Details

sample141.0ms

Algorithm

intervals

Results

71.0ms	105×	body	1280	valid
24.0ms	61×	body	640	valid
21.0ms	13×	body	2560	valid
10.0ms	24×	body	320	valid
3.0ms	40×	body	80	valid
2.0ms	13×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (tan (+ x eps)) (tan x))
4.4b	(tan (+ x eps))

rewrite11.0ms

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:

7.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series144.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (tan (+ x eps)) (tan x))
54.0ms	(tan (+ x eps))

simplify77.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune88.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.0b

localize12.0ms

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))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite64.0ms

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:

11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
42.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series802.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
130.0ms	(+ (tan x) (tan eps))
92.0ms	(* (tan x) (tan eps))
364.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	995

prune290.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

3.0ms	(+ (tan x) (tan eps))
4.0ms	(* (sin x) (sin eps))
6.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
99.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

series630.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (tan x) (tan eps))
54.0ms	(* (sin x) (sin eps))
102.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
377.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	437	917
1	1799	792
2	5001	792

prune336.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 11.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan x) (tan eps)) (cos x))
0.3b	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
7.4b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))) (sin x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

12.0ms	(* (+ (tan x) (tan eps)) (cos x))
9.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
6.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
11.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))) (sin x)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (+ (tan x) (tan eps)) (cos x))
102.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
102.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
211.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))) (sin x)))

simplify107.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	741	1439
1	3713	1259
2	5002	1259

prune413.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes117.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	25
1	28	25

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.6s	3328×	body	1280	valid
1.1s	632×	body	2560	valid
726.0ms	1821×	body	640	valid
213.0ms	769×	body	320	valid
104.0ms	1120×	body	80	valid
64.0ms	330×	body	160	valid