Details

Time bar (total: 8.0s)

sample21.0ms

Algorithm
intervals
Results
6.0ms60×body640valid
4.0ms136×body80valid
2.0ms18×body1280valid
2.0ms26×body320valid
1.0ms16×body160valid

simplify63.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
11815
23115
34115
45215
55915
66815
78615
810715
911715
done11715

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.1b

localize8.0ms

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))
2.7b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite224.0ms

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:
5.0ms
(/ 1.0 (- x 1.0))
5.0ms
(/ 1.0 (+ x 1.0))
36.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
173.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ 1.0 (- x 1.0))
30.0ms
(/ 1.0 (+ x 1.0))
42.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
218.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.6s

Counts
126 → 126
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02131832
14991716
212881630
337761608
done50001607

prune248.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
17.1b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ 1.0 (cbrt (- x 1.0)))))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
9×frac-add add-log-exp
7×add-cube-cbrt
6×cbrt-div flip3-- flip--
4×pow1 add-exp-log add-cbrt-cube
3×frac-times pow1/3 associate-*r/ associate-*l/ frac-sub distribute-lft-out-- difference-of-squares
2×associate-+l+ sum-log
1×+-commutative associate-+l- sub-neg flip3-+ diff-log flip-+
Counts
4 → 69
Calls
4 calls:
2.0ms
(cbrt (- x 1.0))
2.0ms
(cbrt (- x 1.0))
2.0ms
(cbrt (- x 1.0))
159.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ 1.0 (cbrt (- x 1.0)))))

series548.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(cbrt (- x 1.0))
99.0ms
(cbrt (- x 1.0))
104.0ms
(cbrt (- x 1.0))
246.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ 1.0 (cbrt (- x 1.0)))))

simplify621.0ms

Counts
81 → 81
Iterations

Useful iterations: done (618.0ms)

IterNodesCost
01912013
15171859
216021562
done50001498

prune271.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ x 1.0) x)
0.0b
(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b
(* (* (+ x 1.0) x) (- x 1.0))
17.3b
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
46×associate-*l/
16×flip3-- frac-add flip--
13×flip3-+ flip-+
12×frac-times
11×pow1 add-exp-log add-sqr-sqrt *-un-lft-identity add-cbrt-cube
8×associate-*r* add-log-exp
7×add-cube-cbrt
6×associate-*r/
5×sub-neg associate-*l*
4×distribute-rgt-in associate-+l+ distribute-lft-in pow-prod-down prod-exp cbrt-unprod
2×*-commutative
1×+-commutative diff-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 96
Calls
4 calls:
9.0ms
(* (+ x 1.0) x)
2.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
19.0ms
(* (* (+ x 1.0) x) (- x 1.0))
10.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series183.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (+ x 1.0) x)
37.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
99.0ms
(* (* (+ x 1.0) x) (- x 1.0))
1.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify1.5s

Counts
108 → 108
Iterations

Useful iterations: 2 (446.0ms)

IterNodesCost
02242834
17612668
235442528
done50012528

prune275.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ x 1.0) x)
0.0b
(* (* (+ x 1.0) x) (- x 1.0))
0.2b
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log add-cbrt-cube
18×associate-*l/
12×add-sqr-sqrt *-un-lft-identity
10×pow1
8×frac-times add-cube-cbrt associate-*r* associate-/r/
7×flip3-+ prod-exp cbrt-unprod flip-+
6×flip3-- flip--
5×associate-*l*
4×associate-*r/ pow-prod-down
3×cbrt-undiv times-frac div-exp associate-/l* add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in *-commutative
1×frac-2neg clear-num associate-/r* div-inv distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 84
Calls
3 calls:
9.0ms
(* (+ x 1.0) x)
18.0ms
(* (* (+ x 1.0) x) (- x 1.0))
16.0ms
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series232.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(* (+ x 1.0) x)
98.0ms
(* (* (+ x 1.0) x) (- x 1.0))
91.0ms
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify782.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (282.0ms)

IterNodesCost
01541283
14261247
217781075
done50011075

prune170.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes21.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11513
done1513

end0.0ms

sample566.0ms

Algorithm
intervals
Results
191.0ms1837×body640valid
114.0ms4155×body80valid
75.0ms550×body1280valid
73.0ms976×body320valid
25.0ms482×body160valid