Details

sample286.0ms

Algorithm

intervals

Results

11.0ms	45×	body	1280	valid
8.0ms	48×	body	640	valid
6.0ms	137×	body	80	valid
2.0ms	13×	body	320	valid
1.0ms	13×	body	160	valid

simplify17.0ms

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

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))) (+ 1.0 (* (tan x) (tan x))))
0.1b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite27.0ms

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:

7.0ms	(/ (- 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))
8.0ms	(* (tan x) (tan x))

series225.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(- 1.0 (* (tan x) (tan x)))
34.0ms	(* (tan x) (tan x))
60.0ms	(* (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	918
2	5001	882

prune271.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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))
6.0ms	(- (sqrt 1.0) (tan x))
13.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
5.0ms	(* (tan x) (tan x))

series211.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (sqrt 1.0) (tan x))
37.0ms	(- (sqrt 1.0) (tan x))
105.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
33.0ms	(* (tan x) (tan x))

simplify72.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (56.0ms)

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

prune269.0ms

Filtered

175 candidates to 92 candidates (52.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	175	12	187

Merged error: 0.0b

Counts

187 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`prod-diff`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`times-frac`
6×	`tan-quot` `associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `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--` `associate-/l/` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 115

Calls

4 calls:

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

series195.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
61.0ms	(/ (* (tan x) (sin x)) (cos x))
43.0ms	(* (tan x) (sin x))
36.0ms	(* (tan x) (tan x))

simplify71.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	432	1314
1	1872	967
2	5001	929

prune247.0ms

Filtered

127 candidates to 76 candidates (59.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	126	13	139

Merged error: 0.0b

Counts

139 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

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:

10.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
20.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
6.0ms	(- (sqrt 1.0) (tan x))
5.0ms	(* (tan x) (tan x))

series368.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
198.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
42.0ms	(- (sqrt 1.0) (tan x))
33.0ms	(* (tan x) (tan x))

simplify92.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (75.0ms)

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

prune302.0ms

Filtered

179 candidates to 116 candidates (64.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	179	13	192

Merged error: 0.0b

Counts

192 → 13

regimes247.0ms

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

sample928.0ms

Algorithm

intervals

Results

363.0ms	1494×	body	1280	valid
202.0ms	1287×	body	640	valid
155.0ms	4314×	body	80	valid
71.0ms	620×	body	320	valid
25.0ms	285×	body	160	valid