Details

sample200.0ms

Algorithm

intervals

Results

99.0ms	95×	body	1280	valid
41.0ms	23×	body	2560	valid
35.0ms	70×	body	640	valid
6.0ms	19×	body	320	valid
4.0ms	38×	body	80	valid
2.0ms	11×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize9.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (tan (+ x eps)) (tan x))
3.3b	(tan (+ x eps))

rewrite53.0ms

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:

45.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series152.0ms

Counts

2 → 6

Calls

2 calls:

99.0ms	(- (tan (+ x eps)) (tan x))
53.0ms	(tan (+ x eps))

simplify72.0ms

Counts: 31 → 31

prune88.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(- 1 (* (tan x) (tan eps)))
0.2b	(* (tan x) (tan eps))
2.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3-+` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

8.0ms	(+ (tan x) (tan eps))
5.0ms	(- 1 (* (tan x) (tan eps)))
18.0ms	(* (tan x) (tan eps))
81.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series729.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(+ (tan x) (tan eps))
134.0ms	(- 1 (* (tan x) (tan eps)))
98.0ms	(* (tan x) (tan eps))
386.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify133.0ms

Counts: 74 → 74

prune325.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (/ (* (tan x) (sin eps)) (cos eps)))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
2.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
4×	`times-frac` `difference-of-squares`
3×	`tan-quot` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `distribute-lft-out--`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `frac-sub` `div-inv` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

11.0ms	(- 1 (/ (* (tan x) (sin eps)) (cos eps)))
15.0ms	(/ (* (tan x) (sin eps)) (cos eps))
14.0ms	(* (tan x) (sin eps))
154.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series693.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- 1 (/ (* (tan x) (sin eps)) (cos eps)))
101.0ms	(/ (* (tan x) (sin eps)) (cos eps))
71.0ms	(* (tan x) (sin eps))
399.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify42.0ms

Counts: 84 → 84

prune298.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(log (exp (- 1 (* (tan x) (tan eps)))))
0.2b	(exp (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
2.5b	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt` `add-log-exp`
7×	`pow1`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`tan-quot` `log-prod`
4×	`exp-sum` `log-pow`
3×	`sub-neg` `associate-r` `associate-l`
2×	`exp-diff` `diff-log` `rem-exp-log` `difference-of-squares`
1×	`frac-times` `log-div` `flip3--` `times-frac` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

12.0ms	(log (exp (- 1 (* (tan x) (tan eps)))))
12.0ms	(exp (- 1 (* (tan x) (tan eps))))
16.0ms	(* (tan x) (tan eps))
133.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

series775.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(log (exp (- 1 (* (tan x) (tan eps)))))
152.0ms	(exp (- 1 (* (tan x) (tan eps))))
107.0ms	(* (tan x) (tan eps))
396.0ms	(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (* (tan x) (tan eps)))))) (tan x))

simplify90.0ms

Counts: 82 → 82

prune257.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.9b

regimes158.0ms

Accuracy

85.7% (1.1b remaining)

Error of 15.8b against oracle of 14.7b and baseline of 22.1b

bsearch161.0ms

Steps

Iters	Range		Point
8	1.7343539956396646e-31	3.733336396375565e-27	5.540253431343871e-28
5	-3.897528618798951e-93	-1.4489476492269111e-93	-3.821283658645314e-93

simplify1.0ms

end0.0ms

sample8.7s

Algorithm

intervals

Results

4.8s	3371×	body	1280	valid
1.6s	624×	body	2560	valid
1.3s	1855×	body	640	valid
388.0ms	740×	body	320	valid
169.0ms	1069×	body	80	valid
126.0ms	341×	body	160	valid