Details

Time bar (total: 18.6s)

sample46.0ms

Algorithm
intervals
Results
13.0ms63×body640valid
7.0ms123×body80valid
6.0ms36×body320valid
5.0ms17×body1280valid
2.0ms17×body160valid

simplify150.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
11815
23115
34115
45015
55515
66415
78215
89915
910915
done10915

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize18.0ms

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))
3.5b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite823.0ms

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:
11.0ms
(/ 1.0 (- x 1.0))
12.0ms
(/ 1.0 (+ x 1.0))
160.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
534.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ 1.0 (- x 1.0))
39.0ms
(/ 1.0 (+ x 1.0))
44.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
293.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify3.0s

Counts
630 → 630
Iterations

Useful iterations: done (2.9s)

IterNodesCost
050219834
1114917345
2279912902
done500110138

prune1.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (- x 1.0))
0.0b
(/ 1 (+ x 1.0))
0.0b
(fma 1.0 (/ 1 (+ x 1.0)) (- (* (/ 2.0 x) 1)))
3.5b
(+ (fma 1.0 (/ 1 (+ x 1.0)) (- (* (/ 2.0 x) 1))) (+ 0 (/ 1.0 (- x 1.0))))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
32×add-sqr-sqrt
27×times-frac
24×add-cube-cbrt
10×add-exp-log
9×associate-/r* add-log-exp
8×add-cbrt-cube
7×distribute-lft-out
6×associate-/l*
5×pow1
4×expm1-log1p-u associate-/r/ log1p-expm1-u distribute-lft-out-- difference-of-squares
3×fma-def div-exp sum-log
2×cbrt-undiv frac-2neg flip3-+ clear-num flip-+ fma-udef div-inv
1×+-commutative rec-exp associate-+l+ associate-+r+ flip3-- pow-flip 1-exp flip-- inv-pow
Counts
4 → 109
Calls
4 calls:
23.0ms
(/ 1.0 (- x 1.0))
24.0ms
(/ 1 (+ x 1.0))
1.0ms
(fma 1.0 (/ 1 (+ x 1.0)) (- (* (/ 2.0 x) 1)))
103.0ms
(+ (fma 1.0 (/ 1 (+ x 1.0)) (- (* (/ 2.0 x) 1))) (+ 0 (/ 1.0 (- x 1.0))))

series453.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ 1.0 (- x 1.0))
37.0ms
(/ 1 (+ x 1.0))
77.0ms
(fma 1.0 (/ 1 (+ x 1.0)) (- (* (/ 2.0 x) 1)))
293.0ms
(+ (fma 1.0 (/ 1 (+ x 1.0)) (- (* (/ 2.0 x) 1))) (+ 0 (/ 1.0 (- x 1.0))))

simplify3.3s

Counts
121 → 121
Iterations

Useful iterations: done (3.3s)

IterNodesCost
02021664
14561390
212261236
336551228
done50001225

prune377.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 7)))
0.1b
(/ 2.0 (pow x 3))
0.2b
(/ 2.0 (pow x 7))
0.2b
(/ 2.0 (pow x 5))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
105×times-frac
85×*-un-lft-identity
77×add-sqr-sqrt add-cube-cbrt
45×unpow-prod-down
26×associate-/r*
25×fma-def
19×add-exp-log
15×sqr-pow
12×cube-prod
10×add-cbrt-cube
9×div-exp associate-/l*
6×div-inv add-log-exp
5×distribute-lft-out
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num
1×+-commutative flip3-+ frac-add sum-log flip-+
Counts
4 → 205
Calls
4 calls:
88.0ms
(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 7)))
16.0ms
(/ 2.0 (pow x 3))
15.0ms
(/ 2.0 (pow x 7))
15.0ms
(/ 2.0 (pow x 5))

series409.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 7)))
44.0ms
(/ 2.0 (pow x 3))
86.0ms
(/ 2.0 (pow x 7))
66.0ms
(/ 2.0 (pow x 5))

simplify1000.0ms

Counts
217 → 217
Iterations

Useful iterations: done (995.0ms)

IterNodesCost
02632139
14991870
213461802
done50001801

prune943.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 2.0 (* x x)) x)
0.2b
(/ 2.0 (pow x 7))
0.2b
(/ 2.0 (pow x 5))
0.6b
(/ 2.0 (* x x))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
28×add-exp-log
24×unpow-prod-down
22×add-cbrt-cube
18×associate-/r*
16×associate-/l*
13×div-exp
9×cbrt-undiv
8×div-inv sqr-pow
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×pow-to-exp pow-exp prod-exp cbrt-unprod
1×associate-/l/
Counts
4 → 167
Calls
4 calls:
22.0ms
(/ (/ 2.0 (* x x)) x)
7.0ms
(/ 2.0 (pow x 7))
7.0ms
(/ 2.0 (pow x 5))
16.0ms
(/ 2.0 (* x x))

series269.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (/ 2.0 (* x x)) x)
77.0ms
(/ 2.0 (pow x 7))
90.0ms
(/ 2.0 (pow x 5))
28.0ms
(/ 2.0 (* x x))

simplify3.5s

Counts
179 → 179
Iterations

Useful iterations: 2 (317.0ms)

IterNodesCost
02561876
14891703
213091597
345521597
done50001597

prune648.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 9.5b

bsearch110.0ms

Steps
ItersRangePoint
9
9.85435867085541e-08
110.15968793260775
108.28044055233757
8
-3231.0590912120524
-0.1517943218839364
-110.36399629437352

simplify16.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03665
14861
25261
done5261

end0.0ms

sample809.0ms

Algorithm
intervals
Results
252.0ms1881×body640valid
163.0ms4156×body80valid
97.0ms935×body320valid
93.0ms553×body1280valid
32.0ms476×body160valid