Details

sample210.0ms

Algorithm

intervals

Results

92.0ms	97×	body	1280	valid
44.0ms	59×	body	640	valid
40.0ms	21×	body	2560	valid
10.0ms	24×	body	320	valid
6.0ms	42×	body	80	valid
5.0ms	13×	body	160	valid

simplify16.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize81.0ms

Local error

Found 2 expressions with local error:

2.7b	(sin (+ x eps))
1.6b	(- (sin (+ x eps)) (sin x))

rewrite53.0ms

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

38.0ms	(- (sin (+ x eps)) (sin x))
14.0ms	(sin (+ x eps))

series82.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

56.0ms	(- (sin (+ x eps)) (sin x))
26.0ms	(sin (+ x eps))

simplify589.0ms

Counts: 36 → 32

prune254.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize41.0ms

Local error

Found 3 expressions with local error:

2.7b	(cos (/ (+ x (+ x eps)) 2))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
0.0b	(+ x (+ x eps))

rewrite96.0ms

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-+` `sin-cos-mult` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

Slowest

44.0ms	(cos (/ (+ x (+ x eps)) 2))
30.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
21.0ms	(+ x (+ x eps))

series157.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

74.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
43.0ms	(+ x (+ x eps))
39.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify689.0ms

Counts: 54 → 53

prune629.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.5b

localize46.0ms

Local error

Found 4 expressions with local error:

2.7b	(cos (/ (+ x (+ x eps)) 2))
2.7b	(cos (/ (+ x (+ x eps)) 2))
2.7b	(cos (/ (+ x (+ x eps)) 2))
0.4b	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))

rewrite105.0ms

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

40.0ms	(cos (/ (+ x (+ x eps)) 2))
23.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
21.0ms	(cos (/ (+ x (+ x eps)) 2))
20.0ms	(cos (/ (+ x (+ x eps)) 2))

series149.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

44.0ms	(cos (/ (+ x (+ x eps)) 2))
42.0ms	(cos (/ (+ x (+ x eps)) 2))
32.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
31.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify964.0ms

Counts: 48 → 48

prune608.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.5b

localize34.0ms

Local error

Found 4 expressions with local error:

2.7b	(cos (/ (+ x (+ eps x)) 2))
0.5b	(log (exp (cos (/ (+ x (+ eps x)) 2))))
0.2b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ eps x)) 2)))))
0.1b	(exp (cos (/ (+ x (+ eps x)) 2)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

Slowest

40.0ms	(log (exp (cos (/ (+ x (+ eps x)) 2))))
33.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ eps x)) 2)))))
27.0ms	(exp (cos (/ (+ x (+ eps x)) 2)))
18.0ms	(cos (/ (+ x (+ eps x)) 2))

series221.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

75.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ eps x)) 2)))))
63.0ms	(exp (cos (/ (+ x (+ eps x)) 2)))
41.0ms	(cos (/ (+ x (+ eps x)) 2))
41.0ms	(log (exp (cos (/ (+ x (+ eps x)) 2))))

simplify488.0ms

Counts: 84 → 77

prune885.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.5b

regimes357.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 15.3b

bsearch302.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.4s	3329×	body	1280	valid
1.6s	622×	body	2560	valid
1.3s	1859×	body	640	valid
520.0ms	785×	body	320	valid
141.0ms	1073×	body	80	valid
94.0ms	332×	body	160	valid