Details

Time bar (total: 36.4s)

sample190.0ms

Algorithm
intervals
Results
47.0ms280×body80nan
47.0ms256×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02833
15033
210633
337333
4149733
done500133

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.5b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b
(* z (sqrt (+ t a)))
0.3b
(/ 2.0 (* t 3.0))
2.2b
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.9b
(/ (* z (sqrt (+ t a))) t)

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
20×frac-sub
16×add-exp-log add-cbrt-cube
15×add-sqr-sqrt
13×*-un-lft-identity
11×add-cube-cbrt
9×flip3-- flip--
8×frac-times associate-*r/
7×associate-*r*
6×pow1 times-frac associate--r+ add-log-exp
5×flip3-+ sqrt-prod flip-+
4×cbrt-undiv sqrt-div div-exp associate-/r* associate-/l*
3×distribute-rgt-in sub-neg distribute-lft-in associate-*l* prod-exp cbrt-unprod
2×frac-2neg associate-*l/ associate--l+ clear-num div-inv associate-/l/ unswap-sqr
1×diff-log pow-prod-down *-commutative distribute-lft-out
Counts
4 → 101
Calls
4 calls:
51.0ms
(* z (sqrt (+ t a)))
8.0ms
(/ 2.0 (* t 3.0))
67.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
24.0ms
(/ (* z (sqrt (+ t a))) t)

series586.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* z (sqrt (+ t a)))
38.0ms
(/ 2.0 (* t 3.0))
332.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
139.0ms
(/ (* z (sqrt (+ t a))) t)

simplify2.4s

Counts
113 → 113
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
03442616
110152408
243572288
done50002288

prune866.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 0.6666666666666666 t)))
0.3b
(* z (sqrt (+ t a)))
2.2b
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 0.6666666666666666 t))))
5.9b
(/ (* z (sqrt (+ t a))) t)

rewrite416.0ms

Algorithm
rewrite-expression-head
Rules
26×frac-sub
24×add-sqr-sqrt
20×*-un-lft-identity
17×flip3-- flip--
16×frac-times
14×associate-*r*
13×add-exp-log add-cbrt-cube
12×associate-*r/
11×add-cube-cbrt
8×pow1 flip3-+ associate-*l* flip-+
6×distribute-rgt-in distribute-lft-in associate--r+ add-log-exp
5×sub-neg sqrt-prod
4×times-frac sqrt-div associate-*l/ associate--l+
3×prod-exp associate-/r* cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
2×cbrt-undiv div-exp pow-prod-down *-commutative associate-/l/ distribute-lft-out
1×frac-2neg diff-log clear-num div-inv associate-/l*
Counts
4 → 124
Calls
4 calls:
297.0ms
(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 0.6666666666666666 t)))
42.0ms
(* z (sqrt (+ t a)))
54.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 0.6666666666666666 t))))
18.0ms
(/ (* z (sqrt (+ t a))) t)

series629.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 0.6666666666666666 t)))
96.0ms
(* z (sqrt (+ t a)))
293.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 0.6666666666666666 t))))
126.0ms
(/ (* z (sqrt (+ t a))) t)

simplify2.5s

Counts
136 → 136
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
03503379
110113127
243382999
done50022999

prune898.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize64.0ms

Local error

Found 4 expressions with local error:

2.8b
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
3.4b
(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
6.8b
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
26.7b
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
766×associate-*l/
764×associate-*r/
524×frac-sub
498×flip3-- flip--
364×frac-times
240×sqrt-div
162×associate-/l/
120×flip3-+ flip-+
28×add-exp-log add-cbrt-cube
16×distribute-rgt-in distribute-lft-in
14×pow1
12×prod-exp cbrt-unprod
9×sub-neg
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate--r+
7×associate-*l*
6×pow-prod-down add-log-exp
4×cbrt-undiv div-exp
3×times-frac associate-/l*
2×associate-*r* associate-/r/ *-commutative
1×frac-2neg diff-log div-sub clear-num associate-/r* div-inv difference-of-squares
Counts
4 → 437
Calls
4 calls:
44.0ms
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
461.0ms
(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
631.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
1.1s
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

series2.5s

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
304.0ms
(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
978.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
1.1s
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

simplify2.6s

Counts
449 → 449
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0115350141
1461544541
done500043557

prune9.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(* c (+ a 0.8333333333333334))
0.0b
(* y (exp (* 2.0 (- (* c (+ a 0.8333333333333334)) (* a b)))))
0.0b
(/ x (+ x (* y (exp (* 2.0 (- (* c (+ a 0.8333333333333334)) (* a b)))))))
1.8b
(- (* c (+ a 0.8333333333333334)) (* a b))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×*-un-lft-identity
16×add-cube-cbrt
15×associate-*r*
10×add-cbrt-cube
9×add-exp-log times-frac
8×pow1 distribute-rgt-in distribute-lft-in exp-sum
6×associate-*l* associate--l+ add-log-exp
3×sub-neg associate-/r* associate-/l*
2×flip3-+ associate-*r/ pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod flip-+ unswap-sqr
1×cbrt-undiv flip3-- frac-2neg diff-log div-exp clear-num flip-- div-inv distribute-lft-out
Counts
4 → 92
Calls
4 calls:
32.0ms
(* c (+ a 0.8333333333333334))
76.0ms
(* y (exp (* 2.0 (- (* c (+ a 0.8333333333333334)) (* a b)))))
15.0ms
(/ x (+ x (* y (exp (* 2.0 (- (* c (+ a 0.8333333333333334)) (* a b)))))))
22.0ms
(- (* c (+ a 0.8333333333333334)) (* a b))

series367.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* c (+ a 0.8333333333333334))
115.0ms
(* y (exp (* 2.0 (- (* c (+ a 0.8333333333333334)) (* a b)))))
158.0ms
(/ x (+ x (* y (exp (* 2.0 (- (* c (+ a 0.8333333333333334)) (* a b)))))))
47.0ms
(- (* c (+ a 0.8333333333333334)) (* a b))

simplify2.9s

Counts
104 → 104
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01811748
14231669
211631533
341881531
done50011531

prune477.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes407.0ms

Accuracy

-7.5% (3.5b remaining)

Error of 4.0b against oracle of 0.4b and baseline of 3.7b

bsearch574.0ms

Steps
ItersRangePoint
9
2.5571904280608065e-113
1.1606791802233116e-106
3.585798647479515e-110
7
-8.64205799040136e-295
-3.387906247697725e-297
-5.86945893495286e-296

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
054137
175107
done75107

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.8s8000×body80valid
1.2s8153×body80nan