Details

sample173.0ms

Algorithm

intervals

Results

101.0ms	136×	body	1280	valid
30.0ms	68×	body	640	valid
24.0ms	16×	body	2560	valid
8.0ms	25×	body	320	valid
2.0ms	8×	body	160	valid
0.0ms	3×	body	80	valid

simplify16.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

16.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize50.0ms

Local error

Found 2 expressions with local error:

2.5b	(cos (+ x eps))
0.9b	(- (cos (+ x eps)) (cos x))

rewrite19.0ms

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:

Slowest

11.0ms	(- (cos (+ x eps)) (cos x))
7.0ms	(cos (+ x eps))

series110.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

84.0ms	(- (cos (+ x eps)) (cos x))
26.0ms	(cos (+ x eps))

simplify2.3s

Counts

33 → 48

Calls

33 calls:

Slowest

260.0ms	(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
260.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
220.0ms	(fma (sqrt (cos (+ x eps))) (sqrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
208.0ms	(fma 1 (cos (+ x eps)) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))
159.0ms	(fma (* (cbrt (cos (+ x eps))) (cbrt (cos (+ x eps)))) (cbrt (cos (+ x eps))) (- (* (cbrt (cos x)) (* (cbrt (cos x)) (cbrt (cos x))))))

prune482.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize54.0ms

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)))
0.0b	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
0.0b	(+ x (+ eps x))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

Slowest

91.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
90.0ms	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
40.0ms	(sin (/ (+ x (+ eps x)) 2))
11.0ms	(+ x (+ eps x))

series282.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

105.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
105.0ms	(* -2 (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))))
44.0ms	(sin (/ (+ x (+ eps x)) 2))
28.0ms	(+ x (+ eps x))

simplify3.5s

Counts

38 → 87

Calls

38 calls:

Slowest

638.0ms	(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))) (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))))
584.0ms	(* (* (* -2 -2) -2) (* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2)))))
389.0ms	(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
315.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
294.0ms	(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))

prune903.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

Slowest

65.0ms	(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
25.0ms	(sin (/ (+ x (+ eps x)) 2))
11.0ms	(+ x (+ eps x))

series200.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

107.0ms	(* (* -2 (sin (/ (+ x (+ eps x)) 2))) (sin (/ eps 2)))
50.0ms	(sin (/ (+ x (+ eps x)) 2))
42.0ms	(+ x (+ eps x))

simplify2.3s

Counts

24 → 61

Calls

24 calls:

Slowest

611.0ms	(* (* (* (* -2 (sin (/ (+ x (+ eps x)) 2))) (* -2 (sin (/ (+ x (+ eps x)) 2)))) (* -2 (sin (/ (+ x (+ eps x)) 2)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
563.0ms	(* (* (* (* -2 -2) -2) (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
295.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
244.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
94.0ms	(* -2 (* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps))))

prune659.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize44.0ms

Local error

Found 2 expressions with local error:

2.6b	(sin (fma 1/2 eps x))
0.3b	(* (* -2 (sin (fma 1/2 eps x))) (sin (/ eps 2)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`sin-sum` `associate-l` `*-commutative` `fma-udef`

Counts

2 → 32

Calls

2 calls:

Slowest

42.0ms	(* (* -2 (sin (fma 1/2 eps x))) (sin (/ eps 2)))
5.0ms	(sin (fma 1/2 eps x))

series108.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

78.0ms	(* (* -2 (sin (fma 1/2 eps x))) (sin (/ eps 2)))
31.0ms	(sin (fma 1/2 eps x))

simplify2.0s

Counts

16 → 38

Calls

16 calls:

Slowest

614.0ms	(* (* (* (* -2 -2) -2) (* (* (sin (fma 1/2 eps x)) (sin (fma 1/2 eps x))) (sin (fma 1/2 eps x)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
530.0ms	(* (* (* (* -2 (sin (fma 1/2 eps x))) (* -2 (sin (fma 1/2 eps x)))) (* -2 (sin (fma 1/2 eps x)))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
270.0ms	(- (+ x (* 1/2 eps)) (* 1/48 (pow eps 3)))
242.0ms	(- (* 1/24 (pow eps 4)) (+ (* x eps) (* 1/2 (pow eps 2))))
67.0ms	(+ (log (* -2 (sin (fma 1/2 eps x)))) (log (sin (/ eps 2))))

prune440.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes166.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.7s	4571×	body	1280	valid
1.4s	1819×	body	640	valid
1.1s	600×	body	2560	valid
701.0ms	668×	body	320	valid
104.0ms	268×	body	160	valid
9.0ms	74×	body	80	valid