Details

sample151.0ms

Algorithm

intervals

Results

82.0ms	156×	body	1280	valid
21.0ms	62×	body	640	valid
20.0ms	17×	body	2560	valid
11.0ms	10×	body	320	valid
2.0ms	8×	body	160	valid
0.0ms	3×	body	80	valid

simplify20.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.3b

localize19.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
2.6b	(cos (+ x eps))

rewrite90.0ms

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:

70.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(cos (+ x eps))

series117.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (cos (+ x eps)) (cos x))
29.0ms	(cos (+ x eps))

simplify1.1s

Counts: 30 → 30

prune160.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.5b

localize21.0ms

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))
2.1b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite158.0ms

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:

22.0ms	(* (cos x) (cos eps))
32.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
13.0ms	(* (sin x) (sin eps))
87.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series467.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cos x) (cos eps))
125.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
80.0ms	(* (sin x) (sin eps))
187.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify1.9s

Counts: 82 → 82

prune515.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.1b	(* (cos eps) (cos x))
0.2b	(* (sin x) (sin eps))
2.1b	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

18.0ms	(+ (* (sin x) (sin eps)) (cos x))
22.0ms	(* (cos eps) (cos x))
17.0ms	(* (sin x) (sin eps))
43.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (* (sin x) (sin eps)) (cos x))
73.0ms	(* (cos eps) (cos x))
69.0ms	(* (sin x) (sin eps))
209.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify2.4s

Counts: 77 → 77

prune491.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.2b

localize43.0ms

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))
2.1b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.2b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

rewrite445.0ms

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:

194.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
26.0ms	(* (sin x) (sin eps))
95.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
126.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

series648.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
60.0ms	(* (sin x) (sin eps))
203.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
163.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

simplify1.3s

Counts: 91 → 91

prune378.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.2b

regimes359.0ms

Accuracy

86.4% (1.4b remaining)

Error of 15.8b against oracle of 14.4b and baseline of 24.6b

bsearch251.0ms

Steps

Iters	Range		Point
9	7.563871205794625e-15	1.3082252083774056e-05	6.093000978565237e-08
10	-0.0006576197608759923	-8.63582207798018e-19	-7.850247975532501e-05

simplify2.0s

end0.0ms

sample7.0s

Algorithm

intervals

Results

4.0s	4555×	body	1280	valid
1.0s	631×	body	2560	valid
937.0ms	1796×	body	640	valid
581.0ms	669×	body	320	valid
52.0ms	275×	body	160	valid
8.0ms	74×	body	80	valid