Details

sample282.0ms

Algorithm

intervals

Results

12.0ms	46×	body	1280	valid
8.0ms	47×	body	640	valid
6.0ms	135×	body	80	valid
2.0ms	14×	body	320	valid
1.0ms	14×	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))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-sqr-sqrt`
101×	`*-un-lft-identity`
50×	`times-frac`
35×	`difference-of-squares`
29×	`add-cube-cbrt`
24×	`associate-l`
22×	`distribute-lft-out`
18×	`pow1`
14×	`distribute-lft-out--`
13×	`swap-sqr`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`*-commutative` `unswap-sqr`
8×	`tan-quot`
6×	`associate-r` `add-log-exp`
5×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 157

Calls

4 calls:

7.0ms	(- 1.0 (* (tan x) (tan x)))
16.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series215.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- 1.0 (* (tan x) (tan x)))
98.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
36.0ms	(* (tan x) (tan x))
44.0ms	(* (tan x) (tan x))

simplify51.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	351	1571
1	1183	1505
2	5001	1482

prune220.0ms

Filtered

169 candidates to 83 candidates (49.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	155	14	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	14	170

Merged error: 0.0b

Counts

170 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

154×	`*-un-lft-identity`
75×	`times-frac`
60×	`add-sqr-sqrt`
55×	`distribute-lft-out`
47×	`associate-l`
44×	`add-cube-cbrt`
38×	`associate-r`
15×	`associate-/l*`
14×	`flip3-+` `flip-+`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`frac-times`
8×	`distribute-rgt-neg-in` `*-commutative` `associate-/l/` `add-log-exp` `unswap-sqr`
5×	`associate-r/` `associate-l/` `associate-/r*`
4×	`tan-quot`
3×	`+-commutative` `swap-sqr` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `pow-prod-down` `sum-log` `associate-/r/`
1×	`pow2` `neg-sub0` `associate-+r-` `frac-2neg` `pow-plus` `unsub-neg` `neg-log` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 197

Calls

4 calls:

12.0ms	(* (+ (fabs (tan x)) (sqrt 1.0)) (+ (sqrt 1.0) (- (fabs (tan x)))))
23.0ms	(/ (* (+ (fabs (tan x)) (sqrt 1.0)) (+ (sqrt 1.0) (- (fabs (tan x))))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(+ (sqrt 1.0) (- (fabs (tan x))))
5.0ms	(* (tan x) (tan x))

series299.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (+ (fabs (tan x)) (sqrt 1.0)) (+ (sqrt 1.0) (- (fabs (tan x)))))
150.0ms	(/ (* (+ (fabs (tan x)) (sqrt 1.0)) (+ (sqrt 1.0) (- (fabs (tan x))))) (+ 1.0 (* (tan x) (tan x))))
30.0ms	(+ (sqrt 1.0) (- (fabs (tan x))))
37.0ms	(* (tan x) (tan x))

simplify112.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	686	3385
1	3898	3093
2	5002	3078

prune396.0ms

Filtered

209 candidates to 120 candidates (57.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	202	7	209
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	211	12	223

Merged error: 0.0b

Counts

223 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

154×	`*-un-lft-identity`
75×	`times-frac`
60×	`add-sqr-sqrt`
55×	`distribute-lft-out`
47×	`associate-l`
44×	`add-cube-cbrt`
38×	`associate-r`
15×	`associate-/l*`
14×	`flip3-+` `flip-+`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`frac-times`
8×	`distribute-rgt-neg-in` `*-commutative` `associate-/l/` `add-log-exp` `unswap-sqr`
5×	`associate-r/` `associate-l/` `associate-/r*`
4×	`tan-quot`
3×	`+-commutative` `swap-sqr` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `pow-prod-down` `sum-log` `associate-/r/`
1×	`pow2` `neg-sub0` `associate-+r-` `frac-2neg` `pow-plus` `unsub-neg` `neg-log` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 197

Calls

4 calls:

12.0ms	(* (+ (fabs (tan x)) (sqrt 1.0)) (+ (sqrt 1.0) (- (fabs (tan x)))))
25.0ms	(/ (* (+ (fabs (tan x)) (sqrt 1.0)) (+ (sqrt 1.0) (- (fabs (tan x))))) (+ 1.0 (* (tan x) (tan x))))
7.0ms	(+ (sqrt 1.0) (- (fabs (tan x))))
5.0ms	(* (tan x) (tan x))

series296.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (+ (fabs (tan x)) (sqrt 1.0)) (+ (sqrt 1.0) (- (fabs (tan x)))))
150.0ms	(/ (* (+ (fabs (tan x)) (sqrt 1.0)) (+ (sqrt 1.0) (- (fabs (tan x))))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(+ (sqrt 1.0) (- (fabs (tan x))))
33.0ms	(* (tan x) (tan x))

simplify112.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	686	3385
1	3898	3093
2	5002	3078

prune400.0ms

Filtered

209 candidates to 120 candidates (57.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	204	5	209
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	209	12	221

Merged error: 0.0b

Counts

221 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

414×	`*-un-lft-identity`
270×	`times-frac`
153×	`distribute-lft-out`
110×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
34×	`associate-/r*`
33×	`associate-l`
28×	`distribute-rgt-neg-in` `associate-/r/`
15×	`associate-/l*`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1` `flip3-+` `flip-+`
8×	`div-inv` `add-log-exp`
6×	`associate-/l/`
4×	`tan-quot` `cbrt-undiv` `div-exp`
3×	`frac-2neg` `div-sub` `swap-sqr` `associate-r` `clear-num`
2×	`neg-sub0` `associate-+r-` `unsub-neg` `sum-log`
1×	`+-commutative` `pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 284

Calls

4 calls:

12.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (+ (fabs (tan x)) (sqrt 1.0)))
9.0ms	(+ (sqrt 1.0) (- (fabs (tan x))))
23.0ms	(/ (+ (sqrt 1.0) (- (fabs (tan x)))) (/ (+ 1.0 (* (tan x) (tan x))) (+ (fabs (tan x)) (sqrt 1.0))))
5.0ms	(* (tan x) (tan x))

series308.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (+ (fabs (tan x)) (sqrt 1.0)))
32.0ms	(+ (sqrt 1.0) (- (fabs (tan x))))
152.0ms	(/ (+ (sqrt 1.0) (- (fabs (tan x)))) (/ (+ 1.0 (* (tan x) (tan x))) (+ (fabs (tan x)) (sqrt 1.0))))
33.0ms	(* (tan x) (tan x))

simplify122.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	725	5679
1	3792	5333
2	5001	5250

prune447.0ms

Filtered

296 candidates to 139 candidates (47.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	292	4	296
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	295	13	308

Merged error: 0b

Counts

308 → 13

regimes221.0ms

Accuracy

0% (0.3b 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	21	15
1	23	15
2	23	15

end0.0ms

sample927.0ms

Algorithm

intervals

Results

370.0ms	1478×	body	1280	valid
192.0ms	1180×	body	640	valid
157.0ms	4439×	body	80	valid
69.0ms	608×	body	320	valid
24.0ms	295×	body	160	valid