Details

Time bar (total: 10.4s)

sample25.0ms

Algorithm
intervals
Results
6.0ms55×body640valid
5.0ms31×body320valid
4.0ms135×body80valid
3.0ms22×body1280valid
1.0ms13×body160valid

simplify84.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
11815
23115
34115
45215
56515
68015
710315
812315
914115
done14115

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.4b

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))
1.9b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite364.0ms

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))
6.0ms
(/ 1.0 (+ x 1.0))
54.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
243.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series315.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ 1.0 (- x 1.0))
29.0ms
(/ 1.0 (+ x 1.0))
42.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
216.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.5s

Counts
630 → 630
Iterations

Useful iterations: done (1.4s)

IterNodesCost
050219834
1115917345
2359912902
done500012830

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b
(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.0b
(* (* (+ x 1.0) x) (- x 1.0))
30.0b
(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt prod-diff
18×add-exp-log add-cbrt-cube
16×associate-*l/
11×distribute-rgt-in distribute-lft-in
9×pow1
8×frac-times associate-/r/
7×flip3-- flip--
6×flip3-+ prod-exp cbrt-unprod flip-+ add-log-exp
5×associate-*r*
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×cbrt-undiv sub-neg times-frac div-exp pow-prod-down associate-/l*
1×frac-2neg fma-neg diff-log associate-*l* clear-num associate-/r* *-commutative fma-udef div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 111
Calls
4 calls:
3.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
17.0ms
(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
26.0ms
(* (* (+ x 1.0) x) (- x 1.0))
1.0ms
(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

series632.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
303.0ms
(/ (fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
99.0ms
(* (* (+ x 1.0) x) (- x 1.0))
186.0ms
(fma (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0) (* (* (+ x 1.0) x) 1.0))

simplify1.2s

Counts
123 → 123
Iterations

Useful iterations: 2 (212.0ms)

IterNodesCost
02273140
16412926
228602460
done50002460

prune274.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.9b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 2.0 (pow x 5))
0.2b
(/ 2.0 (pow x 7))
0.9b
(/ 2.0 (pow x 3))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
60×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
36×unpow-prod-down
26×associate-/r*
18×add-exp-log
12×cube-prod sqr-pow
9×div-exp add-cbrt-cube associate-/l*
4×cube-mult unpow3
3×pow1 cbrt-undiv expm1-log1p-u pow-to-exp frac-2neg pow-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
3 → 161
Calls
3 calls:
4.0ms
(/ 2.0 (pow x 5))
4.0ms
(/ 2.0 (pow x 7))
6.0ms
(/ 2.0 (pow x 3))

series180.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(/ 2.0 (pow x 5))
81.0ms
(/ 2.0 (pow x 7))
49.0ms
(/ 2.0 (pow x 3))

simplify645.0ms

Counts
170 → 170
Iterations

Useful iterations: 2 (179.0ms)

IterNodesCost
02341776
14401542
215361494
done50001494

prune440.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (pow x 5))
0.1b
(* (/ 1 (* x x)) (/ 2.0 x))
0.2b
(/ 2.0 (pow x 7))
0.5b
(/ 1 (* x x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
70×add-exp-log
64×times-frac
60×add-sqr-sqrt
49×*-un-lft-identity
47×add-cube-cbrt
34×add-cbrt-cube
25×div-exp
24×unpow-prod-down
23×prod-exp
15×associate-/r*
14×pow1
13×associate-*r*
11×cbrt-undiv
9×cbrt-unprod associate-/l*
8×sqr-pow
7×associate-*l*
6×rec-exp pow-flip 1-exp unswap-sqr
5×div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×pow-to-exp pow-prod-down pow-exp
1×pow2 frac-times pow-plus associate-*r/ associate-*l/ pow-sqr *-commutative pow-prod-up inv-pow
Counts
4 → 188
Calls
4 calls:
4.0ms
(/ 2.0 (pow x 5))
22.0ms
(* (/ 1 (* x x)) (/ 2.0 x))
4.0ms
(/ 2.0 (pow x 7))
5.0ms
(/ 1 (* x x))

series174.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ 2.0 (pow x 5))
44.0ms
(* (/ 1 (* x x)) (/ 2.0 x))
60.0ms
(/ 2.0 (pow x 7))
21.0ms
(/ 1 (* x x))

simplify2.0s

Counts
200 → 200
Iterations

Useful iterations: 2 (508.0ms)

IterNodesCost
02772109
16611808
230401551
done50001551

prune465.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes61.0ms

Accuracy

94.8% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 9.7b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
036102
148102
done48102

end0.0ms

sample603.0ms

Algorithm
intervals
Results
203.0ms1886×body640valid
124.0ms4185×body80valid
80.0ms550×body1280valid
79.0ms961×body320valid
23.0ms420×body160valid