Details

sample86.0ms

Algorithm

intervals

Results

44.0ms	113×	body	1280	valid
16.0ms	19×	body	2560	valid
11.0ms	55×	body	640	valid
3.0ms	23×	body	320	valid
2.0ms	42×	body	80	valid
0.0ms	4×	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: 36.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (tan (+ x eps)) (tan x))
2.6b	(tan (+ x eps))

rewrite12.0ms

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:

7.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series140.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (tan (+ x eps)) (tan x))
53.0ms	(tan (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (68.0ms)

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

prune116.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.8b

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

rewrite40.0ms

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:

8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
14.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series728.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(+ (tan x) (tan eps))
88.0ms	(* (tan x) (tan eps))
344.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify72.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (52.0ms)

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

prune413.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
3.0b	(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`tan-quot`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `frac-times` `pow-unpow` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `cbrt-unprod`
2×	`pow-pow` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `fma-udef` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
6.0ms	(pow (* (tan x) (tan eps)) 3)
1.0ms	(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (tan x) (tan eps))
88.0ms	(* (tan x) (tan eps))
119.0ms	(pow (* (tan x) (tan eps)) 3)
847.0ms	(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (- (tan x)))

simplify70.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	483	922
1	2591	827
2	5002	826

prune451.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos eps) 3)
0.4b	(pow (cos eps) 3)
0.4b	(pow (cos eps) 3)
1.8b	(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x))) (/ (sin x) (cos x)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

131×	`times-frac`
117×	`prod-diff`
113×	`*-un-lft-identity`
111×	`add-sqr-sqrt`
106×	`add-cube-cbrt`
28×	`associate-*l/` `associate-/r/`
25×	`div-inv`
15×	`flip3--` `flip--`
9×	`unpow-prod-down` `pow-unpow` `fma-neg` `cube-prod`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `distribute-rgt-out--` `log1p-expm1-u`
3×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
2×	`distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

4 → 224

Calls

4 calls:

3.0ms	(pow (cos eps) 3)
3.0ms	(pow (cos eps) 3)
3.0ms	(pow (cos eps) 3)
27.0ms	(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x))) (/ (sin x) (cos x)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (cos eps) 3)
27.0ms	(pow (cos eps) 3)
32.0ms	(pow (cos eps) 3)
234.0ms	(- (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x))) (/ (sin x) (cos x)))

simplify128.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	738	8188
1	2877	6189
2	5002	5715

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes147.0ms

Accuracy

0% (0.3b 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	72	143
1	72	143

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3279×	body	1280	valid
545.0ms	634×	body	2560	valid
379.0ms	1821×	body	640	valid
101.0ms	754×	body	320	valid
48.0ms	1151×	body	80	valid
34.0ms	361×	body	160	valid