Details

sample260.0ms

Algorithm

intervals

Results

138.0ms	99×	body	1280	valid
45.0ms	65×	body	640	valid
40.0ms	17×	body	2560	valid
13.0ms	29×	body	320	valid
5.0ms	33×	body	80	valid
4.0ms	13×	body	160	valid

simplify16.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize21.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
4.0b	(tan (+ x eps))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

21.0ms	(- (tan (+ x eps)) (tan x))
54.0ms	(tan (+ x eps))

series206.0ms

Counts

2 → 6

Calls

2 calls:

128.0ms	(- (tan (+ x eps)) (tan x))
78.0ms	(tan (+ x eps))

simplify1.4s

Counts: 31 → 31

prune149.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

17.0ms	(+ (tan x) (tan eps))
59.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
35.0ms	(* (tan x) (tan eps))
146.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

134.0ms	(+ (tan x) (tan eps))
315.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
141.0ms	(* (tan x) (tan eps))
568.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify781.0ms

Counts: 98 → 98

prune458.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (sin eps))
0.2b	(* (tan x) (tan eps))
0.3b	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))))
6.6b	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps)))) (tan x))

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`tan-quot` `prod-exp` `associate-/r/` `cbrt-unprod`
3×	`cbrt-undiv` `frac-times` `flip3--` `times-frac` `div-exp` `associate-l/` `cos-mult` `flip--` `associate-/l`
2×	`associate-r/` `pow-prod-down` `-commutative` `associate-/l/` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `clear-num` `associate-/r*` `frac-sub` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 84

Calls

4 calls:

12.0ms	(* (cos x) (sin eps))
16.0ms	(* (tan x) (tan eps))
92.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))))
263.0ms	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (cos x) (sin eps))
121.0ms	(* (tan x) (tan eps))
399.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))))
569.0ms	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps)))) (tan x))

simplify1.3s

Counts: 96 → 96

prune611.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
0.3b	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (/ (* (tan x) (sin eps)) (cos eps))) (* (cos x) (cos eps))))
6.6b	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (/ (* (tan x) (sin eps)) (cos eps))) (* (cos x) (cos eps)))) (tan x))

rewrite441.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
6×	`pow1` `times-frac` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
4×	`associate-l/` `associate-/r` `associate-/l*`
3×	`tan-quot` `flip3--` `associate-r` `associate-l` `cos-mult` `flip--` `associate-/l/`
2×	`frac-times` `frac-2neg` `clear-num` `div-inv`
1×	`sub-neg` `flip3-+` `diff-log` `associate-r/` `pow-prod-down` `-commutative` `frac-sub` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

20.0ms	(/ (* (tan x) (sin eps)) (cos eps))
29.0ms	(* (tan x) (sin eps))
134.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (/ (* (tan x) (sin eps)) (cos eps))) (* (cos x) (cos eps))))
254.0ms	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (/ (* (tan x) (sin eps)) (cos eps))) (* (cos x) (cos eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (* (tan x) (sin eps)) (cos eps))
74.0ms	(* (tan x) (sin eps))
405.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (/ (* (tan x) (sin eps)) (cos eps))) (* (cos x) (cos eps))))
578.0ms	(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (- 1 (/ (* (tan x) (sin eps)) (cos eps))) (* (cos x) (cos eps)))) (tan x))

simplify1.3s

Counts: 98 → 98

prune546.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.2b

regimes330.0ms

Accuracy

88.8% (0.9b remaining)

Error of 15.0b against oracle of 14.1b and baseline of 22.2b

bsearch302.0ms

Steps

Iters	Range		Point
7	9.893396450191569e-20	8.666561730544872e-18	1.084923224249313e-19
9	-1.6407970181994926e-76	-4.024269261797611e-82	-6.929244313528967e-77

simplify1.1s

end0.0ms

sample11.4s

Algorithm

intervals

Results

5.8s	3301×	body	1280	valid
2.2s	598×	body	2560	valid
2.1s	1873×	body	640	valid
449.0ms	797×	body	320	valid
269.0ms	1085×	body	80	valid
172.0ms	346×	body	160	valid