Details

sample281.0ms

Algorithm

intervals

Results

13.0ms	52×	body	1280	valid
6.0ms	145×	body	80	valid
4.0ms	27×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	12×	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

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)))
0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))
0.2b	(* (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)))
6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series231.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- 1.0 (* (tan x) (tan x)))
100.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))

simplify49.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (35.0ms)

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

prune250.0ms

Filtered

117 candidates to 77 candidates (65.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	107	10	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Merged error: 0.0b

Counts

118 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
0.2b	(- (sqrt 1.0) (tan x))
0.2b	(* (tan x) (tan x))

rewrite33.0ms

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:

8.0ms	(+ (sqrt 1.0) (tan x))
12.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series217.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(+ (sqrt 1.0) (tan x))
110.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
38.0ms	(- (sqrt 1.0) (tan x))
34.0ms	(* (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

prune245.0ms

Filtered

101 candidates to 67 candidates (66.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	101	10	111

Merged error: 0.0b

Counts

111 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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

series264.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))
161.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify39.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	266	869
1	914	800
2	5002	784

prune234.0ms

Filtered

118 candidates to 69 candidates (58.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	117	11	128

Merged error: 0.0b

Counts

128 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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:

9.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(* (tan x) (sin x))
5.0ms	(* (tan x) (tan x))

series259.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
64.0ms	(/ (* (tan x) (sin x)) (cos x))
43.0ms	(* (tan x) (sin x))
36.0ms	(* (tan x) (tan x))

simplify62.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	441	1158
1	1849	1060
2	5001	1054

prune304.0ms

Filtered

121 candidates to 82 candidates (67.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	121	11	132

Merged error: 0.0b

Counts

132 → 11

regimes140.0ms

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	12
1	13	12

end0.0ms

sample923.0ms

Algorithm

intervals

Results

370.0ms	1534×	body	1280	valid
202.0ms	1236×	body	640	valid
144.0ms	4308×	body	80	valid
70.0ms	613×	body	320	valid
24.0ms	309×	body	160	valid