Details

sample325.0ms

Algorithm

intervals

Results

154.0ms	110×	body	1280	valid
95.0ms	21×	body	2560	valid
35.0ms	43×	body	640	valid
14.0ms	25×	body	320	valid
6.0ms	42×	body	80	valid
5.0ms	15×	body	160	valid

simplify15.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize9.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (tan (+ x eps)) (tan x))
3.3b	(tan (+ x eps))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

37.0ms	(- (tan (+ x eps)) (tan x))
13.0ms	(tan (+ x eps))

series614.0ms

Counts

2 → 6

Calls

2 calls:

502.0ms	(- (tan (+ x eps)) (tan x))
112.0ms	(tan (+ x eps))

simplify1.3s

Counts: 31 → 31

prune157.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan eps) (tan x))
3.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

rewrite248.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

39.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
9.0ms	(+ (tan x) (tan eps))
23.0ms	(* (tan eps) (tan x))
175.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

356.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
132.0ms	(+ (tan x) (tan eps))
138.0ms	(* (tan eps) (tan x))
575.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify712.0ms

Counts: 98 → 98

prune440.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (tan eps))
0.6b	(cbrt (tan eps))
0.6b	(cbrt (tan eps))
3.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (tan eps)) (cbrt (tan eps))) (* (cbrt (tan eps)) (tan x))))) (tan x))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`cbrt-prod` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`tan-quot` `pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (tan eps))
2.0ms	(cbrt (tan eps))
2.0ms	(cbrt (tan eps))
121.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (tan eps)) (cbrt (tan eps))) (* (cbrt (tan eps)) (tan x))))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (tan eps))
180.0ms	(cbrt (tan eps))
190.0ms	(cbrt (tan eps))
523.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (tan eps)) (cbrt (tan eps))) (* (cbrt (tan eps)) (tan x))))) (tan x))

simplify666.0ms

Counts: 64 → 64

prune362.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.4b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

21×	`associate-l`
17×	`add-sqr-sqrt`
13×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`tan-quot`
9×	`associate-r`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-*l/` `distribute-neg-frac` `add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`distribute-lft-neg-out`
3×	`frac-times` `associate-r/` `-commutative`
2×	`neg-mul-1` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 92

Calls

4 calls:

33.0ms	(* (- (tan x)) (tan eps))
24.0ms	(* (- (tan x)) (tan eps))
42.0ms	(* (* (- (tan x)) (tan eps)) (sin x))
50.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (sin x))

series724.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(* (- (tan x)) (tan eps))
178.0ms	(* (- (tan x)) (tan eps))
196.0ms	(* (* (- (tan x)) (tan eps)) (sin x))
156.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (sin x))

simplify955.0ms

Counts: 104 → 104

prune579.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes151.0ms

Accuracy

0.4% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify508.0ms

end0.0ms

sample10.5s

Algorithm

intervals

Results

5.1s	3237×	body	1280	valid
2.3s	709×	body	2560	valid
1.5s	1822×	body	640	valid
892.0ms	765×	body	320	valid
206.0ms	1105×	body	80	valid
162.0ms	362×	body	160	valid