Details

sample501.0ms

Algorithm

intervals

Results

207.0ms	106×	body	1280	valid
183.0ms	34×	body	2560	valid
57.0ms	47×	body	640	valid
27.0ms	32×	body	320	valid
7.0ms	12×	body	160	valid
7.0ms	25×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize14.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (tan (+ x eps)) (tan x))
3.5b	(tan (+ x eps))

rewrite34.0ms

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:

28.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series208.0ms

Counts

2 → 6

Calls

2 calls:

120.0ms	(- (tan (+ x eps)) (tan x))
88.0ms	(tan (+ x eps))

simplify3.4s

Counts

49 → 49

Iterations

Iter	Nodes
4	3889
3	1289
2	437
1	203
0	96

prune428.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite139.0ms

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:

26.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
87.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

236.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
123.0ms	(+ (tan x) (tan eps))
121.0ms	(* (tan x) (tan eps))
538.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.4s

Counts

185 → 185

Iterations

Iter	Nodes
3	5442
2	1570
1	577
0	242

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
0.2b	(* (sin x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

183×	`*-un-lft-identity`
138×	`add-sqr-sqrt`
100×	`times-frac`
90×	`prod-diff`
83×	`add-cube-cbrt`
34×	`difference-of-squares`
30×	`fma-neg`
25×	`distribute-lft-out`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r/` `add-log-exp`
6×	`pow1`
5×	`flip3--` `tan-quot` `div-inv` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `fma-def` `associate-r` `associate-l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-*r/` `cbrt-unprod`
1×	`+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `-commutative` `frac-sub` `flip-+` `associate-/l` `unswap-sqr` `associate-/l/`

Counts

4 → 205

Calls

4 calls:

10.0ms	(+ (tan x) (tan eps))
14.0ms	(/ (* (sin x) (tan eps)) (cos x))
12.0ms	(* (sin x) (tan eps))
191.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series981.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(+ (tan x) (tan eps))
136.0ms	(/ (* (sin x) (tan eps)) (cos x))
113.0ms	(* (sin x) (tan eps))
569.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify3.2s

Counts

217 → 217

Iterations

Iter	Nodes
3	6977
2	1871
1	695
0	299

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.2b

localize90.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
0.2b	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
2.0b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (/ (sin x) (cos x)))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

1393×	`times-frac`
890×	`add-sqr-sqrt`
851×	`*-un-lft-identity`
845×	`add-cube-cbrt`
585×	`prod-diff`
106×	`div-inv`
45×	`fma-neg`
30×	`add-cbrt-cube` `add-exp-log`
28×	`associate-/r/`
26×	`associate-r` `associate-l`
15×	`flip3--` `flip--`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `distribute-lft-out--`
1×	`quot-tan` `clear-num` `sub-neg` `frac-2neg` `diff-log` `frac-sub`

Counts

4 → 791

Calls

4 calls:

17.0ms	(/ (sin x) (cos x))
24.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
24.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
83.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (/ (sin x) (cos x)))

series687.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (sin x) (cos x))
131.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
160.0ms	(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
375.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (/ (sin x) (cos x)))

simplify1.5s

Counts

803 → 803

Iterations

Iter	Nodes
1	2177
0	934

prune13.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.1b

regimes219.0ms

Accuracy

0% (0.4b remaining)

Error of 12.9b against oracle of 12.5b and baseline of 12.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	19
1	19
0	17

end0.0ms

sample10.6s

Algorithm

intervals

Results

5.2s	3382×	body	1280	valid
2.2s	1731×	body	640	valid
2.0s	645×	body	2560	valid
518.0ms	795×	body	320	valid
236.0ms	1072×	body	80	valid
162.0ms	375×	body	160	valid