Details

sample199.0ms

Algorithm

intervals

Results

82.0ms	96×	body	1280	valid
60.0ms	31×	body	2560	valid
32.0ms	64×	body	640	valid
7.0ms	21×	body	320	valid
3.0ms	31×	body	80	valid
3.0ms	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
4.7b	(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))

series49.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (70.0ms)

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

prune260.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.4b

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))
0.3b	(* (tan x) (tan eps))
2.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite77.0ms

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))
50.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series222.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
23.0ms	(+ (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
115.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify73.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (52.0ms)

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

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.2b	(- (/ (* (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
41×	`tan-quot`
37×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `prod-diff`
27×	`add-cube-cbrt`
20×	`add-exp-log` `times-frac` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
11×	`fma-neg`
10×	`prod-exp` `cbrt-unprod`
9×	`difference-of-squares`
8×	`associate-/r/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `div-inv`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `sub-neg` `diff-log` `swap-sqr` `frac-sub` `distribute-lft-out--`

Counts

4 → 158

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
21.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
30.0ms	(- (/ (* (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))

series384.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (tan x) (tan eps))
23.0ms	(* (tan x) (tan eps))
36.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
303.0ms	(- (/ (* (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))

simplify92.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	652	2690
1	2938	2162
2	5001	2157

prune1.6s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos eps) 2)
0.3b	(pow (sin eps) 2)
0.3b	(* (tan x) (tan x))
2.2b	(- (/ (* (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (/ (* (* (tan x) (tan x)) (pow (sin eps) 2)) (pow (cos eps) 2)))) (tan x))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
24×	`times-frac`
13×	`pow1`
12×	`fma-neg`
9×	`difference-of-squares`
8×	`add-exp-log` `associate-/r/`
6×	`unpow-prod-down` `pow-unpow` `add-cbrt-cube` `add-log-exp`
5×	`tan-quot` `flip3--` `flip--` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`pow-to-exp` `pow-pow` `pow-exp` `unpow2` `sqr-pow`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 135

Calls

4 calls:

2.0ms	(pow (cos eps) 2)
1.0ms	(pow (sin eps) 2)
5.0ms	(* (tan x) (tan x))
126.0ms	(- (/ (* (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (/ (* (* (tan x) (tan x)) (pow (sin eps) 2)) (pow (cos eps) 2)))) (tan x))

series326.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (cos eps) 2)
3.0ms	(pow (sin eps) 2)
11.0ms	(* (tan x) (tan x))
308.0ms	(- (/ (* (+ (tan x) (tan eps)) (fma (tan x) (tan eps) 1)) (- 1 (/ (* (* (tan x) (tan x)) (pow (sin eps) 2)) (pow (cos eps) 2)))) (tan x))

simplify75.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	579	2692
1	2397	2181
2	5001	2173

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.2b

regimes546.0ms

Accuracy

87% (0.9b remaining)

Error of 15.8b against oracle of 14.9b and baseline of 22.1b

bsearch140.0ms

Steps

Iters	Range		Point
9	1.9540685346212126e-24	9.316647860064626e-18	1.047829285418837e-23
8	-5.529960614046254e-31	-1.2848272222116945e-35	-4.530799695865795e-32

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	80
1	54	80

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.1s	3364×	body	1280	valid
1.3s	667×	body	2560	valid
952.0ms	1800×	body	640	valid
281.0ms	787×	body	320	valid
120.0ms	1032×	body	80	valid
83.0ms	350×	body	160	valid