Details

sample206.0ms

Algorithm

intervals

Results

87.0ms	94×	body	1280	valid
70.0ms	65×	body	640	valid
19.0ms	12×	body	2560	valid
9.0ms	25×	body	320	valid
5.0ms	19×	body	160	valid
5.0ms	41×	body	80	valid

simplify9.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

9.0ms

(- (sin (+ x eps)) (sin x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize26.0ms

Local error

Found 2 expressions with local error:

4.4b	(sin (+ x eps))
1.9b	(- (sin (+ x eps)) (sin x))

rewrite71.0ms

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` `add-cbrt-cube` `sin-sum` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

Slowest

61.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series79.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

59.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify2.0s

Counts

33 → 48

Calls

33 calls:

Slowest

250.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
194.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
186.0ms	(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
172.0ms	(fma (* (cbrt (sin (+ x eps))) (cbrt (sin (+ x eps)))) (cbrt (sin (+ x eps))) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
166.0ms	(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))

prune446.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 3 expressions with local error:

4.4b	(cos (/ (+ x (+ eps x)) 2))
0.2b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `sum-log` `fma-def` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 52

Calls

3 calls:

Slowest

32.0ms	(cos (/ (+ x (+ eps x)) 2))
19.0ms	(+ x (+ eps x))
11.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series170.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

101.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
41.0ms	(cos (/ (+ x (+ eps x)) 2))
27.0ms	(+ x (+ eps x))

simplify1.6s

Counts

25 → 61

Calls

25 calls:

Slowest

461.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
347.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
189.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
75.0ms	(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
67.0ms	(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune677.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

4.4b	(cos (/ (+ x (+ eps x)) 2))
0.2b	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.2b	(expm1 (log1p (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
0.2b	(log1p (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))

rewrite35.0ms

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` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `expm1-udef` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

Slowest

22.0ms	(cos (/ (+ x (+ eps x)) 2))
11.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0ms	(log1p (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
0.0ms	(expm1 (log1p (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))

series409.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

155.0ms	(log1p (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
120.0ms	(expm1 (log1p (* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
102.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
32.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify2.3s

Counts

24 → 67

Calls

24 calls:

Slowest

415.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
388.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
358.0ms	(- (* 1/2 eps) (+ (* 1/4 (* (pow x 2) eps)) (* 1/8 (pow eps 2))))
232.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
219.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune831.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize66.0ms

Local error

Found 4 expressions with local error:

4.4b	(cos (/ (+ x (+ eps x)) 2))
0.4b	(log (exp (cos (/ (+ x (+ eps x)) 2))))
0.2b	(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
0.1b	(exp (cos (/ (+ x (+ eps x)) 2)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `associate-r`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

Slowest

73.0ms	(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
47.0ms	(log (exp (cos (/ (+ x (+ eps x)) 2))))
29.0ms	(exp (cos (/ (+ x (+ eps x)) 2)))
27.0ms	(cos (/ (+ x (+ eps x)) 2))

series210.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

81.0ms	(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
66.0ms	(exp (cos (/ (+ x (+ eps x)) 2)))
32.0ms	(cos (/ (+ x (+ eps x)) 2))
30.0ms	(log (exp (cos (/ (+ x (+ eps x)) 2))))

simplify2.8s

Counts

36 → 79

Calls

36 calls:

Slowest

431.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
398.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
397.0ms	(* (* (* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (log (exp (cos (/ (+ x (+ eps x)) 2))))) (log (exp (cos (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
297.0ms	(- E (+ (* 1/2 (* x (* E eps))) (* 1/2 (* (pow x 2) E))))
239.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))

prune924.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

regimes191.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 15.1b

bsearch124.0ms

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.7s	3255×	body	1280	valid
2.0s	1904×	body	640	valid
1.7s	613×	body	2560	valid
377.0ms	763×	body	320	valid
157.0ms	1099×	body	80	valid
119.0ms	366×	body	160	valid