Details

sample83.0ms

Algorithm

intervals

Results

38.0ms	103×	body	1280	valid
14.0ms	17×	body	2560	valid
14.0ms	57×	body	640	valid
5.0ms	37×	body	320	valid
1.0ms	32×	body	80	valid
1.0ms	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))

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))

series138.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (tan (+ x eps)) (tan x))
49.0ms	(tan (+ x eps))

simplify73.0ms

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

prune113.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.3b

localize14.0ms

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))

rewrite34.0ms

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:

3.0ms	(- 1 (* (tan x) (tan eps)))
5.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
15.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series624.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- 1 (* (tan x) (tan eps)))
88.0ms	(+ (tan x) (tan eps))
88.0ms	(* (tan x) (tan eps))
347.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify65.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (48.0ms)

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

prune373.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.2b

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

rewrite48.0ms

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:

5.0ms	(+ (tan x) (tan eps))
6.0ms	(/ (* (tan x) (sin eps)) (cos eps))
5.0ms	(* (tan x) (sin eps))
22.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series598.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (tan x) (tan eps))
92.0ms	(/ (* (tan x) (sin eps)) (cos eps))
65.0ms	(* (tan x) (sin eps))
353.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify89.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (59.0ms)

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

prune498.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin eps))
0.3b	(* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps)))
0.3b	(pow (/ (* (tan x) (sin eps)) (cos eps)) 3)
3.4b	(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (/ (* (tan x) (sin eps)) (cos eps)) 3))) (+ (* 1 1) (+ (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))) (* 1 (/ (* (tan x) (sin eps)) (cos eps))))) (- (tan x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log` `add-cbrt-cube`
23×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
17×	`prod-exp` `cbrt-unprod`
14×	`pow1` `cbrt-undiv` `div-exp`
10×	`associate-r` `associate-l`
7×	`unpow-prod-down` `cube-prod` `swap-sqr`
6×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-exp` `rem-cube-cbrt`
2×	`pow-prod-down` `associate-l/` `-commutative` `unswap-sqr`
1×	`tan-quot` `cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `pow-pow` `pow-plus` `unpow3` `associate-*r/` `pow-sqr` `pow-prod-up` `fma-udef` `sqr-pow`

Counts

4 → 127

Calls

4 calls:

5.0ms	(* (tan x) (sin eps))
12.0ms	(* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps)))
6.0ms	(pow (/ (* (tan x) (sin eps)) (cos eps)) 3)
1.0ms	(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (/ (* (tan x) (sin eps)) (cos eps)) 3))) (+ (* 1 1) (+ (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))) (* 1 (/ (* (tan x) (sin eps)) (cos eps))))) (- (tan x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (tan x) (sin eps))
120.0ms	(* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps)))
124.0ms	(pow (/ (* (tan x) (sin eps)) (cos eps)) 3)
898.0ms	(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (/ (* (tan x) (sin eps)) (cos eps)) 3))) (+ (* 1 1) (+ (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))) (* 1 (/ (* (tan x) (sin eps)) (cos eps))))) (- (tan x)))

simplify145.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	824	1673
1	4917	1465
2	5001	1465

prune525.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

regimes132.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	112
1	57	112

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3316×	body	1280	valid
535.0ms	623×	body	2560	valid
392.0ms	1858×	body	640	valid
107.0ms	777×	body	320	valid
49.0ms	1076×	body	80	valid
33.0ms	350×	body	160	valid