Details

Time bar (total: 27.3s)

sample73.0ms

Algorithm
intervals
Results
26.0ms38×body2560valid
13.0ms38×body1280valid
12.0ms56×body640valid
4.0ms25×body320valid
4.0ms80×body80valid
3.0ms19×body160valid

simplify12.0ms

Counts
1 → 1
Iterations
IterNodes
done28
428
326
221
113
06

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize13.0ms

Local error

Found 2 expressions with local error:

1.6b
(- 1.0 (cos x))
12.0b
(/ (- 1.0 (cos x)) (* x x))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
7×add-cbrt-cube add-exp-log
5×times-frac associate-/l*
4×add-log-exp
3×fma-neg distribute-lft-out-- difference-of-squares
2×expm1-log1p-u pow1 cbrt-undiv flip3-- div-exp log1p-expm1-u flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub prod-exp cbrt-unprod div-inv
Counts
2 → 58
Calls
2 calls:
6.0ms
(- 1.0 (cos x))
50.0ms
(/ (- 1.0 (cos x)) (* x x))

series72.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(- 1.0 (cos x))
50.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify1.0s

Counts
64 → 64
Iterations
IterNodes
done5001
21734
1301
0116

prune289.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1.0 x) x)
0.1b
(/ (cos x) x)
0.2b
(/ (/ (cos x) x) x)
14.7b
(- (/ (/ 1.0 x) x) (/ (/ (cos x) x) x))

rewrite592.0ms

Algorithm
rewrite-expression-head
Rules
5967×times-frac
3193×add-sqr-sqrt
3183×*-un-lft-identity
3157×add-cube-cbrt
1849×prod-diff
367×div-inv
43×fma-neg
29×associate-/l*
16×add-cbrt-cube add-exp-log
13×distribute-lft-out--
9×associate-/r* difference-of-squares
7×cbrt-undiv div-exp
6×add-log-exp
4×expm1-log1p-u pow1 distribute-rgt-out-- log1p-expm1-u
3×clear-num frac-2neg
2×associate-/l/
1×sub-neg flip3-- diff-log frac-sub flip-- sub-div
Counts
4 → 2107
Calls
4 calls:
18.0ms
(/ (/ 1.0 x) x)
13.0ms
(/ (cos x) x)
23.0ms
(/ (/ (cos x) x) x)
224.0ms
(- (/ (/ 1.0 x) x) (/ (/ (cos x) x) x))

series686.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (/ 1.0 x) x)
35.0ms
(/ (cos x) x)
34.0ms
(/ (/ (cos x) x) x)
585.0ms
(- (/ (/ 1.0 x) x) (/ (/ (cos x) x) x))

simplify1.4s

Counts
2119 → 2119
Iterations
IterNodes
done5001
02352

prune14.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 x) x)
0.1b
(/ (/ 1 x) x)
14.7b
(fma 1 (/ (/ 1.0 x) x) (* (- (/ (/ 1 x) x)) (cos x)))
28.6b
(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
88×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
26×associate-/l*
22×add-exp-log
14×add-cbrt-cube
12×div-exp
10×pow1 div-inv
6×cbrt-undiv associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp pow-div
2×rec-exp clear-num frac-2neg 1-exp fma-udef pow-flip inv-pow associate-/l/
Counts
4 → 172
Calls
4 calls:
11.0ms
(/ (/ 1 x) x)
10.0ms
(/ (/ 1 x) x)
0.0ms
(fma 1 (/ (/ 1.0 x) x) (* (- (/ (/ 1 x) x)) (cos x)))
0.0ms
(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (/ 1 x) x)
37.0ms
(/ (/ 1 x) x)
152.0ms
(fma 1 (/ (/ 1.0 x) x) (* (- (/ (/ 1 x) x)) (cos x)))
100.0ms
(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))

simplify1.0s

Counts
184 → 184
Iterations
IterNodes
done5001
21514
1382
0180

prune970.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 x) x)
0.1b
(/ (/ 1 x) x)
28.6b
(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))
28.8b
(fma (/ 1.0 x) (/ 1 x) (* (- (/ (/ 1 x) x)) (cos x)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
88×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
26×associate-/l*
22×add-exp-log
14×add-cbrt-cube
12×div-exp
10×pow1 div-inv
6×cbrt-undiv associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp pow-div
2×rec-exp clear-num frac-2neg 1-exp fma-udef pow-flip inv-pow associate-/l/
Counts
4 → 172
Calls
4 calls:
10.0ms
(/ (/ 1 x) x)
9.0ms
(/ (/ 1 x) x)
0.0ms
(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))
0.0ms
(fma (/ 1.0 x) (/ 1 x) (* (- (/ (/ 1 x) x)) (cos x)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ (/ 1 x) x)
21.0ms
(/ (/ 1 x) x)
99.0ms
(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))
158.0ms
(fma (/ 1.0 x) (/ 1 x) (* (- (/ (/ 1 x) x)) (cos x)))

simplify985.0ms

Counts
184 → 184
Iterations
IterNodes
done5001
21509
1384
0179

prune586.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes104.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.3b

bsearch99.0ms

Steps
ItersRangePoint
8
0.00104763160503943
5.1212688054922095
0.0329978667264259
9
-205.8624528279525
-0.0007095347148853646
-0.0346527842528457

simplify25.0ms

Iterations
IterNodes
done47
247
141
029

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.8s1504×body2560valid
690.0ms1298×body1280valid
549.0ms1529×body640valid
271.0ms980×body320valid
196.0ms2199×body80valid
113.0ms490×body160valid