Details

sample442.0ms

Algorithm

intervals

Results

220.0ms	112×	body	1280	valid
108.0ms	53×	body	640	valid
62.0ms	20×	body	2560	valid
20.0ms	25×	body	320	valid
11.0ms	16×	body	160	valid
9.0ms	30×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize14.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (tan (+ x eps)) (tan x))
3.1b	(tan (+ x eps))

rewrite57.0ms

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` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

48.0ms	(- (tan (+ x eps)) (tan x))
8.0ms	(tan (+ x eps))

series178.0ms

Counts

2 → 6

Calls

2 calls:

111.0ms	(- (tan (+ x eps)) (tan x))
67.0ms	(tan (+ x eps))

simplify3.4s

Counts

47 → 47

Iterations

Iter	Nodes
4	3727
3	1285
2	436
1	201
0	94

prune454.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.3b

localize23.0ms

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))
3.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite127.0ms

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` `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 → 169

Calls

4 calls:

22.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
10.0ms	(+ (tan x) (tan eps))
25.0ms	(* (tan x) (tan eps))
68.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

347.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
104.0ms	(+ (tan x) (tan eps))
98.0ms	(* (tan x) (tan eps))
551.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.9s

Counts

181 → 181

Iterations

Iter	Nodes
3	5311
2	1580
1	573
0	238

prune2.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
0.2b	(* (sin x) (/ (sin eps) (cos eps)))
0.2b	(* (sin x) (/ (sin eps) (cos eps)))
3.1b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

2640×	`times-frac`
1971×	`add-sqr-sqrt`
1951×	`*-un-lft-identity`
1394×	`add-cube-cbrt`
1092×	`prod-diff`
370×	`difference-of-squares`
186×	`distribute-lft-out--`
185×	`div-inv`
84×	`fma-neg`
28×	`associate-/r/`
26×	`associate-r`
23×	`add-cbrt-cube` `add-exp-log`
15×	`flip3--` `flip--`
8×	`pow1`
6×	`cbrt-undiv` `div-exp` `associate-l` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`associate-/r` `associate-r/`
2×	`pow-prod-down` `*-commutative`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `frac-sub` `associate-/l*` `associate-/l/`

Counts

4 → 1294

Calls

4 calls:

22.0ms	(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
26.0ms	(* (sin x) (/ (sin eps) (cos eps)))
19.0ms	(* (sin x) (/ (sin eps) (cos eps)))
129.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

series735.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
129.0ms	(* (sin x) (/ (sin eps) (cos eps)))
134.0ms	(* (sin x) (/ (sin eps) (cos eps)))
343.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

simplify2.7s

Counts

1306 → 1306

Iterations

Iter	Nodes
1	2943
0	1320

prune27.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (/ (sin eps) (cos eps)))
0.3b	(* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps))))
3.1b	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))
26.0b	(cbrt (* (* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps)))) (* (sin x) (/ (sin eps) (cos eps)))))

rewrite349.0ms

Algorithm

rewrite-expression-head

Rules

2627×	`times-frac`
1956×	`add-sqr-sqrt`
1941×	`*-un-lft-identity`
1384×	`add-cube-cbrt`
1092×	`prod-diff`
370×	`difference-of-squares`
186×	`distribute-lft-out--`
183×	`div-inv`
84×	`fma-neg`
45×	`pow1` `add-cbrt-cube` `add-exp-log`
28×	`associate-/r/`
23×	`prod-exp` `cbrt-unprod`
21×	`associate-*r/`
18×	`pow-prod-down`
15×	`flip3--` `flip--`
14×	`associate-r`
7×	`cbrt-undiv` `cbrt-div` `div-exp`
6×	`frac-times` `associate-*l/` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `pow-sqr` `pow-prod-up` `log1p-expm1-u`
2×	`pow-plus` `*-commutative` `unswap-sqr`
1×	`cbrt-prod` `pow2` `sub-neg` `pow1/3` `diff-log` `swap-sqr` `pow3` `frac-sub` `rem-cbrt-cube`

Counts

4 → 1302

Calls

4 calls:

14.0ms	(* (sin x) (/ (sin eps) (cos eps)))
44.0ms	(* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps))))
104.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))
136.0ms	(cbrt (* (* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps)))) (* (sin x) (/ (sin eps) (cos eps)))))

series513.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (sin x) (/ (sin eps) (cos eps)))
96.0ms	(* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps))))
238.0ms	(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))
95.0ms	(cbrt (* (* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps)))) (* (sin x) (/ (sin eps) (cos eps)))))

simplify1.8s

Counts

1314 → 1314

Iterations

Iter	Nodes
1	3046
0	1363

prune20.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.9b

regimes209.0ms

Accuracy

0% (0.3b remaining)

Error of 12.6b against oracle of 12.4b and baseline of 12.6b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	26
1	26
0	23

end0.0ms

sample9.9s

Algorithm

intervals

Results

4.8s	3316×	body	1280	valid
2.3s	1875×	body	640	valid
1.9s	624×	body	2560	valid
465.0ms	761×	body	320	valid
202.0ms	1103×	body	80	valid
136.0ms	321×	body	160	valid