Details

sample227.0ms

Algorithm

intervals

Results

122.0ms	94×	body	1280	valid
48.0ms	65×	body	640	valid
21.0ms	12×	body	2560	valid
11.0ms	25×	body	320	valid
6.0ms	19×	body	160	valid
6.0ms	41×	body	80	valid

simplify17.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

17.0ms

(- (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))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `sin-sum` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

Slowest

69.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series81.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

54.0ms	(- (sin (+ x eps)) (sin x))
27.0ms	(sin (+ x eps))

simplify851.0ms

Counts

13 → 32

Calls

13 calls:

Slowest

408.0ms	(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
251.0ms	(- (+ x eps) (* 1/6 (pow x 3)))
58.0ms	(* (sin (/ (- (+ x eps) x) 2)) (cos (/ (+ (+ x eps) x) 2)))
37.0ms	(/ (exp (sin (+ x eps))) (exp (sin x)))
19.0ms	(- (sin (+ x eps)) (sin x))

prune268.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

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))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

Slowest

23.0ms	(cos (/ (+ x (+ eps x)) 2))
22.0ms	(+ x (+ eps x))
20.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))

series187.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

114.0ms	(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
45.0ms	(cos (/ (+ x (+ eps x)) 2))
27.0ms	(+ x (+ eps x))

simplify1.3s

Counts

23 → 52

Calls

23 calls:

Slowest

404.0ms	(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
259.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
172.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
57.0ms	(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
51.0ms	(* (cos (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))

prune625.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.3b

localize37.0ms

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)))

rewrite177.0ms

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×	`insert-posit16`
3×	`log-prod` `associate-r`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 59

Calls

4 calls:

Slowest

61.0ms	(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
46.0ms	(log (exp (cos (/ (+ x (+ eps x)) 2))))
40.0ms	(exp (cos (/ (+ x (+ eps x)) 2)))
28.0ms	(cos (/ (+ x (+ eps x)) 2))

series222.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

82.0ms	(* (log (exp (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
73.0ms	(exp (cos (/ (+ x (+ eps x)) 2)))
35.0ms	(log (exp (cos (/ (+ x (+ eps x)) 2))))
32.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify2.3s

Counts

36 → 71

Calls

36 calls:

Slowest

363.0ms	(* (* (* (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))))
295.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
261.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
199.0ms	(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
163.0ms	(- E (+ (* 1/2 (* x (* E eps))) (* 1/2 (* (pow x 2) E))))

prune795.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 4 expressions with local error:

4.4b	(cos (/ (+ x (+ eps x)) 2))
4.4b	(cos (/ (+ x (+ eps x)) 2))
4.4b	(cos (/ (+ x (+ eps x)) 2))
0.5b	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 36

Calls

4 calls:

Slowest

33.0ms	(cos (/ (+ x (+ eps x)) 2))
32.0ms	(cos (/ (+ x (+ eps x)) 2))
19.0ms	(cos (/ (+ x (+ eps x)) 2))
11.0ms	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

39.0ms	(cos (/ (+ x (+ eps x)) 2))
33.0ms	(cbrt (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))))
33.0ms	(cos (/ (+ x (+ eps x)) 2))
25.0ms	(cos (/ (+ x (+ eps x)) 2))

simplify1.5s

Counts

15 → 48

Calls

15 calls:

Slowest

318.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
262.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
242.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
225.0ms	(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
55.0ms	(cos (* 1/2 (+ (* 2 x) eps)))

prune620.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.3b

regimes196.0ms

Accuracy

98.4% (0.2b remaining)

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

bsearch85.0ms

end0.0ms

sample8.3s

Algorithm

intervals

Results

4.0s	3255×	body	1280	valid
1.7s	1904×	body	640	valid
1.2s	613×	body	2560	valid
833.0ms	763×	body	320	valid
196.0ms	1099×	body	80	valid
108.0ms	366×	body	160	valid