Details

Time bar (total: 27.1s)

sample75.0ms

Algorithm
intervals
Results
28.0ms67×body640valid
13.0ms120×body80valid
11.0ms32×body320valid
9.0ms17×body1280valid
4.0ms20×body160valid

simplify203.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.2b

localize26.0ms

Local error

Found 4 expressions with local error:

2.9b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b
(- (/ 1 (+ x 1)) (/ 2 x))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
58×add-sqr-sqrt
56×times-frac
25×add-cube-cbrt
18×distribute-lft-out--
17×distribute-lft-out
14×difference-of-squares
12×add-exp-log
11×associate-/r* add-log-exp
8×add-cbrt-cube div-inv
6×pow1 associate-/l*
4×difference-of-sqr-1 div-exp associate-/r/ insert-posit16
3×flip3-- frac-add flip--
2×cbrt-undiv rec-exp associate-+l+ clear-num sum-log sub-neg frac-2neg flip3-+ diff-log 1-exp frac-sub flip-+ pow-flip inv-pow
1×+-commutative associate-+l-
Counts
4 → 141
Calls
4 calls:
Slowest
164.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
31.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
14.0ms
(/ 1 (- x 1))
14.0ms
(/ 1 (+ x 1))

series169.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
40.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
15.0ms
(/ 1 (- x 1))
14.0ms
(/ 1 (+ x 1))

simplify1.8s

Counts
153 → 153

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

2.9b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
2.9b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
2.9b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.3b
(* (cbrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))) (cbrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
597×*-un-lft-identity
192×distribute-lft-out
164×cbrt-prod
156×times-frac
154×distribute-lft-out--
95×div-inv
70×swap-sqr
60×cbrt-div
45×frac-add
25×frac-times
20×add-sqr-sqrt
19×add-log-exp
16×associate-*r* associate-*l*
15×flip3-+ flip3-- frac-sub flip-+ flip--
12×add-cube-cbrt
11×pow1
6×associate-+l+ sum-log pow1/3 add-exp-log
5×associate-*l/ associate-*r/
4×add-cbrt-cube insert-posit16 unswap-sqr
3×+-commutative sub-neg diff-log associate-+l-
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 247
Calls
4 calls:
Slowest
867.0ms
(* (cbrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))) (cbrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))))
164.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
163.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
157.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series652.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
268.0ms
(* (cbrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))) (cbrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))))
149.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
132.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
103.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify2.5s

Counts
259 → 259

prune2.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize62.0ms

Local error

Found 4 expressions with local error:

2.9b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
2.9b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
2.9b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
2.9b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite664.0ms

Algorithm
rewrite-expression-head
Rules
160×*-un-lft-identity
48×times-frac distribute-lft-out
40×distribute-lft-out--
24×add-log-exp
20×div-inv
12×frac-add
8×associate-+l+ sum-log
4×add-sqr-sqrt pow1 +-commutative sub-neg flip3-+ flip3-- add-cbrt-cube diff-log add-exp-log frac-sub add-cube-cbrt associate-+l- flip-+ insert-posit16 flip--
Counts
4 → 116
Calls
4 calls:
Slowest
196.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
179.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
153.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
130.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series520.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
135.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
127.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
116.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify1.5s

Counts
128 → 128

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

17.0b
(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
2.9b
(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
0.3b
(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
0.1b
(* (/ 1 (- x 1)) (/ 1 (- x 1)))

rewrite830.0ms

Algorithm
rewrite-expression-head
Rules
440×*-un-lft-identity
306×times-frac
271×add-sqr-sqrt
196×frac-sub
146×distribute-lft-out--
112×frac-times
87×difference-of-squares
82×add-cube-cbrt
80×flip3-- flip--
62×swap-sqr associate-/l/
58×associate-*l/ associate-*r/
48×add-exp-log
40×associate-*r* associate-*l* div-inv
31×un-div-inv
26×pow1
20×add-cbrt-cube
18×difference-of-sqr-1
17×div-exp prod-exp
16×associate-/r* distribute-lft-out
13×associate-/r/
10×unswap-sqr
8×rec-exp 1-exp pow-flip inv-pow
6×pow-prod-up add-log-exp
5×cbrt-undiv sub-neg cbrt-unprod
4×distribute-rgt-in distribute-lft-in pow-prod-down associate--l+ pow-sqr insert-posit16 associate-/l*
2×pow2 pow-plus *-commutative
1×clear-num frac-2neg diff-log div-sub
Counts
4 → 476
Calls
4 calls:
Slowest
459.0ms
(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
190.0ms
(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
122.0ms
(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
35.0ms
(* (/ 1 (- x 1)) (/ 1 (- x 1)))

series635.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
449.0ms
(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
124.0ms
(- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1))))
35.0ms
(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
27.0ms
(* (/ 1 (- x 1)) (/ 1 (- x 1)))

simplify1.4s

Counts
488 → 488

prune6.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes173.0ms

Accuracy

99.6% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 9.8b

bsearch166.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
989.0ms1865×body640valid
426.0ms4150×body80valid
362.0ms919×body320valid
324.0ms623×body1280valid
85.0ms445×body160valid