Details

Time bar (total: 40.3s)

sample181.0ms

Algorithm
intervals
Results
95.0ms143×body1280valid
29.0ms21×body2560valid
21.0ms46×body640valid
9.0ms28×body320valid
3.0ms13×body160valid
0.0ms5×body80valid

simplify44.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize84.0ms

Local error

Found 2 expressions with local error:

0.9b
(- (cos (+ x eps)) (cos x))
3.8b
(cos (+ x eps))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 cos-sum add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×associate--l- sub-neg flip3-- diff-log diff-cos flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 42
Calls
2 calls:
50.0ms
(- (cos (+ x eps)) (cos x))
46.0ms
(cos (+ x eps))

series166.0ms

Counts
2 → 6
Calls
2 calls:
123.0ms
(- (cos (+ x eps)) (cos x))
43.0ms
(cos (+ x eps))

simplify7.2s

Counts
48 → 48
Iterations
IterNodes
done5003
43387
31175
2433
1202
093

prune647.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize158.0ms

Local error

Found 4 expressions with local error:

0.0b
(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
0.2b
(/ (fma 2 x eps) 2)
0.3b
(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
3.4b
(sin (/ (fma 2 x eps) 2))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
13×add-cbrt-cube add-exp-log
11×pow1
9×times-frac
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×*-commutative sin-mult
1×cbrt-undiv clear-num frac-2neg div-exp associate-*r/ div-inv unswap-sqr
Counts
4 → 84
Calls
4 calls:
98.0ms
(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
11.0ms
(/ (fma 2 x eps) 2)
67.0ms
(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
9.0ms
(sin (/ (fma 2 x eps) 2))

series404.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
75.0ms
(/ (fma 2 x eps) 2)
132.0ms
(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
55.0ms
(sin (/ (fma 2 x eps) 2))

simplify6.7s

Counts
96 → 96
Iterations
IterNodes
done5011
33420
2906
1307
0150

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize146.0ms

Local error

Found 4 expressions with local error:

0.2b
(expm1 (log1p (sin (fma eps 1/2 x))))
0.3b
(* (sin (* eps 1/2)) (expm1 (log1p (sin (fma eps 1/2 x)))))
0.5b
(log1p (sin (fma eps 1/2 x)))
3.4b
(sin (fma eps 1/2 x))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×log1p-udef expm1-log1p sin-sum pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod fma-udef expm1-udef unswap-sqr
Counts
4 → 56
Calls
4 calls:
3.0ms
(expm1 (log1p (sin (fma eps 1/2 x))))
78.0ms
(* (sin (* eps 1/2)) (expm1 (log1p (sin (fma eps 1/2 x)))))
1.0ms
(log1p (sin (fma eps 1/2 x)))
7.0ms
(sin (fma eps 1/2 x))

series593.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(expm1 (log1p (sin (fma eps 1/2 x))))
254.0ms
(* (sin (* eps 1/2)) (expm1 (log1p (sin (fma eps 1/2 x)))))
120.0ms
(log1p (sin (fma eps 1/2 x)))
66.0ms
(sin (fma eps 1/2 x))

simplify4.9s

Counts
68 → 68
Iterations
IterNodes
done5000
42011
3833
2372
1173
092

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize186.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos (* eps 1/2)) (sin x))
0.2b
(expm1 (log1p (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))))
0.3b
(* (sin (* eps 1/2)) (expm1 (log1p (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))))))
0.5b
(log1p (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef
Counts
4 → 66
Calls
4 calls:
66.0ms
(* (cos (* eps 1/2)) (sin x))
1.0ms
(expm1 (log1p (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))))
58.0ms
(* (sin (* eps 1/2)) (expm1 (log1p (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))))))
2.0ms
(log1p (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))))

series1.4s

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (cos (* eps 1/2)) (sin x))
390.0ms
(expm1 (log1p (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))))
536.0ms
(* (sin (* eps 1/2)) (expm1 (log1p (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))))))
318.0ms
(log1p (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))))

simplify4.8s

Counts
78 → 78
Iterations
IterNodes
done5000
31949
2701
1268
0125

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes703.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done20
120
014

end0.0ms

sample7.9s

Algorithm
intervals
Results
4.5s4357×body1280valid
1.2s617×body2560valid
1.1s1935×body640valid
700.0ms707×body320valid
110.0ms294×body160valid
11.0ms90×body80valid