Details

Time bar (total: 8.6s)

sample26.0ms

Algorithm
intervals
Results
7.0ms136×body80valid
6.0ms60×body640valid
2.0ms18×body1280valid
2.0ms26×body320valid
1.0ms16×body160valid

simplify68.0ms

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

localize9.0ms

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)))

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
725×*-un-lft-identity
703×times-frac
524×add-sqr-sqrt
492×add-cube-cbrt
468×prod-diff
236×associate-+l+
95×distribute-lft-out
65×div-inv
58×associate-/r/
29×flip3-+ flip-+
18×fma-neg
17×distribute-lft-out--
12×difference-of-squares
11×add-log-exp
10×fma-def
9×associate-/r*
8×add-exp-log add-cbrt-cube
6×associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u
3×flip3-- frac-add flip--
2×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num sum-log frac-sub
1×+-commutative associate-+l-
Counts
4 → 618
Calls
4 calls:
5.0ms
(/ 1.0 (- x 1.0))
5.0ms
(/ 1.0 (+ x 1.0))
50.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
226.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ 1.0 (- x 1.0))
26.0ms
(/ 1.0 (+ x 1.0))
49.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
213.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.2s

Counts
630 → 630
Iterations

Useful iterations: done (1.2s)

IterNodesCost
050219834
1110017345
2290312902
done500012830

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

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))
30.1b
(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt prod-diff
11×pow1 add-exp-log distribute-rgt-in distribute-lft-in add-cbrt-cube
10×associate-*l/
8×associate-*r*
6×add-log-exp
5×associate-*l*
4×expm1-log1p-u frac-times flip3-- flip3-+ pow-prod-down prod-exp flip-- cbrt-unprod flip-+ log1p-expm1-u
3×sub-neg
2×associate-*r/ *-commutative
1×fma-neg diff-log fma-udef distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 101
Calls
4 calls:
9.0ms
(* (+ x 1.0) x)
3.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
25.0ms
(* (* (+ x 1.0) x) (- x 1.0))
0.0ms
(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

series371.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (+ x 1.0) x)
44.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
98.0ms
(* (* (+ x 1.0) x) (- x 1.0))
183.0ms
(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

simplify1.1s

Counts
113 → 113
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01881892
14981690
219631463
done50001445

prune235.0ms

Pruning

4 alts after pruning (4 fresh and 0 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)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
19×add-exp-log add-cbrt-cube
18×prod-diff associate-*l/
11×distribute-rgt-in distribute-lft-in
10×pow1
8×frac-times 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 expm1-log1p-u times-frac div-exp log1p-expm1-u associate-/l* add-log-exp
2×sub-neg *-commutative
1×frac-2neg clear-num associate-/r* div-inv distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 108
Calls
3 calls:
10.0ms
(* (+ x 1.0) x)
25.0ms
(* (* (+ x 1.0) x) (- x 1.0))
17.0ms
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series239.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(* (+ x 1.0) x)
98.0ms
(* (* (+ x 1.0) x) (- x 1.0))
92.0ms
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify1.0s

Counts
117 → 117
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02061975
15581770
222371511
done50001493

prune188.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (- x 1.0))
0.0b
(* (+ x 1.0) x)
0.1b
(* (/ 1 (* (+ x 1.0) x)) (/ 2.0 (- x 1.0)))
0.4b
(/ 1 (* (+ x 1.0) x))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
50×add-sqr-sqrt
45×*-un-lft-identity
37×times-frac
34×add-cbrt-cube
29×add-cube-cbrt
24×associate-*r* prod-exp
20×div-exp
13×associate-*l*
11×pow1
10×cbrt-undiv cbrt-unprod
8×associate-/r/
7×associate-*l/ distribute-lft-out-- difference-of-squares
6×rec-exp 1-exp associate-/r* associate-/l*
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×flip3-+ pow-prod-down flip-+ unswap-sqr
2×flip3-- pow-flip frac-2neg clear-num *-commutative flip--
1×frac-times associate-*r/ distribute-lft-out inv-pow
Counts
4 → 160
Calls
4 calls:
5.0ms
(/ 2.0 (- x 1.0))
10.0ms
(* (+ x 1.0) x)
42.0ms
(* (/ 1 (* (+ x 1.0) x)) (/ 2.0 (- x 1.0)))
8.0ms
(/ 1 (* (+ x 1.0) x))

series202.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ 2.0 (- x 1.0))
48.0ms
(* (+ x 1.0) x)
93.0ms
(* (/ 1 (* (+ x 1.0) x)) (/ 2.0 (- x 1.0)))
31.0ms
(/ 1 (* (+ x 1.0) x))

simplify814.0ms

Counts
172 → 172
Iterations

Useful iterations: 2 (310.0ms)

IterNodesCost
02452225
16661974
222051700
done50011700

prune294.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes24.0ms

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: 1 (1.0ms)

IterNodesCost
01013
11211
done1211

end0.0ms

sample596.0ms

Algorithm
intervals
Results
200.0ms1837×body640valid
124.0ms4155×body80valid
77.0ms976×body320valid
76.0ms550×body1280valid
26.0ms482×body160valid