Details

sample215.0ms

Algorithm

intervals

Results

117.0ms	139×	body	1280	valid
38.0ms	16×	body	2560	valid
37.0ms	66×	body	640	valid
8.0ms	21×	body	320	valid
3.0ms	7×	body	160	valid
1.0ms	7×	body	80	valid

simplify16.0ms

Calls

1 calls:

Slowest

16.0ms

(- (cos (+ x eps)) (cos x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize53.0ms

Local error

Found 2 expressions with local error:

2.5b	(cos (+ x eps))
0.8b	(- (cos (+ x eps)) (cos x))

rewrite10.0ms

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`

Calls

2 calls:

Slowest

8.0ms	(- (cos (+ x eps)) (cos x))
2.0ms	(cos (+ x eps))

series68.0ms

Calls

2 calls:

Slowest

53.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify1.4s

Calls

33 calls:

Slowest

321.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
194.0ms	(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
91.0ms	(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
65.0ms	(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
63.0ms	(fma 1 (cos (+ x eps)) (- (* (cos x) 1)))

prune434.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize43.0ms

Local error

Found 4 expressions with local error:

2.5b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.2b	(/ (+ x (+ eps x)) 2)
0.0b	(+ x (+ eps x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `associate-/l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+r+` `clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sin-mult`

Calls

4 calls:

Slowest

9.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
6.0ms	(/ (+ x (+ eps x)) 2)
5.0ms	(sin (/ (+ x (+ eps x)) 2))
1.0ms	(+ x (+ eps x))

series167.0ms

Calls

4 calls:

Slowest

102.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
31.0ms	(sin (/ (+ x (+ eps x)) 2))
22.0ms	(/ (+ x (+ eps x)) 2)
12.0ms	(+ x (+ eps x))

simplify1.6s

Calls

25 calls:

Slowest

519.0ms	(+ (pow x 3) (pow (+ eps x) 3))
176.0ms	(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
148.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
143.0ms	(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
114.0ms	(- (* x x) (* (+ eps x) (+ eps x)))

prune896.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

2.5b	(sin (/ (+ x (+ eps x)) 2))
2.5b	(sin (/ (+ x (+ eps x)) 2))
2.5b	(sin (/ (+ x (+ eps x)) 2))
0.6b	(cbrt (sin (/ (+ x (+ eps x)) 2)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Calls

4 calls:

Slowest

7.0ms	(sin (/ (+ x (+ eps x)) 2))
6.0ms	(sin (/ (+ x (+ eps x)) 2))
6.0ms	(sin (/ (+ x (+ eps x)) 2))
3.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))

series179.0ms

Calls

4 calls:

Slowest

83.0ms	(cbrt (sin (/ (+ x (+ eps x)) 2)))
37.0ms	(sin (/ (+ x (+ eps x)) 2))
34.0ms	(sin (/ (+ x (+ eps x)) 2))
25.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.2s

Calls

15 calls:

Slowest

285.0ms	(- (+ (* 1/3 (* x (exp (* 1/3 (- (log 4) (* 2 (log eps))))))) (exp (* 1/3 (+ (log 1/2) (log eps))))) (* 7/81 (* (pow x 2) (exp (* 1/3 (+ (log 1/2) (log eps)))))))
175.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
146.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
128.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
72.0ms	(pow (sin (* 1/2 (+ (* 2 x) eps))) 1/3)

prune771.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

2.5b	(sin (/ (+ x (+ eps x)) 2))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Calls

4 calls:

Slowest

6.0ms	(sin (/ (+ x (+ eps x)) 2))
2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))

series501.0ms

Calls

4 calls:

Slowest

170.0ms	(cbrt (sin (/ eps 2)))
153.0ms	(cbrt (sin (/ eps 2)))
146.0ms	(cbrt (sin (/ eps 2)))
31.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify994.0ms

Calls

21 calls:

Slowest

232.0ms	(- (exp (* 1/3 (+ (log 1/2) (log eps)))) (+ (* 1/51840 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 4))) (* 1/72 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 2)))))
232.0ms	(- (exp (* 1/3 (+ (log 1/2) (log eps)))) (+ (* 1/51840 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 4))) (* 1/72 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 2)))))
228.0ms	(- (exp (* 1/3 (+ (log 1/2) (log eps)))) (+ (* 1/51840 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 4))) (* 1/72 (* (exp (* 1/3 (+ (log 1/2) (log eps)))) (pow eps 2)))))
120.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
47.0ms	(sin (* 1/2 (+ (* 2 x) eps)))

prune802.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

regimes269.0ms

Accuracy

93.9% (1.0b remaining)

Error of 1.4b against oracle of 0.4b and baseline of 16.2b

bsearch202.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.8s	4464×	body	1280	valid
1.7s	1853×	body	640	valid
1.1s	617×	body	2560	valid
358.0ms	661×	body	320	valid
86.0ms	323×	body	160	valid
40.0ms	82×	body	80	valid