Details

sample301.0ms

Algorithm

intervals

Results

12.0ms	45×	body	1280	valid
8.0ms	148×	body	80	valid
7.0ms	43×	body	640	valid
2.0ms	15×	body	320	valid
0.0ms	5×	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)))
0.1b	(/ (- 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))

series217.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- 1.0 (* (tan x) (tan x)))
95.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
31.0ms	(* (tan x) (tan x))
59.0ms	(* (tan x) (tan x))

simplify52.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (37.0ms)

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

prune278.0ms

Filtered

131 candidates to 91 candidates (69.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	13	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	13	132

Merged error: 0.0b

Counts

132 → 13

localize14.0ms

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
54×	`prod-diff`
50×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`pow1`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-l`
6×	`fma-def` `fma-neg`
5×	`frac-times`
4×	`tan-quot` `expm1-log1p-u` `flip3--` `flip3-+` `flip--` `flip-+` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `associate-r/` `swap-sqr` `associate-l/`
2×	`pow-prod-down` `prod-exp` `*-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 → 163

Calls

4 calls:

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

series210.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (sqrt 1.0) (tan x))
104.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
38.0ms	(+ (sqrt 1.0) (tan x))
32.0ms	(* (tan x) (tan x))

simplify75.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	550	2052
1	2400	1381
2	5001	1360

prune270.0ms

Filtered

175 candidates to 91 candidates (52.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	169	6	175
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	175	13	188

Merged error: 0.0b

Counts

188 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`pow1` `add-cube-cbrt`
9×	`fma-def`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
2×	`+-commutative` `distribute-lft-neg-out` `associate-+r+` `flip3-+` `sum-log` `flip-+` `fma-udef`
1×	`pow2` `distribute-rgt-in` `frac-times` `associate-+l+` `distribute-lft-in` `pow-plus` `associate-r/` `unsub-neg` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

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

series251.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(+ (fma (tan x) (sqrt 1.0) 1.0) (* (- (tan x)) (+ (sqrt 1.0) (tan x))))
45.0ms	(fma (tan x) (sqrt 1.0) 1.0)
37.0ms	(+ (sqrt 1.0) (tan x))
31.0ms	(* (tan x) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	312	521
1	1345	466
2	5001	438

prune226.0ms

Filtered

93 candidates to 70 candidates (75.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	93	13	106

Merged error: 0.0b

Counts

106 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 117

Calls

4 calls:

8.0ms	(* (tan x) (sin x))
10.0ms	(/ (- 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) (tan x))

series243.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (tan x) (sin x))
109.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
62.0ms	(/ (* (tan x) (sin x)) (cos x))
31.0ms	(* (tan x) (tan x))

simplify64.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	455	1207
1	1904	1099
2	5001	1091

prune262.0ms

Filtered

129 candidates to 91 candidates (70.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	129	13	142

Merged error: 0.0b

Counts

142 → 13

regimes249.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

end0.0ms

sample1.0s

Algorithm

intervals

Results

407.0ms	1547×	body	1280	valid
216.0ms	1268×	body	640	valid
166.0ms	4260×	body	80	valid
74.0ms	612×	body	320	valid
31.0ms	313×	body	160	valid

Details

sample301.0ms

simplify16.0ms

prune3.0ms

localize10.0ms

rewrite26.0ms

series217.0ms

simplify52.0ms

prune278.0ms

localize14.0ms

rewrite34.0ms

series210.0ms

simplify75.0ms

prune270.0ms

localize13.0ms

rewrite16.0ms

series251.0ms

simplify44.0ms

prune226.0ms

localize14.0ms

rewrite32.0ms

series243.0ms

simplify64.0ms

prune262.0ms

regimes249.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.0s

Profiling