Details

sample176.0ms

Algorithm

intervals

Results

111.0ms	151×	body	1280	valid
27.0ms	20×	body	2560	valid
20.0ms	50×	body	640	valid
6.0ms	21×	body	320	valid
2.0ms	11×	body	160	valid
0.0ms	3×	body	80	valid

simplify8.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize13.0ms

Local error

Found 2 expressions with local error:

3.7b	(cos (+ x eps))
0.7b	(- (cos (+ x eps)) (cos x))

rewrite60.0ms

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

48.0ms	(- (cos (+ x eps)) (cos x))
9.0ms	(cos (+ x eps))

series140.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

99.0ms	(- (cos (+ x eps)) (cos x))
41.0ms	(cos (+ x eps))

simplify1.3s

Counts: 48 → 48

prune391.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize31.0ms

Local error

Found 4 expressions with local error:

3.7b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
0.2b	(/ (+ x (+ eps x)) 2)
0.0b	(+ x (+ eps x))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
15×	`times-frac` `distribute-lft-out`
9×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `sum-log` `fma-def` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

Slowest

74.0ms	(/ (+ x (+ eps x)) 2)
63.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
42.0ms	(sin (/ (+ x (+ eps x)) 2))
22.0ms	(+ x (+ eps x))

series189.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

72.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ eps x)) 2)))
51.0ms	(/ (+ x (+ eps x)) 2)
34.0ms	(sin (/ (+ x (+ eps x)) 2))
31.0ms	(+ x (+ eps x))

simplify1.2s

Counts: 105 → 105

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize44.0ms

Local error

Found 3 expressions with local error:

3.7b	(sin (fma eps 1/2 x))
0.3b	(* (sin (fma eps 1/2 x)) (sin (/ eps 2)))
0.0b	(* -2 (* (sin (fma eps 1/2 x)) (sin (/ eps 2))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
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×	`sin-sum` `associate-*r/` `fma-udef` `unswap-sqr`

Counts

3 → 55

Calls

3 calls:

Slowest

20.0ms	(* -2 (* (sin (fma eps 1/2 x)) (sin (/ eps 2))))
15.0ms	(* (sin (fma eps 1/2 x)) (sin (/ eps 2)))
5.0ms	(sin (fma eps 1/2 x))

series203.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

82.0ms	(* -2 (* (sin (fma eps 1/2 x)) (sin (/ eps 2))))
77.0ms	(* (sin (fma eps 1/2 x)) (sin (/ eps 2)))
44.0ms	(sin (fma eps 1/2 x))

simplify727.0ms

Counts: 64 → 64

prune719.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite188.0ms

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-*l/` `flip-+`
1×	`+-commutative` `sum-log` `fma-def` `sin-cos-mult`

Counts

4 → 81

Calls

4 calls:

Slowest

93.0ms	(* (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))) (sin (/ eps 2)))
50.0ms	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
26.0ms	(* (cos (* eps 1/2)) (sin x))
17.0ms	(* (sin (* eps 1/2)) (cos x))

series509.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

226.0ms	(* (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))) (sin (/ eps 2)))
162.0ms	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
62.0ms	(* (cos (* eps 1/2)) (sin x))
59.0ms	(* (sin (* eps 1/2)) (cos x))

simplify2.1s

Counts: 93 → 93

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes192.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample8.9s

Algorithm

intervals

Results

4.8s	4439×	body	1280	valid
2.1s	1881×	body	640	valid
1.2s	667×	body	2560	valid
391.0ms	688×	body	320	valid
113.0ms	256×	body	160	valid
9.0ms	69×	body	80	valid