Details

Time bar (total: 19.4s)

sample53.0ms

Algorithm
intervals
Results
16.0ms70×body640valid
10.0ms31×body320valid
7.0ms124×body80valid
6.0ms20×body1280valid
1.0ms11×body160valid

simplify117.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (- x 1.0))
0.0b
(/ 1.0 (+ x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.4b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite566.0ms

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity
47×times-frac
43×add-sqr-sqrt
23×add-cube-cbrt
14×distribute-lft-out--
13×distribute-lft-out
11×add-log-exp
9×associate-/r*
8×add-exp-log add-cbrt-cube difference-of-squares
6×associate-/l*
4×pow1 associate-/r/
3×flip3-- frac-add flip--
2×cbrt-undiv sub-neg associate-+l+ frac-2neg flip3-+ diff-log div-exp clear-num sum-log frac-sub flip-+ div-inv
1×+-commutative associate-+l-
Counts
4 → 114
Calls
4 calls:
21.0ms
(/ 1.0 (- x 1.0))
23.0ms
(/ 1.0 (+ x 1.0))
91.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
424.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ 1.0 (- x 1.0))
46.0ms
(/ 1.0 (+ x 1.0))
75.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
297.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify730.0ms

Counts
126 → 126

prune407.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
0.2b
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
1.4b
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
15.3b
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
340×*-un-lft-identity
225×times-frac
176×add-sqr-sqrt
150×frac-sub
101×distribute-lft-out--
94×frac-times
65×add-cube-cbrt
64×flip3-- flip--
52×associate-*r/ associate-*l/
51×difference-of-squares
47×associate-/l/
41×swap-sqr
31×associate-*r* associate-*l*
20×add-exp-log add-cbrt-cube
18×pow1
16×distribute-lft-out
13×associate-/r/
11×associate-/r*
6×add-log-exp
5×cbrt-undiv sub-neg div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×distribute-rgt-in distribute-lft-in associate--l+ associate-/l*
2×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up
1×frac-2neg diff-log div-sub clear-num
Counts
4 → 352
Calls
4 calls:
116.0ms
(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
609.0ms
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
235.0ms
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
1.0s
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
90.0ms
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
344.0ms
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
1.0s
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

simplify1.1s

Counts
364 → 364

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
1.4b
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
15.2b
(sqrt (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))))
15.2b
(sqrt (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
276×frac-sub
168×frac-times
100×flip3-- flip--
96×associate-*r/ associate-*l/
94×sqrt-div
8×add-sqr-sqrt associate--l+ sqrt-prod add-log-exp
6×pow1 add-cube-cbrt sub-neg *-un-lft-identity
4×add-exp-log distribute-rgt-in distribute-lft-in add-cbrt-cube difference-of-squares
2×rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 246
Calls
4 calls:
185.0ms
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
281.0ms
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
348.0ms
(sqrt (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))))
325.0ms
(sqrt (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))))

series2.0s

Counts
4 → 12
Calls
4 calls:
318.0ms
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
360.0ms
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
630.0ms
(sqrt (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))))
669.0ms
(sqrt (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))))

simplify1.9s

Counts
258 → 258

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
0.0b
(/ 1 (pow x 7))
0.2b
(/ 1 (pow x 5))
0.2b
(/ 1 (pow x 3))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
73×*-un-lft-identity
63×add-sqr-sqrt add-cube-cbrt
36×unpow-prod-down
31×add-exp-log
26×associate-/r*
18×div-exp
12×cube-prod sqr-pow
10×add-cbrt-cube
9×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
7×div-inv distribute-lft-out
6×add-log-exp
4×pow1 cube-mult unpow3
3×cbrt-undiv pow-flip frac-2neg clear-num inv-pow
1×+-commutative flip3-+ frac-add sum-log flip-+
Counts
4 → 198
Calls
4 calls:
94.0ms
(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
15.0ms
(/ 1 (pow x 7))
10.0ms
(/ 1 (pow x 5))
13.0ms
(/ 1 (pow x 3))

series419.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(+ (/ 1 (pow x 5)) (/ 1 (pow x 3)))
99.0ms
(/ 1 (pow x 7))
70.0ms
(/ 1 (pow x 5))
55.0ms
(/ 1 (pow x 3))

simplify945.0ms

Counts
210 → 210

prune875.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes41.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 25.6b

bsearch200.0ms

Steps
ItersRangePoint
9
15.61478477777618
1958959.7701095298
467.25477516617156
10
-380908646326105.1
-0.06705623481545048
-75080727.03464015

simplify703.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
487.0ms1876×body640valid
358.0ms4183×body80valid
186.0ms551×body1280valid
175.0ms906×body320valid
48.0ms486×body160valid