Details

sample287.0ms

Algorithm

intervals

Results

13.0ms	51×	body	1280	valid
7.0ms	131×	body	80	valid
6.0ms	37×	body	640	valid
3.0ms	23×	body	320	valid
1.0ms	14×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	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))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`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×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `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 → 119

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))
7.0ms	(* (tan x) (tan x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
94.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
59.0ms	(* (tan x) (tan x))

simplify50.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	917
2	5001	882

prune278.0ms

Filtered

131 candidates to 91 candidates (69.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	119	12	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	12	132

Merged error: 0.0b

Counts

132 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

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))
0.3b	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

29×	`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`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `associate-/l*` `add-log-exp` `difference-of-squares`
3×	`associate-/r*`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `log1p-udef` `flip3--` `frac-2neg` `flip3-+` `div-sub` `log1p-expm1` `div-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 109

Calls

4 calls:

10.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
1.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))

series371.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(* (tan x) (tan x))
30.0ms	(* (tan x) (tan x))
216.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	366	1025
1	1339	934
2	5002	895

prune259.0ms

Filtered

121 candidates to 83 candidates (68.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	121	12	133

Merged error: 0.0b

Counts

133 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (tan x) (tan x) 1.0)
0.1b	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
0.2b	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
86×	`add-sqr-sqrt`
68×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-/r*`
19×	`add-exp-log`
16×	`difference-of-squares`
13×	`add-cbrt-cube`
12×	`pow1`
11×	`associate-/r/`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
5×	`flip3--` `flip--`
4×	`tan-quot` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow2` `frac-times` `pow-flip` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

1.0ms	(fma (tan x) (tan x) 1.0)
4.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
7.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
6.0ms	(* (tan x) (tan x))

series281.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma (tan x) (tan x) 1.0)
102.0ms	(/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x))))
106.0ms	(/ 1 (/ (fma (tan x) (tan x) 1.0) (- 1.0 (* (tan x) (tan x)))))
31.0ms	(* (tan x) (tan x))

simplify78.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	576	2372
1	2645	2169
2	5001	2069

prune297.0ms

Filtered

185 candidates to 111 candidates (60.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	185	12	197

Merged error: 0.0b

Counts

197 → 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)) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
44×	`add-cube-cbrt`
37×	`times-frac`
27×	`associate-r`
20×	`sqrt-prod`
18×	`prod-diff`
16×	`difference-of-squares`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--`
7×	`associate-l`
6×	`fma-neg` `associate-/l*` `add-log-exp`
4×	`tan-quot` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`frac-times` `swap-sqr` `associate-l/` `prod-exp` `associate-/r` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv` `associate-/l/`
1×	`pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `clear-num` `pow-sqr` `pow-prod-up` `distribute-lft-out`

Counts

4 → 167

Calls

4 calls:

6.0ms	(- (sqrt 1.0) (tan x))
9.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
16.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series355.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (sqrt 1.0) (tan x))
92.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
192.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))

simplify95.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	644	2081
1	3040	1700
2	5001	1673

prune301.0ms

Filtered

179 candidates to 116 candidates (64.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	179	12	191

Merged error: 0b

Counts

191 → 12

regimes189.0ms

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	11	9
1	11	9

end0.0ms

sample972.0ms

Algorithm

intervals

Results

387.0ms	1510×	body	1280	valid
208.0ms	1229×	body	640	valid
165.0ms	4323×	body	80	valid
74.0ms	627×	body	320	valid
26.0ms	311×	body	160	valid