Details

sample44.0ms

Algorithm

intervals

Results

15.0ms	48×	body	1280	valid
8.0ms	47×	body	640	valid
6.0ms	136×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	10×	body	160	valid

simplify570.0ms

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

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)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite34.0ms

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))

series71.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
10.0ms	(- 1.0 (* (tan x) (tan x)))
9.0ms	(* (tan x) (tan x))
20.0ms	(* (tan x) (tan x))

simplify41.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (32.0ms)

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

prune197.0ms

Filtered

77 candidates to 117 candidates (-51.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	105	12	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	12	118

Merged error: 0.0b

Counts

118 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

5.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
4.0ms	(* (tan x) (sin x))
5.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(* (tan x) (tan x))

series51.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
10.0ms	(* (tan x) (sin x))
18.0ms	(/ (* (tan x) (sin x)) (cos x))
9.0ms	(* (tan x) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	291	567
1	1265	503
2	5001	495

prune117.0ms

Filtered

62 candidates to 95 candidates (-53.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	95	12	107

Merged error: 0.0b

Counts

107 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
184×	`*-un-lft-identity`
172×	`add-sqr-sqrt`
94×	`add-cube-cbrt`
38×	`difference-of-squares`
30×	`associate-/r*`
26×	`distribute-lft-out`
19×	`sqrt-prod` `distribute-lft-out--`
13×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
11×	`pow1`
7×	`div-inv` `associate-/l*`
6×	`flip3--` `flip--` `add-log-exp`
4×	`tan-quot` `cbrt-undiv` `div-exp` `associate-/l/`
3×	`flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 224

Calls

4 calls:

15.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
4.0ms	(+ (sqrt 1.0) (tan x))
8.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series84.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
7.0ms	(+ (sqrt 1.0) (tan x))
25.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
9.0ms	(* (tan x) (tan x))

simplify115.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	735	4155
1	3740	3919
2	5001	3901

prune426.0ms

Filtered

144 candidates to 236 candidates (-63.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	233	3	236
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	235	13	248

Merged error: 0.0b

Counts

248 → 13

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
4×	`times-frac` `associate-/r/` `difference-of-squares`
3×	`pow2` `frac-times` `distribute-rgt-out--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
13.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (tan x) (tan x))
9.0ms	(* (tan x) (tan x))
9.0ms	(* (tan x) (tan x))
52.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify37.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	266	869
1	914	800
2	5002	794

prune99.0ms

Filtered

69 candidates to 118 candidates (-71.0%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	117	14	131

Merged error: 0.0b

Counts

131 → 14

regimes388.0ms

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	13	11
1	13	11

end0.0ms

sample1.0s

Algorithm

intervals

Results

396.0ms	1517×	body	1280	valid
210.0ms	1194×	body	640	valid
171.0ms	4366×	body	80	valid
73.0ms	592×	body	320	valid
29.0ms	331×	body	160	valid

Details

sample44.0ms

simplify570.0ms

prune4.0ms

localize10.0ms

rewrite34.0ms

series71.0ms

simplify41.0ms

prune197.0ms

localize14.0ms

rewrite21.0ms

series51.0ms

simplify43.0ms

prune117.0ms

localize11.0ms

rewrite45.0ms

series84.0ms

simplify115.0ms

prune426.0ms

localize9.0ms

rewrite32.0ms

series79.0ms

simplify37.0ms

prune99.0ms

regimes388.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

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