Details

sample346.0ms

Algorithm

intervals

Results

161.0ms	111×	body	1280	valid
55.0ms	60×	body	640	valid
55.0ms	19×	body	2560	valid
51.0ms	22×	body	320	valid
6.0ms	34×	body	80	valid
5.0ms	10×	body	160	valid

simplify10.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize52.0ms

Local error

Found 2 expressions with local error:

2.9b	(tan (+ x eps))
1.2b	(- (tan (+ x eps)) (tan x))

rewrite20.0ms

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))

series644.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

499.0ms	(tan (+ x eps))
145.0ms	(- (tan (+ x eps)) (tan x))

simplify1.3s

Counts: 49 → 49

prune666.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.6b

localize57.0ms

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)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))

rewrite175.0ms

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

100.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
34.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
30.0ms	(* (tan x) (tan eps))
7.0ms	(+ (tan x) (tan eps))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

602.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
271.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
151.0ms	(+ (tan x) (tan eps))
140.0ms	(* (tan x) (tan eps))

simplify750.0ms

Counts: 185 → 185

prune2.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.4b

localize107.0ms

Local error

Found 4 expressions with local error:

4.6b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b	(/ (sin x) (cos x))

rewrite197.0ms

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:

Slowest

101.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
32.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
19.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
11.0ms	(/ (sin x) (cos x))

series596.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

311.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
132.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
132.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
21.0ms	(/ (sin x) (cos x))

simplify2.0s

Counts: 803 → 803

prune16.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.4b

localize71.0ms

Local error

Found 4 expressions with local error:

4.6b	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
4.6b	(log (exp (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

1384×	`times-frac`
883×	`add-sqr-sqrt`
844×	`*-un-lft-identity`
838×	`add-cube-cbrt`
585×	`prod-diff`
105×	`div-inv`
45×	`fma-neg`
28×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
26×	`associate-r` `associate-l`
15×	`flip3--` `flip--`
9×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
7×	`add-log-exp`
6×	`difference-of-squares`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `log-pow`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `distribute-lft-out--`
1×	`exp-prod` `sub-neg` `exp-to-pow` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 777

Calls

4 calls:

Slowest

55.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
20.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
18.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
5.0ms	(log (exp (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))

series602.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

268.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
113.0ms	(log (exp (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))
112.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
109.0ms	(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))

simplify1.9s

Counts: 789 → 789

prune13.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.3b

regimes259.0ms

Accuracy

0% (0.4b remaining)

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

bsearch3.0ms

end0.0ms

sample9.4s

Algorithm

intervals

Results

5.1s	3328×	body	1280	valid
1.8s	1822×	body	640	valid
1.5s	615×	body	2560	valid
414.0ms	733×	body	320	valid
218.0ms	1144×	body	80	valid
162.0ms	358×	body	160	valid