Details

Time bar (total: 26.3s)

sample81.0ms

Algorithm
intervals
Results
29.0ms56×body2560valid
20.0ms45×body640valid
11.0ms42×body1280valid
5.0ms38×body320valid
3.0ms59×body80valid
2.0ms16×body160valid

simplify18.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize19.0ms

Local error

Found 2 expressions with local error:

2.1b
(- 1.0 (cos x))
15.3b
(/ (- 1.0 (cos x)) (* x x))

rewrite51.0ms

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:
12.0ms
(- 1.0 (cos x))
36.0ms
(/ (- 1.0 (cos x)) (* x x))

series114.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(- 1.0 (cos x))
92.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify793.0ms

Counts
64 → 64
Iterations
IterNodes
done5001
21734
1301
0116

prune264.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.5b
(fma 1/720 (pow x 4) 1/2)
10.4b
(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
0.0ms
(fma 1/720 (pow x 4) 1/2)
0.0ms
(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

series165.0ms

Counts
2 → 6
Calls
2 calls:
99.0ms
(fma 1/720 (pow x 4) 1/2)
66.0ms
(fma (* x x) -1/24 (fma 1/720 (pow x 4) 1/2))

simplify1.1s

Counts
26 → 26
Iterations
IterNodes
done5000
31192
2207
158
035

prune134.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (cos x) x)
0.2b
(/ (/ (cos x) x) x)
0.2b
(/ (/ 1.0 x) x)
18.2b
(- (/ (/ 1.0 x) x) (/ (/ (cos x) x) x))

rewrite521.0ms

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:
11.0ms
(/ (cos x) x)
11.0ms
(/ (/ (cos x) x) x)
9.0ms
(/ (/ 1.0 x) x)
185.0ms
(- (/ (/ 1.0 x) x) (/ (/ (cos x) x) x))

series206.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ (cos x) x)
34.0ms
(/ (/ (cos x) x) x)
30.0ms
(/ (/ 1.0 x) x)
105.0ms
(- (/ (/ 1.0 x) x) (/ (/ (cos x) x) x))

simplify1.3s

Counts
2119 → 2119
Iterations
IterNodes
done5001
02352

prune15.0s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

27.4b
(sqrt (/ (/ 1.0 x) x))
27.4b
(sqrt (/ (/ 1.0 x) x))
31.4b
(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))
33.3b
(fma (sqrt (/ (/ 1.0 x) x)) (sqrt (/ (/ 1.0 x) x)) (* (- (/ (/ 1 x) x)) (cos x)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
86×add-sqr-sqrt sqrt-prod
74×*-un-lft-identity add-cube-cbrt
8×div-inv
6×pow1 rem-sqrt-square
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
2×sqrt-pow1 pow1/2 sqrt-div fma-udef
Counts
4 → 136
Calls
4 calls:
9.0ms
(sqrt (/ (/ 1.0 x) x))
10.0ms
(sqrt (/ (/ 1.0 x) x))
0.0ms
(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))
0.0ms
(fma (sqrt (/ (/ 1.0 x) x)) (sqrt (/ (/ 1.0 x) x)) (* (- (/ (/ 1 x) x)) (cos x)))

series491.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(sqrt (/ (/ 1.0 x) x))
53.0ms
(sqrt (/ (/ 1.0 x) x))
143.0ms
(fma (- (/ (/ 1 x) x)) (cos x) (* (/ (/ 1 x) x) (cos x)))
231.0ms
(fma (sqrt (/ (/ 1.0 x) x)) (sqrt (/ (/ 1.0 x) x)) (* (- (/ (/ 1 x) x)) (cos x)))

simplify823.0ms

Counts
148 → 148
Iterations
IterNodes
done5001
21303
1393
0228

prune958.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.1b

regimes262.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 32.0b

bsearch114.0ms

Steps
ItersRangePoint
10
5.09324609688744e-06
47495130.80298876
0.022350989698977898
10
-1138.2876542095912
-1.6260248627107784e-07
-0.03428006622296721

simplify7.0ms

Iterations
IterNodes
done39
239
136
030

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.6s1580×body2560valid
603.0ms1234×body1280valid
589.0ms2260×body80valid
498.0ms1494×body640valid
186.0ms946×body320valid
67.0ms486×body160valid