Details

sample257.0ms

Algorithm

intervals

Results

136.0ms	146×	body	1280	valid
59.0ms	56×	body	640	valid
34.0ms	19×	body	2560	valid
10.0ms	22×	body	320	valid
3.0ms	10×	body	160	valid
0.0ms	3×	body	80	valid

simplify16.0ms

Counts: 1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize33.0ms

Local error

Found 2 expressions with local error:

3.0b	(cos (+ x eps))
1.1b	(- (cos (+ x eps)) (cos x))

rewrite70.0ms

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

42.0ms	(cos (+ x eps))
27.0ms	(- (cos (+ x eps)) (cos x))

series102.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

79.0ms	(- (cos (+ x eps)) (cos x))
23.0ms	(cos (+ x eps))

simplify1.3s

Counts: 48 → 48

prune631.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.8b

localize44.0ms

Local error

Found 4 expressions with local error:

2.9b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
0.2b	(/ (+ x (+ eps x)) 2)
0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
15×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
12×	`distribute-lft-out`
11×	`pow1`
6×	`associate-l`
5×	`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*`
2×	`*-commutative` `sin-mult` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-*r/` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

Slowest

63.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
60.0ms	(/ (+ x (+ eps x)) 2)
58.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
28.0ms	(sin (/ (+ x (+ eps x)) 2))

series270.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

92.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2))))
72.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
59.0ms	(/ (+ x (+ eps x)) 2)
46.0ms	(sin (/ (+ x (+ eps x)) 2))

simplify1.4s

Counts: 106 → 106

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

Local error

Found 3 expressions with local error:

2.9b	(sin (fma 1/2 eps x))
0.3b	(* (sin (/ eps 2)) (sin (fma 1/2 eps x)))
0.0b	(* -2 (* (sin (/ eps 2)) (sin (fma 1/2 eps x))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`sin-sum` `fma-udef`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

Slowest

26.0ms	(* (sin (/ eps 2)) (sin (fma 1/2 eps x)))
26.0ms	(* -2 (* (sin (/ eps 2)) (sin (fma 1/2 eps x))))
5.0ms	(sin (fma 1/2 eps x))

series218.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

109.0ms	(* -2 (* (sin (/ eps 2)) (sin (fma 1/2 eps x))))
83.0ms	(* (sin (/ eps 2)) (sin (fma 1/2 eps x)))
26.0ms	(sin (fma 1/2 eps x))

simplify980.0ms

Counts: 70 → 70

prune963.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

Slowest

130.0ms	(* (sin (/ eps 2)) (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))))
47.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
35.0ms	(* (cos (* 1/2 eps)) (sin x))
33.0ms	(* (sin (* 1/2 eps)) (cos x))

series541.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

225.0ms	(* (sin (/ eps 2)) (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))))
152.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
91.0ms	(* (sin (* 1/2 eps)) (cos x))
73.0ms	(* (cos (* 1/2 eps)) (sin x))

simplify2.4s

Counts: 95 → 95

prune1.9s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes283.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.8s	4478×	body	1280	valid
1.3s	1840×	body	640	valid
1.1s	615×	body	2560	valid
395.0ms	691×	body	320	valid
81.0ms	291×	body	160	valid
11.0ms	85×	body	80	valid