Details

analyze724.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample41.0ms

Algorithm

intervals

Results

13.0ms	48×	body	1280	valid
8.0ms	42×	body	640	valid
6.0ms	141×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	8×	body	160	valid

simplify511.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5284	15

prune4.0ms

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))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite35.0ms

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 → 104

Calls

4 calls:

6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
15.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series68.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

simplify53.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4951	1205
1	4951	1205

prune241.0ms

Filtered

82 candidates to 116 candidates (-41.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	104	12	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	12	117

Merged error: 0.1b

Counts

117 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2)))
0.2b	(- 1.0 (pow (tan x) 2))
0.2b	(pow (tan x) 2)
0.2b	(pow (tan x) 2)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
32×	`times-frac`
24×	`difference-of-squares`
22×	`add-cube-cbrt`
12×	`unpow-prod-down`
9×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*` `unpow2` `sqr-pow`
6×	`pow1` `pow-unpow` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp`
4×	`associate-/l*`
2×	`pow-to-exp` `flip3--` `pow-pow` `pow-exp` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 112

Calls

4 calls:

12.0ms	(/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2)))
5.0ms	(- 1.0 (pow (tan x) 2))
3.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)

series59.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2)))
9.0ms	(- 1.0 (pow (tan x) 2))
8.0ms	(pow (tan x) 2)
9.0ms	(pow (tan x) 2)

simplify38.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5006	1681

prune226.0ms

Filtered

77 candidates to 124 candidates (-61.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	124	12	136

Merged error: 0.0b

Counts

136 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (pow (tan x) 2))
0.2b	(* (+ (pow (tan x) 2) 1.0) (/ 1 (- 1.0 (pow (tan x) 2))))
0.2b	(pow (tan x) 2)
0.2b	(pow (tan x) 2)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
30×	`associate-r`
26×	`times-frac`
21×	`add-cube-cbrt`
16×	`difference-of-squares`
15×	`add-exp-log`
10×	`unpow-prod-down`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`pow-unpow` `unpow2` `add-log-exp` `sqr-pow`
4×	`associate-l` `prod-exp` `distribute-lft-out--`
3×	`unswap-sqr`
2×	`frac-times` `pow-to-exp` `flip3--` `pow-pow` `flip3-+` `div-exp` `associate-*l/` `pow-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 110

Calls

4 calls:

5.0ms	(- 1.0 (pow (tan x) 2))
20.0ms	(* (+ (pow (tan x) 2) 1.0) (/ 1 (- 1.0 (pow (tan x) 2))))
3.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)

series59.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- 1.0 (pow (tan x) 2))
33.0ms	(* (+ (pow (tan x) 2) 1.0) (/ 1 (- 1.0 (pow (tan x) 2))))
9.0ms	(pow (tan x) 2)
9.0ms	(pow (tan x) 2)

simplify71.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4943	1343
1	4943	1343

prune238.0ms

Filtered

83 candidates to 122 candidates (-47.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	122	12	134

Merged error: 0.0b

Counts

134 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt 1.0) (tan x))
0.2b	(/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0))
0.2b	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0)))
0.2b	(pow (tan x) 2)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
49×	`times-frac`
30×	`add-cube-cbrt` `associate-r`
20×	`difference-of-squares`
14×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`sqrt-prod` `distribute-lft-out--`
7×	`pow1`
6×	`associate-/l*` `add-log-exp`
4×	`flip3-+` `associate-l` `associate-/r*` `associate-/r/` `flip-+`
3×	`unpow-prod-down` `pow-unpow`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `unpow2` `sqr-pow`

Counts

4 → 137

Calls

4 calls:

4.0ms	(- (sqrt 1.0) (tan x))
11.0ms	(/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0))
21.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0)))
3.0ms	(pow (tan x) 2)

series86.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (sqrt 1.0) (tan x))
27.0ms	(/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0))
41.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0)))
11.0ms	(pow (tan x) 2)

simplify68.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4966	2307
1	4966	2307

prune255.0ms

Filtered

93 candidates to 149 candidates (-60.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	149	12	161

Merged error: 0.0b

Counts

161 → 12

regimes157.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	15
1	21	15

end0.0ms

sample1.0s

Algorithm

intervals

Results

408.0ms	1527×	body	1280	valid
224.0ms	1259×	body	640	valid
174.0ms	4314×	body	80	valid
71.0ms	573×	body	320	valid
29.0ms	327×	body	160	valid

Details

analyze724.0ms

sample41.0ms

simplify511.0ms

prune4.0ms

localize10.0ms

rewrite35.0ms

series68.0ms

simplify53.0ms

prune241.0ms

localize10.0ms

rewrite27.0ms

series59.0ms

simplify38.0ms

prune226.0ms

localize11.0ms

rewrite35.0ms

series59.0ms

simplify71.0ms

prune238.0ms

localize11.0ms

rewrite45.0ms

series86.0ms

simplify68.0ms

prune255.0ms

regimes157.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling