Details

sample286.0ms

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

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	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

30×	`add-sqr-sqrt`
21×	`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×	`associate-/l*`
3×	`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 → 105

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
7.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series221.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1.0 (* (tan x) (tan x)))
96.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
60.0ms	(* (tan x) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5001	824

prune240.0ms

Filtered

117 candidates to 77 candidates (65.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	104	13	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	13	118

Merged error: 0.0b

Counts

118 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
80×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube` `difference-of-squares`
9×	`associate-/r/`
8×	`tan-quot`
7×	`div-exp`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`flip3--` `flip--` `div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow2` `frac-times` `rec-exp` `pow-plus` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `clear-num` `inv-pow`

Counts

4 → 165

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
9.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
6.0ms	(* (tan x) (tan x))
6.0ms	(* (tan x) (tan x))

series192.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1.0 (* (tan x) (tan x)))
92.0ms	(/ 1 (/ (+ 1.0 (* (tan x) (tan x))) (- 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))

simplify75.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	545	2150
1	2567	1968
2	5001	1866

prune240.0ms

Filtered

177 candidates to 91 candidates (51.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	174	3	177
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	177	13	190

Merged error: 0.0b

Counts

190 → 13

localize11.0ms

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))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
37×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-r`
16×	`difference-of-squares`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`sqrt-prod` `distribute-lft-out--`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
4×	`tan-quot` `flip3-+` `associate-/r/` `flip-+`
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 → 135

Calls

4 calls:

9.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- (sqrt 1.0) (tan x))
18.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
6.0ms	(* (tan x) (tan x))

series353.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
36.0ms	(- (sqrt 1.0) (tan x))
189.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))

simplify84.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	561	1675
1	2800	1512
2	5001	1496

prune292.0ms

Filtered

147 candidates to 99 candidates (67.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	146	14	160

Merged error: 0.0b

Counts

160 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
6×	`tan-quot` `associate-r` `associate-l` `associate-/r` `associate-/l`
4×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`pow2` `frac-times` `flip3--` `flip3-+` `pow-plus` `div-sub` `associate-*r/` `pow-sqr` `pow-prod-up` `flip--` `flip-+`

Counts

4 → 109

Calls

4 calls:

7.0ms	(/ (* (tan x) (sin x)) (cos x))
10.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(* (tan x) (sin x))
6.0ms	(* (tan x) (tan x))

series250.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (* (tan x) (sin x)) (cos x))
110.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
46.0ms	(* (tan x) (sin x))
32.0ms	(* (tan x) (tan x))

simplify60.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	441	1158
1	1849	1062
2	5001	1056

prune236.0ms

Filtered

121 candidates to 83 candidates (68.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	3	9	12
Picked	0	1	1
Done	0	1	1
Total	123	12	135

Merged error: 0.0b

Counts

135 → 12

regimes237.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

end0.0ms

sample993.0ms

Algorithm

intervals

Results

393.0ms	1496×	body	1280	valid
216.0ms	1282×	body	640	valid
169.0ms	4317×	body	80	valid
70.0ms	579×	body	320	valid
30.0ms	326×	body	160	valid