Details

sample454.0ms

Algorithm

intervals

Results

243.0ms	103×	body	1280	valid
86.0ms	50×	body	640	valid
56.0ms	16×	body	2560	valid
29.0ms	34×	body	320	valid
11.0ms	41×	body	80	valid
7.0ms	12×	body	160	valid

simplify16.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize24.0ms

Local error

Found 2 expressions with local error:

2.6b	(tan (+ x eps))
1.9b	(- (tan (+ x eps)) (tan x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

Slowest

14.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series193.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

114.0ms	(- (tan (+ x eps)) (tan x))
79.0ms	(tan (+ x eps))

simplify1.3s

Counts: 49 → 49

prune488.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.5b

localize34.0ms

Local error

Found 4 expressions with local error:

3.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b	(* (tan x) (tan eps))
0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `fma-def` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

Slowest

71.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
38.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
29.0ms	(* (tan x) (tan eps))
16.0ms	(+ (tan x) (tan eps))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

496.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
328.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
158.0ms	(* (tan x) (tan eps))
146.0ms	(+ (tan x) (tan eps))

simplify656.0ms

Counts: 185 → 185

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.4b

localize82.0ms

Local error

Found 4 expressions with local error:

3.5b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
0.2b	(/ (sin x) (cos x))
0.2b	(/ (sin x) (cos x))
0.2b	(/ (sin x) (cos x))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

1367×	`times-frac`
854×	`add-sqr-sqrt`
839×	`*-un-lft-identity`
833×	`add-cube-cbrt`
585×	`prod-diff`
104×	`div-inv`
45×	`fma-neg`
28×	`associate-/r/`
15×	`flip3--` `flip--`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r` `associate-/l`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `quot-tan` `clear-num` `frac-2neg` `div-exp`
2×	`distribute-lft-out--`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

4 → 747

Calls

4 calls:

Slowest

88.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
20.0ms	(/ (sin x) (cos x))
17.0ms	(/ (sin x) (cos x))
16.0ms	(/ (sin x) (cos x))

series872.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

778.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
37.0ms	(/ (sin x) (cos x))
33.0ms	(/ (sin x) (cos x))
24.0ms	(/ (sin x) (cos x))

simplify2.1s

Counts: 759 → 759

prune14.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.3b

localize68.0ms

Local error

Found 4 expressions with local error:

3.5b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (* (cos eps) (cos x)) (sin eps))))) (/ (sin x) (cos x)))
0.3b	(/ (sin x) (/ (* (cos eps) (cos x)) (sin eps)))
0.2b	(/ (sin x) (cos x))
0.2b	(/ (sin x) (cos x))

rewrite434.0ms

Algorithm

rewrite-expression-head

Rules

3882×	`times-frac`
3263×	`add-sqr-sqrt`
2525×	`*-un-lft-identity`
1786×	`add-cube-cbrt`
1430×	`prod-diff`
734×	`difference-of-squares`
243×	`div-inv`
186×	`distribute-lft-out--`
110×	`fma-neg`
29×	`associate-/r/`
17×	`add-cbrt-cube` `add-exp-log`
15×	`flip3--` `flip--`
13×	`associate-/r*`
9×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`quot-tan`
1×	`sub-neg` `diff-log` `prod-exp` `frac-sub` `cbrt-unprod`

Counts

4 → 1678

Calls

4 calls:

Slowest

282.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (* (cos eps) (cos x)) (sin eps))))) (/ (sin x) (cos x)))
27.0ms	(/ (sin x) (/ (* (cos eps) (cos x)) (sin eps)))
9.0ms	(/ (sin x) (cos x))
9.0ms	(/ (sin x) (cos x))

series612.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

373.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (* (cos eps) (cos x)) (sin eps))))) (/ (sin x) (cos x)))
165.0ms	(/ (sin x) (/ (* (cos eps) (cos x)) (sin eps)))
38.0ms	(/ (sin x) (cos x))
36.0ms	(/ (sin x) (cos x))

simplify4.5s

Counts: 1690 → 1690

prune26.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.3b

regimes149.0ms

Accuracy

0% (0.4b remaining)

Error of 12.6b against oracle of 12.2b and baseline of 12.6b

bsearch4.0ms

end0.0ms

sample9.7s

Algorithm

intervals

Results

5.5s	3352×	body	1280	valid
1.7s	1845×	body	640	valid
1.5s	650×	body	2560	valid
398.0ms	764×	body	320	valid
185.0ms	1035×	body	80	valid
159.0ms	354×	body	160	valid