Details

sample163.0ms

Algorithm

intervals

Results

74.0ms	106×	body	1280	valid
41.0ms	25×	body	2560	valid
28.0ms	61×	body	640	valid
5.0ms	20×	body	320	valid
3.0ms	32×	body	80	valid
2.0ms	12×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize9.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
3.5b	(tan (+ x eps))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

8.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series145.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (tan (+ x eps)) (tan x))
55.0ms	(tan (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	192	420
1	538	319
2	2593	310
3	5001	255

prune120.0ms

Filtered

47 candidates to 33 candidates (70.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.5b

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))
1.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `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` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

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))
52.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series767.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
96.0ms	(+ (tan x) (tan eps))
95.0ms	(* (tan x) (tan eps))
362.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify78.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	559	2915
1	2054	2366
2	5001	2345

prune425.0ms

Filtered

181 candidates to 110 candidates (60.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
1.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

183×	`*-un-lft-identity`
138×	`add-sqr-sqrt`
100×	`times-frac`
90×	`prod-diff`
83×	`add-cube-cbrt`
34×	`difference-of-squares`
30×	`fma-neg`
25×	`distribute-lft-out`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/` `add-log-exp`
6×	`pow1`
5×	`tan-quot` `flip3--` `flip--` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `clear-num` `sum-log` `-commutative` `frac-sub` `flip-+` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

4 → 201

Calls

4 calls:

3.0ms	(+ (tan x) (tan eps))
5.0ms	(/ (* (tan x) (sin eps)) (cos eps))
5.0ms	(* (tan x) (sin eps))
102.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series628.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (tan x) (tan eps))
98.0ms	(/ (* (tan x) (sin eps)) (cos eps))
64.0ms	(* (tan x) (sin eps))
372.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify94.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	670	4171
1	2493	3274
2	5001	3235

prune506.0ms

Filtered

213 candidates to 105 candidates (49.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin eps))
0.2b	(/ (cos eps) (* (tan x) (sin eps)))
0.5b	(/ 1 (/ (cos eps) (* (tan x) (sin eps))))
1.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ 1 (/ (cos eps) (* (tan x) (sin eps)))))) (tan x))

rewrite344.0ms

Algorithm

rewrite-expression-head

Rules

357×	`*-un-lft-identity`
322×	`add-sqr-sqrt`
280×	`times-frac`
150×	`prod-diff`
139×	`add-cube-cbrt`
98×	`difference-of-squares`
50×	`fma-neg`
44×	`distribute-lft-out`
33×	`distribute-lft-out--`
32×	`add-exp-log`
26×	`div-inv`
20×	`add-cbrt-cube`
14×	`div-exp` `associate-/r/`
9×	`associate-/r*`
7×	`tan-quot` `pow1` `cbrt-undiv`
6×	`associate-l/` `associate-/l` `add-log-exp`
5×	`flip3--` `prod-exp` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `associate-r` `associate-l` `cbrt-unprod`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `inv-pow` `unswap-sqr`

Counts

4 → 325

Calls

4 calls:

5.0ms	(* (tan x) (sin eps))
5.0ms	(/ (cos eps) (* (tan x) (sin eps)))
9.0ms	(/ 1 (/ (cos eps) (* (tan x) (sin eps))))
300.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ 1 (/ (cos eps) (* (tan x) (sin eps)))))) (tan x))

series656.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (tan x) (sin eps))
107.0ms	(/ (cos eps) (* (tan x) (sin eps)))
105.0ms	(/ 1 (/ (cos eps) (* (tan x) (sin eps))))
372.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ 1 (/ (cos eps) (* (tan x) (sin eps)))))) (tan x))

simplify119.0ms

Algorithm

egg-herbie

Counts

337 → 337

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	931	7284
1	3643	5686
2	5002	5614

prune619.0ms

Filtered

337 candidates to 135 candidates (40.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.3b

regimes172.0ms

Accuracy

72.2% (2.0b remaining)

Error of 15.8b against oracle of 13.8b and baseline of 21.1b

bsearch247.0ms

Steps

Iters	Range		Point
9	4.017695445394683e-173	5.816336440788529e-167	5.748527172026931e-167
10	-2.3022776580077488e-90	-1.7535355178555737e-102	-1.4968426811240258e-90

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	50
1	51	50
2	51	50

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.4s	3292×	body	1280	valid
1.1s	636×	body	2560	valid
743.0ms	1787×	body	640	valid
225.0ms	805×	body	320	valid
90.0ms	1118×	body	80	valid
64.0ms	362×	body	160	valid