4s
(+ (pow (/ (+ alpha beta) (/ (+ (+ 2.0 (+ alpha beta)) (* i 2.0)) (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta))))) 3) (pow 1.0 3))

series8.3s

Counts
4 → 12
Calls
4 calls:
365.0ms
(/ (+ alpha beta) (/ (+ (+ 2.0 (+ alpha beta)) (* i 2.0)) (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))))
314.0ms
(/ (+ alpha beta) (/ (+ (+ 2.0 (+ alpha beta)) (* i 2.0)) (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))))
340.0ms
(/ (+ alpha beta) (/ (+ (+ 2.0 (+ alpha beta)) (* i 2.0)) (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta)))))
7.3s
(+ (pow (/ (+ alpha beta) (/ (+ (+ 2.0 (+ alpha beta)) (* i 2.0)) (/ (- beta alpha) (+ alpha (+ (* i 2.0) beta))))) 3) (pow 1.0 3))

simplify1.7s

Counts
1343 → 1343
Iterations
IterNodes
done5001
11996
0669

prune11.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.3b

regimes566.0ms

Accuracy

-13.3% (7.5b remaining)

Error of 13.1b against oracle of 5.7b and baseline of 12.3b

bsearch209.0ms

Steps
ItersRangePoint
8
5.969670028271364e+165
2.0864758149000452e+170
2.2669802580153736e+166
9
1.2707568867468327e+57
9.927202395589815e+62
9.76982660809476e+62

simplify9.0ms

Iterations
IterNodes
done76
376
270
164
048

end0.0ms

sample2.4s

Algorithm
intervals
Results
721.0ms8000×pre80true
648.0ms6362×body80valid
240.0ms583×body640valid
223.0ms542×body1280valid
127.0ms329×body320valid
32.0ms184×body160valid