Details

analyze1.7s

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample251.0ms

Algorithm

intervals

Results

150.0ms	47×	body	2560	valid
62.0ms	103×	body	1280	valid
17.0ms	53×	body	640	valid
6.0ms	29×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	11×	body	80	valid

simplify90.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	14

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: 32.5b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.2b	(- x (sin x))
1.2b	(- x (tan x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 78

Calls

3 calls:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series69.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (sin x))
48.0ms	(- x (tan x))

simplify85.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4870	1817
1	4870	1817

prune127.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	3	88

Merged error: 0b

Counts

88 → 3

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) 9/40)
0.3b	(* 27/2800 (pow x 4))
16.1b	(- (* (* x x) 9/40) (+ 1/2 (* 27/2800 (pow x 4))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `add-sqr-sqrt`
10×	`associate-r` `add-cbrt-cube`
8×	`pow1` `add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`prod-exp`
4×	`unpow-prod-down` `associate-l` `cbrt-unprod` `unswap-sqr`
3×	`pow-prod-down`
2×	`diff-log` `*-commutative` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-exp` `sum-log` `flip--` `associate--r+`

Counts

3 → 57

Calls

3 calls:

10.0ms	(* (* x x) 9/40)
9.0ms	(* 27/2800 (pow x 4))
14.0ms	(- (* (* x x) 9/40) (+ 1/2 (* 27/2800 (pow x 4))))

series23.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(* (* x x) 9/40)
8.0ms	(* 27/2800 (pow x 4))
9.0ms	(- (* (* x x) 9/40) (+ 1/2 (* 27/2800 (pow x 4))))

simplify73.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5096	850

prune132.0ms

Filtered

40 candidates to 66 candidates (-65.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	66	3	69

Merged error: 0b

Counts

69 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (tan x)) (- x (sin x)))
0.0b	(/ 1 (/ (- x (tan x)) (- x (sin x))))
1.2b	(- x (sin x))
1.2b	(- x (tan x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
200×	`add-sqr-sqrt` `*-un-lft-identity`
92×	`add-cube-cbrt`
54×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3--` `div-exp` `flip--` `associate-/l*` `add-log-exp`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv`
2×	`sub-neg` `rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `inv-pow`

Counts

4 → 226

Calls

4 calls:

8.0ms	(/ (- x (tan x)) (- x (sin x)))
13.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
5.0ms	(- x (sin x))
7.0ms	(- x (tan x))

series67.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (- x (tan x)) (- x (sin x)))
20.0ms	(/ 1 (/ (- x (tan x)) (- x (sin x))))
10.0ms	(- x (sin x))
21.0ms	(- x (tan x))

simplify143.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4934	6285
1	4934	6285

prune199.0ms

Filtered

137 candidates to 238 candidates (-73.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	238	3	241

Merged error: 0b

Counts

241 → 3

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 3)
1.2b	(- x (tan x))
1.2b	(- (pow x 3) (pow (sin x) 3))
33.4b	(/ (- (pow x 3) (pow (sin x) 3)) (+ (* x x) (* (sin x) (+ x (sin x)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

159×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
81×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
26×	`distribute-lft-out--`
25×	`associate-/l*`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 189

Calls

4 calls:

3.0ms	(pow (sin x) 3)
6.0ms	(- x (tan x))
15.0ms	(- (pow x 3) (pow (sin x) 3))
41.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (+ (* x x) (* (sin x) (+ x (sin x)))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(pow (sin x) 3)
11.0ms	(- x (tan x))
13.0ms	(- (pow x 3) (pow (sin x) 3))
34.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (+ (* x x) (* (sin x) (+ x (sin x)))))

simplify108.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5110	7714

prune276.0ms

Filtered

106 candidates to 201 candidates (-89.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	201	3	204

Merged error: 0b

Counts

204 → 3

regimes57.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch43.0ms

Steps

Iters	Range		Point
10	6.514980418782966e-06	106750393.31639235	0.027677485715175896
8	-6.321099269650897	-0.0050779378224239235	-0.026395687002885145

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	89	50
1	89	50

end0.0ms

sample7.8s

Algorithm

intervals

Results

4.9s	1617×	body	2560	valid
1.9s	2803×	body	1280	valid
586.0ms	1848×	body	640	valid
187.0ms	882×	body	320	valid
70.0ms	475×	body	160	valid
33.0ms	375×	body	80	valid

Details

analyze1.7s

sample251.0ms

simplify90.0ms

prune4.0ms

localize9.0ms

rewrite21.0ms

series69.0ms

simplify85.0ms

prune127.0ms

localize17.0ms

rewrite36.0ms

series23.0ms

simplify73.0ms

prune132.0ms

localize17.0ms

rewrite51.0ms

series67.0ms

simplify143.0ms

prune199.0ms

localize33.0ms

rewrite77.0ms

series63.0ms

simplify108.0ms

prune276.0ms

regimes57.0ms

bsearch43.0ms

simplify6.0ms

end0.0ms

sample7.8s

Profiling