Details

sample297.0ms

Algorithm

intervals

Results

11.0ms	45×	body	1280	valid
8.0ms	48×	body	640	valid
6.0ms	137×	body	80	valid
1.0ms	13×	body	320	valid
1.0ms	13×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

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

rewrite25.0ms

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:

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

series219.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
35.0ms	(- 1.0 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
56.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

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

prune226.0ms

Filtered

117 candidates to 77 candidates (65.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	11	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 0.0b

Counts

118 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`pow1`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
5×	`frac-times`
4×	`tan-quot` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `pow2` `pow-plus` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`

Counts

4 → 89

Calls

4 calls:

4.0ms	(+ (sqrt 1.0) (tan x))
4.0ms	(- (sqrt 1.0) (tan x))
13.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series212.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (sqrt 1.0) (tan x))
39.0ms	(- (sqrt 1.0) (tan x))
105.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
33.0ms	(* (tan x) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	328	693
1	1582	618
2	5001	607

prune201.0ms

Filtered

101 candidates to 68 candidates (67.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	101	11	112

Merged error: 0.0b

Counts

112 → 11

localize9.0ms

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 (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
21×	`-un-lft-identity` `associate-r*`
20×	`pow1` `add-cube-cbrt`
17×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`times-frac`
10×	`associate-l`
8×	`tan-quot`
6×	`swap-sqr` `prod-exp` `add-log-exp`
5×	`unswap-sqr`
4×	`frac-times` `associate-*l/` `cbrt-unprod`
3×	`flip3--` `associate-r/` `pow-prod-down` `-commutative` `flip--`
2×	`pow2` `pow-plus` `div-exp` `associate-/r/` `pow-sqr` `pow-prod-up` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `flip3-+` `diff-log` `1-exp` `un-div-inv` `flip-+` `div-inv`

Counts

4 → 112

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
13.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series192.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- 1.0 (* (tan x) (tan x)))
92.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
32.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

simplify57.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	382	946
1	1727	838
2	5001	797

prune195.0ms

Filtered

124 candidates to 76 candidates (61.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	124	11	135

Merged error: 0.0b

Counts

135 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (tan x) (sin x))
0.2b	(* (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

6.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(* (tan x) (sin x))
13.0ms	(* (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series248.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (* (tan x) (sin x)) (cos x))
43.0ms	(* (tan x) (sin x))
110.0ms	(* (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))

simplify72.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	521	1119
1	2507	993
2	5001	975

prune254.0ms

Filtered

125 candidates to 84 candidates (67.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	124	12	136

Merged error: 0.0b

Counts

136 → 12

regimes172.0ms

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	10
1	13	10

end0.0ms

sample918.0ms

Algorithm

intervals

Results

360.0ms	1494×	body	1280	valid
207.0ms	1287×	body	640	valid
145.0ms	4314×	body	80	valid
71.0ms	620×	body	320	valid
22.0ms	285×	body	160	valid