Details

sample371.0ms

Algorithm

intervals

Results

179.0ms	113×	body	1280	valid
101.0ms	20×	body	2560	valid
50.0ms	53×	body	640	valid
13.0ms	21×	body	320	valid
10.0ms	12×	body	160	valid
7.0ms	37×	body	80	valid

simplify8.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize18.0ms

Local error

Found 2 expressions with local error:

3.8b	(tan (+ x eps))
1.0b	(- (tan (+ x eps)) (tan x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

Slowest

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

series215.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

123.0ms	(- (tan (+ x eps)) (tan x))
91.0ms	(tan (+ x eps))

simplify1.3s

Counts: 33 → 33

prune425.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.1b

localize45.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (/ (+ (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))))

rewrite108.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`insert-posit16` `associate-/l*`
3×	`associate-/r` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `flip3--` `frac-add` `associate-/r/` `flip-+` `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` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

Slowest

59.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
25.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(* (tan x) (tan eps))
9.0ms	(+ (tan x) (tan eps))

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

520.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
284.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
119.0ms	(+ (tan x) (tan eps))
102.0ms	(* (tan x) (tan eps))

simplify1.5s

Counts: 102 → 102

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.9b

localize72.0ms

Local error

Found 4 expressions with local error:

8.2b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (+ (tan x) (tan eps)) (cos x))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
9×	`associate-r`
6×	`frac-sub` `add-log-exp`
4×	`flip3--` `insert-posit16` `flip--`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `diff-log` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

Slowest

33.0ms	(* (+ (tan x) (tan eps)) (cos x))
30.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
27.0ms	(* (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))

series721.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

292.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
155.0ms	(* (+ (tan x) (tan eps)) (cos x))
139.0ms	(* (tan x) (tan eps))
134.0ms	(* (tan x) (tan eps))

simplify833.0ms

Counts: 98 → 98

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (cos x) (/ (sin eps) (cos eps))) (sin x))
0.3b	(/ (cos x) (/ (cos eps) (sin eps)))
0.2b	(* (tan x) (tan eps))
0.2b	(/ (sin x) (/ (/ (cos x) (/ (sin eps) (cos eps))) (sin x)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

2199×	`times-frac`
972×	`add-sqr-sqrt`
970×	`*-un-lft-identity` `add-cube-cbrt`
152×	`associate-/r*`
75×	`div-inv`
50×	`associate-/l*`
34×	`add-cbrt-cube` `add-exp-log`
19×	`cbrt-undiv` `div-exp`
18×	`associate-/r/`
6×	`pow1`
4×	`tan-quot` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `associate-l`
1×	`frac-times` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `unswap-sqr` `associate-/l/`

Counts

4 → 857

Calls

4 calls:

Slowest

32.0ms	(/ (/ (cos x) (/ (sin eps) (cos eps))) (sin x))
25.0ms	(/ (sin x) (/ (/ (cos x) (/ (sin eps) (cos eps))) (sin x)))
14.0ms	(* (tan x) (tan eps))
11.0ms	(/ (cos x) (/ (cos eps) (sin eps)))

series604.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

174.0ms	(* (tan x) (tan eps))
166.0ms	(/ (/ (cos x) (/ (sin eps) (cos eps))) (sin x))
137.0ms	(/ (cos x) (/ (cos eps) (sin eps)))
127.0ms	(/ (sin x) (/ (/ (cos x) (/ (sin eps) (cos eps))) (sin x)))

simplify3.8s

Counts: 869 → 869

prune15.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

regimes288.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch6.0ms

end0.0ms

sample11.6s

Algorithm

intervals

Results

5.5s	3278×	body	1280	valid
2.5s	1863×	body	640	valid
1.9s	667×	body	2560	valid
861.0ms	770×	body	320	valid
596.0ms	1103×	body	80	valid
127.0ms	319×	body	160	valid