Details

sample175.0ms

Algorithm

intervals

Results

88.0ms	119×	body	1280	valid
48.0ms	29×	body	2560	valid
21.0ms	55×	body	640	valid
5.0ms	18×	body	320	valid
3.0ms	30×	body	80	valid
1.0ms	5×	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: 40.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (tan (+ x eps)) (tan x))
2.9b	(tan (+ x eps))

rewrite13.0ms

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

series145.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (tan (+ x eps)) (tan x))
55.0ms	(tan (+ x eps))

simplify81.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (24.0ms)

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

prune85.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.0b

localize11.0ms

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))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite61.0ms

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))
40.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series745.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
90.0ms	(+ (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
353.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (38.0ms)

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

prune290.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 18.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.2b	(* (tan x) (tan eps))
0.3b	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (cos x) (cos eps)))
9.1b	(- (/ (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (cos x) (cos eps))) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
5.0ms	(* (tan x) (tan eps))
11.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (cos x) (cos eps)))
57.0ms	(- (/ (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (cos x) (cos eps))) (- 1 (* (tan x) (tan eps)))) (tan x))

series638.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos x) (sin eps))
91.0ms	(* (tan x) (tan eps))
147.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (cos x) (cos eps)))
358.0ms	(- (/ (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (cos x) (cos eps))) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify62.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	480	1177
1	1956	1046
2	5001	1028

prune401.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 18.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (cos x) (cos eps)))
4.0b	(- (* (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (cos x) (cos eps))) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
11.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (cos x) (cos eps)))
12.0ms	(- (* (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (cos x) (cos eps))) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
148.0ms	(/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (cos x) (cos eps)))
164.0ms	(- (* (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (* (cos x) (cos eps))) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	511	1160
1	2231	1033
2	5001	1033

prune390.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

regimes134.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	21
1	29	21

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.5s	3323×	body	1280	valid
1.1s	663×	body	2560	valid
743.0ms	1849×	body	640	valid
198.0ms	749×	body	320	valid
91.0ms	1069×	body	80	valid
60.0ms	347×	body	160	valid