Details

sample149.0ms

Algorithm

intervals

Results

74.0ms	141×	body	1280	valid
25.0ms	70×	body	640	valid
19.0ms	26×	body	320	valid
13.0ms	11×	body	2560	valid
1.0ms	7×	body	160	valid
0.0ms	1×	body	80	valid

simplify25.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize19.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
4.6b	(cos (+ x eps))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

17.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

series156.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(- (cos (+ x eps)) (cos x))
59.0ms	(cos (+ x eps))

simplify1.1s

Counts: 30 → 30

prune145.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
1.8b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`diff-log`
3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

17.0ms	(* (cos x) (cos eps))
36.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
14.0ms	(* (sin x) (sin eps))
88.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series408.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (cos x) (cos eps))
103.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
64.0ms	(* (sin x) (sin eps))
173.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify2.0s

Counts: 82 → 82

prune427.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
0.2b	(* (sin x) (sin eps))
1.8b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))
1.8b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite477.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-log-exp`
10×	`exp-prod`
9×	`add-cube-cbrt`
8×	`exp-sum`
7×	`pow1` `log-prod`
6×	`add-exp-log` `sub-neg` `diff-log` `associate--l+` `log-pow` `add-cbrt-cube`
3×	`associate-r` `associate-l` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`
2×	`exp-diff`
1×	`associate--l-` `log-div` `flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

193.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
27.0ms	(* (sin x) (sin eps))
131.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))
123.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series784.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
85.0ms	(* (sin x) (sin eps))
206.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))
243.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify1.1s

Counts: 91 → 91

prune528.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))))
0.2b	(* (sin x) (sin eps))
1.8b	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))
1.8b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-log-exp`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`log-prod`
4×	`diff-log` `exp-sum` `log-pow`
3×	`sub-neg` `associate-r` `associate-l` `rem-exp-log`
2×	`exp-diff` `sum-log` `cos-mult` `frac-sub`
1×	`log-div` `flip3--` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `sin-mult` `associate--r+` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

122.0ms	(exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))))
14.0ms	(* (sin x) (sin eps))
91.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))
36.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series720.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))))
91.0ms	(* (sin x) (sin eps))
209.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))
160.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify2.2s

Counts: 81 → 81

prune391.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.5b

regimes281.0ms

Accuracy

85% (1.5b remaining)

Error of 16.1b against oracle of 14.6b and baseline of 24.5b

bsearch209.0ms

Steps

Iters	Range		Point
8	1.1818035649232606e-17	6.13479054788606e-13	4.159942496741691e-13
10	-5.99435871131559e-06	-5.279240705745917e-16	-1.7050403444468194e-08

simplify1.3s

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.6s	4483×	body	1280	valid
1.2s	1867×	body	640	valid
1.0s	616×	body	2560	valid
229.0ms	664×	body	320	valid
52.0ms	291×	body	160	valid
7.0ms	79×	body	80	valid