Details

sample147.0ms

Algorithm

intervals

Results

74.0ms	103×	body	1280	valid
27.0ms	17×	body	2560	valid
23.0ms	57×	body	640	valid
9.0ms	37×	body	320	valid
3.0ms	32×	body	80	valid
2.0ms	10×	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: 39.6b

localize8.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (tan (+ x eps)) (tan x))
3.3b	(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))

series142.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(- (tan (+ x eps)) (tan x))
54.0ms	(tan (+ x eps))

simplify71.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (67.0ms)

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

prune109.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

87×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
59×	`add-cube-cbrt`
57×	`prod-diff`
49×	`times-frac`
21×	`fma-neg`
13×	`distribute-lft-out`
10×	`add-log-exp`
8×	`associate-/r/`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-def` `associate-r` `associate-l`
2×	`sub-neg` `diff-log` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 151

Calls

4 calls:

2.0ms	(- 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))

series649.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- 1 (* (tan x) (tan eps)))
93.0ms	(+ (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
357.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify72.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	542	2573
1	1893	2021
2	5002	1996

prune381.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.2b

localize16.0ms

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))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite127.0ms

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:

4.0ms	(+ (tan x) (tan eps))
5.0ms	(/ (* (tan x) (sin eps)) (cos eps))
5.0ms	(* (tan x) (sin eps))
103.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series637.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (tan x) (tan eps))
100.0ms	(/ (* (tan x) (sin eps)) (cos eps))
71.0ms	(* (tan x) (sin eps))
372.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify97.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (60.0ms)

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

prune522.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.1b

localize19.0ms

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))
3.5b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (tan x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log` `add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`add-cube-cbrt`
6×	`pow1` `add-log-exp`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `frac-add` `clear-num` `sum-log` `-commutative` `flip-+` `fma-udef` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

3.0ms	(+ (tan x) (tan eps))
5.0ms	(/ (* (tan x) (sin eps)) (cos eps))
5.0ms	(* (tan x) (sin eps))
0.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (tan x)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (tan x) (tan eps))
98.0ms	(/ (* (tan x) (sin eps)) (cos eps))
71.0ms	(* (tan x) (sin eps))
302.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (tan x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	350	661
1	1333	582
2	5001	581

prune294.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.1b

regimes182.0ms

Accuracy

87.8% (0.9b remaining)

Error of 15.1b against oracle of 14.2b and baseline of 21.4b

bsearch136.0ms

Steps

Iters	Range		Point
7	7.475162141923425e-25	1.4540068674601437e-22	1.0217107006174054e-22
7	-2.130734117157608e-37	-3.254557815371694e-39	-6.303458796209113e-39

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	41
1	38	41

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.5s	3319×	body	1280	valid
1.1s	623×	body	2560	valid
788.0ms	1857×	body	640	valid
213.0ms	775×	body	320	valid
88.0ms	1072×	body	80	valid
64.0ms	354×	body	160	valid