Details

sample283.0ms

Algorithm

intervals

Results

11.0ms	43×	body	1280	valid
7.0ms	145×	body	80	valid
6.0ms	38×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 119

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series234.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- 1.0 (* (tan x) (tan x)))
102.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
64.0ms	(* (tan x) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	917
2	5001	882

prune277.0ms

Filtered

131 candidates to 91 candidates (69.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	119	12	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	12	132

Merged error: 0.0b

Counts

132 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.1b	(- 1.0 (* (tan x) (tan x)))
0.1b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
76×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
13×	`difference-of-squares`
12×	`pow1`
11×	`add-cbrt-cube`
9×	`associate-/r/`
7×	`div-exp`
6×	`add-log-exp`
5×	`flip3--` `flip--` `div-inv`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-neg` `swap-sqr` `associate-r` `associate-l` `prod-diff` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`pow2` `frac-times` `sub-neg` `pow-flip` `frac-2neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 159

Calls

4 calls:

1.0ms	(fma (tan x) (tan x) 1.0)
3.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series225.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(fma (tan x) (tan x) 1.0)
34.0ms	(- 1.0 (* (tan x) (tan x)))
110.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))

simplify77.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	570	2046
1	2617	1859
2	5002	1752

prune275.0ms

Filtered

171 candidates to 98 candidates (57.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	168	3	171
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	171	12	183

Merged error: 0.0b

Counts

183 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
44×	`add-cube-cbrt`
37×	`times-frac`
27×	`associate-r`
20×	`sqrt-prod`
18×	`prod-diff`
16×	`difference-of-squares`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--`
7×	`associate-l`
6×	`fma-neg` `associate-/l*` `add-log-exp`
4×	`tan-quot` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`frac-times` `swap-sqr` `associate-l/` `prod-exp` `associate-/r` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv` `associate-/l/`
1×	`pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `clear-num` `pow-sqr` `pow-prod-up` `distribute-lft-out`

Counts

4 → 167

Calls

4 calls:

9.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(- (sqrt 1.0) (tan x))
20.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series382.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
43.0ms	(- (sqrt 1.0) (tan x))
205.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))

simplify93.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	644	2081
1	3040	1700
2	5002	1673

prune333.0ms

Filtered

179 candidates to 115 candidates (64.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	179	12	191

Merged error: 0.0b

Counts

191 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (fma (tan x) (tan x) 1.0))
0.1b	(/ (fma (tan x) (tan x) 1.0) (tan x))
0.3b	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
0.3b	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

1436×	`times-frac`
888×	`add-sqr-sqrt`
873×	`*-un-lft-identity`
867×	`add-cube-cbrt`
611×	`prod-diff`
107×	`div-inv`
58×	`associate-/r/`
45×	`tan-quot`
20×	`associate-/r*`
13×	`add-exp-log` `fma-neg` `add-cbrt-cube`
9×	`associate-/l*`
6×	`add-log-exp` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `associate-/l/`

Counts

4 → 783

Calls

4 calls:

3.0ms	(/ 1.0 (fma (tan x) (tan x) 1.0))
4.0ms	(/ (fma (tan x) (tan x) 1.0) (tan x))
7.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
47.0ms	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ 1.0 (fma (tan x) (tan x) 1.0))
85.0ms	(/ (fma (tan x) (tan x) 1.0) (tan x))
109.0ms	(/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x)))
193.0ms	(- (/ 1.0 (fma (tan x) (tan x) 1.0)) (/ (tan x) (/ (fma (tan x) (tan x) 1.0) (tan x))))

simplify317.0ms

Algorithm

egg-herbie

Counts

795 → 795

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2457	44315
1	5001	35123

prune1.8s

Filtered

795 candidates to 508 candidates (63.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	792	3	795
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	795	12	807

Merged error: 0.0b

Counts

807 → 12

regimes192.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	12
1	13	12

end0.0ms

sample975.0ms

Algorithm

intervals

Results

382.0ms	1496×	body	1280	valid
214.0ms	1282×	body	640	valid
164.0ms	4317×	body	80	valid
69.0ms	579×	body	320	valid
31.0ms	326×	body	160	valid