Details

sample404.0ms

Algorithm

intervals

Results

232.0ms	111×	body	1280	valid
66.0ms	60×	body	640	valid
64.0ms	19×	body	2560	valid
16.0ms	22×	body	320	valid
9.0ms	34×	body	80	valid
5.0ms	10×	body	160	valid

simplify9.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

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

30.0ms	(- (tan (+ x eps)) (tan x))
5.0ms	(tan (+ x eps))

series178.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

94.0ms	(- (tan (+ x eps)) (tan x))
84.0ms	(tan (+ x eps))

simplify1.4s

Counts: 33 → 33

prune410.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.6b

localize54.0ms

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))

rewrite122.0ms

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

70.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
23.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
21.0ms	(* (tan x) (tan eps))
7.0ms	(+ (tan x) (tan eps))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

520.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
319.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
141.0ms	(* (tan x) (tan eps))
126.0ms	(+ (tan x) (tan eps))

simplify1.2s

Counts: 102 → 102

prune1.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 15.4b

localize62.0ms

Local error

Found 4 expressions with local error:

3.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b	(* (sin x) (sin eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))

rewrite389.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
26×	`times-frac`
20×	`add-cbrt-cube` `add-exp-log`
18×	`add-cube-cbrt`
12×	`difference-of-squares`
7×	`associate-/r*` `distribute-lft-out`
6×	`pow1` `distribute-lft-out--` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
4×	`insert-posit16` `associate-/l/`
3×	`associate-r` `associate-l` `tan-quot` `associate-/r/`
2×	`clear-num` `frac-2neg` `flip3--` `div-inv` `flip--` `sin-mult`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `cos-mult` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`

Counts

4 → 113

Calls

4 calls:

Slowest

291.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
66.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
19.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
11.0ms	(* (sin x) (sin eps))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

579.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
349.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
146.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
82.0ms	(* (sin x) (sin eps))

simplify893.0ms

Counts: 125 → 125

prune2.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.4b

localize70.0ms

Local error

Found 4 expressions with local error:

9.0b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (sin x)))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b	(* (sin x) (sin eps))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-cbrt-cube` `add-exp-log`
12×	`associate-*l/`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `cbrt-undiv` `div-exp`
6×	`pow1` `*-un-lft-identity` `frac-sub` `add-cube-cbrt` `add-log-exp`
4×	`flip3--` `tan-quot` `insert-posit16` `flip--`
3×	`associate-r` `associate-l` `sin-mult`
2×	`clear-num` `associate-/r` `frac-2neg` `flip3-+` `times-frac` `frac-add` `associate-/r/` `cos-mult` `flip-+` `div-inv` `associate-/l` `associate-/l/`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

Slowest

50.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (sin x)))
34.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
32.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
21.0ms	(* (sin x) (sin eps))

series680.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

299.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (sin x)))
178.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
152.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
51.0ms	(* (sin x) (sin eps))

simplify1.1s

Counts: 99 → 99

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

regimes200.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample14.6s

Algorithm

intervals

Results

8.1s	3328×	body	1280	valid
2.3s	615×	body	2560	valid
2.2s	1822×	body	640	valid
1.1s	733×	body	320	valid
307.0ms	1144×	body	80	valid
224.0ms	358×	body	160	valid