Details

Time bar (total: 16.7s)

sample32.0ms

Algorithm
intervals
Results
11.0ms124×body80valid
7.0ms62×body640valid
4.0ms48×body320valid
1.0ms22×body160valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11211
21511
done1511

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (- x 1.0))
0.0b
(/ 1.0 (+ x 1.0))
2.2b
(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite275.0ms

Algorithm
rewrite-expression-head
Rules
662×*-un-lft-identity
589×times-frac
496×add-sqr-sqrt
378×prod-diff
368×add-cube-cbrt
86×associate-/r/
79×distribute-lft-out--
76×distribute-lft-out
62×difference-of-squares
44×div-inv
24×flip-+
23×flip3-+
21×flip--
20×flip3--
18×fma-neg
9×associate-/r*
7×add-exp-log add-cbrt-cube
6×associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg diff-log frac-sub
Counts
3 → 504
Calls
3 calls:
18.0ms
(/ 1.0 (- x 1.0))
24.0ms
(/ 1.0 (+ x 1.0))
180.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series312.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ 1.0 (- x 1.0))
27.0ms
(/ 1.0 (+ x 1.0))
248.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify3.0s

Counts
513 → 513
Iterations

Useful iterations: done (2.9s)

IterNodesCost
052524322
1119421760
2266016242
done500212452

prune702.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 2.0 (* x x)) (/ 2.0 (pow x 4)))
0.1b
(/ 2.0 (pow x 6))
0.2b
(/ 2.0 (pow x 4))
0.3b
(/ 2.0 (* x x))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
42×*-un-lft-identity
40×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
19×add-exp-log
15×associate-/r*
13×add-cbrt-cube
9×associate-/l*
8×div-exp sqr-pow
7×fma-def
6×div-inv add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num
2×pow-to-exp pow-exp distribute-lft-out
1×+-commutative flip3-+ frac-add prod-exp sum-log cbrt-unprod flip-+
Counts
4 → 140
Calls
4 calls:
79.0ms
(+ (/ 2.0 (* x x)) (/ 2.0 (pow x 4)))
15.0ms
(/ 2.0 (pow x 6))
14.0ms
(/ 2.0 (pow x 4))
16.0ms
(/ 2.0 (* x x))

series288.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(+ (/ 2.0 (* x x)) (/ 2.0 (pow x 4)))
59.0ms
(/ 2.0 (pow x 6))
51.0ms
(/ 2.0 (pow x 4))
39.0ms
(/ 2.0 (* x x))

simplify1.7s

Counts
152 → 152
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02171559
14311423
211971321
done50001265

prune516.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))
0.1b
(/ 2.0 (pow x 6))
0.1b
(/ (/ 2.0 x) x)
0.2b
(/ 2.0 (pow x 4))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
185×times-frac
119×*-un-lft-identity
113×add-sqr-sqrt add-cube-cbrt
43×fma-def
24×unpow-prod-down
19×add-exp-log associate-/l*
17×associate-/r*
13×add-cbrt-cube
11×div-inv
9×div-exp
8×sqr-pow
6×add-log-exp
5×cbrt-undiv
4×pow1 expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num
2×pow-to-exp pow-exp distribute-lft-out
1×+-commutative flip3-+ frac-add sum-log flip-+ associate-/l/
Counts
4 → 225
Calls
4 calls:
99.0ms
(+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))
21.0ms
(/ 2.0 (pow x 6))
12.0ms
(/ (/ 2.0 x) x)
10.0ms
(/ 2.0 (pow x 4))

series256.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))
60.0ms
(/ 2.0 (pow x 6))
28.0ms
(/ (/ 2.0 x) x)
46.0ms
(/ 2.0 (pow x 4))

simplify1.4s

Counts
237 → 237
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03072234
16342060
214431883
done50001863

prune932.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 2.0 (pow x 4))
0.2b
(* (sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))) (sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))))
23.7b
(sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4))))
23.7b
(sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4))))

rewrite998.0ms

Algorithm
rewrite-expression-head
Rules
128×add-sqr-sqrt
75×times-frac
72×*-un-lft-identity
40×sqrt-prod
30×add-cube-cbrt sqrt-div
24×hypot-def
21×pow1
18×unpow-prod-down
14×distribute-lft-out
12×swap-sqr
11×add-exp-log
10×sqrt-pow1 flip3-+ pow1/2 frac-add flip-+ sqr-pow
9×frac-times
8×associate-*r* associate-*l* add-cbrt-cube
7×associate-/r*
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×associate-*r/ div-exp pow-prod-down associate-*l/ pow-sqr associate-/l*
2×rem-sqrt-square
1×cbrt-undiv pow2 pow-to-exp frac-2neg pow-plus sqrt-unprod pow-exp prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod div-inv
Counts
4 → 185
Calls
4 calls:
8.0ms
(/ 2.0 (pow x 4))
598.0ms
(* (sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))) (sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))))
197.0ms
(sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4))))
186.0ms
(sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4))))

series394.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ 2.0 (pow x 4))
131.0ms
(* (sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))) (sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))))
104.0ms
(sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4))))
111.0ms
(sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4))))

simplify3.3s

Counts
197 → 197
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
02164026
14112975
211352751
340072609
done50002609

prune838.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes85.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch130.0ms

Steps
ItersRangePoint
9
0.0033303272193615503
311302.39110615524
328.31674351864234
7
-1204.6599638446712
-30.191575632521864
-193.4128241359247

simplify23.0ms

Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
03471
14554
done4554

end0.0ms

sample1.1s

Algorithm
intervals
Results
413.0ms1905×body640valid
279.0ms4182×body80valid
216.0ms1302×body320valid
52.0ms611×body160valid