Details

sample318.0ms

Algorithm

intervals

Results

10.0ms	39×	body	1280	valid
8.0ms	43×	body	640	valid
7.0ms	146×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	8×	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

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))))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite45.0ms

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))))
25.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series207.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- 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))
46.0ms	(* (tan x) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5002	824

prune224.0ms

Filtered

117 candidates to 77 candidates (65.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	105	12	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	12	118

Merged error: 0.0b

Counts

118 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin x) 2)
0.2b	(pow (sin x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (cos x) 2)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

2.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)
2.0ms	(pow (cos x) 2)
2.0ms	(pow (cos x) 2)

series72.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin x) 2)
21.0ms	(pow (sin x) 2)
16.0ms	(pow (cos x) 2)
16.0ms	(pow (cos x) 2)

simplify62.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	141	284
1	469	240
2	1588	240
3	5001	236

prune166.0ms

Filtered

84 candidates to 48 candidates (57.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	84	12	96

Merged error: 0.0b

Counts

96 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
184×	`*-un-lft-identity`
172×	`add-sqr-sqrt`
94×	`add-cube-cbrt`
38×	`difference-of-squares`
30×	`associate-/r*`
26×	`distribute-lft-out`
19×	`sqrt-prod` `distribute-lft-out--`
13×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
11×	`pow1`
7×	`div-inv` `associate-/l*`
6×	`flip3--` `flip--` `add-log-exp`
4×	`tan-quot` `cbrt-undiv` `div-exp` `associate-/l/`
3×	`flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 224

Calls

4 calls:

8.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
4.0ms	(+ (sqrt 1.0) (tan x))
15.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
5.0ms	(* (tan x) (tan x))

series362.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
32.0ms	(+ (sqrt 1.0) (tan x))
186.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
36.0ms	(* (tan x) (tan x))

simplify123.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	735	4155
1	3740	3919
2	5002	3901

prune411.0ms

Filtered

236 candidates to 143 candidates (60.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	234	2	236
Fresh	1	9	10
Picked	0	1	1
Done	1	0	1
Total	236	12	248

Merged error: 0.0b

Counts

248 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

354×	`times-frac`
261×	`add-sqr-sqrt`
259×	`*-un-lft-identity`
151×	`add-cube-cbrt`
130×	`log-pow`
108×	`exp-prod`
54×	`difference-of-squares`
37×	`pow1`
27×	`sqrt-prod` `distribute-lft-out` `distribute-lft-out--`
24×	`associate-/r*`
19×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
9×	`flip3--` `flip--`
8×	`associate-/l*`
7×	`add-log-exp`
4×	`tan-quot` `log-prod`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-r` `associate-l`
2×	`exp-sum` `rem-exp-log`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 298

Calls

4 calls:

5.0ms	(log (exp (+ (sqrt 1.0) (tan x))))
18.0ms	(/ (log (exp (+ (sqrt 1.0) (tan x)))) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
5.0ms	(* (tan x) (tan x))
5.0ms	(exp (+ (sqrt 1.0) (tan x)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(log (exp (+ (sqrt 1.0) (tan x))))
190.0ms	(/ (log (exp (+ (sqrt 1.0) (tan x)))) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
37.0ms	(* (tan x) (tan x))
61.0ms	(exp (+ (sqrt 1.0) (tan x)))

simplify136.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	886	6461
1	3930	6020
2	5001	5991

prune441.0ms

Filtered

310 candidates to 159 candidates (51.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	308	2	310
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	310	12	322

Merged error: 0.0b

Counts

322 → 12

regimes182.0ms

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	12	12
1	12	12

end0.0ms

sample991.0ms

Algorithm

intervals

Results

383.0ms	1518×	body	1280	valid
219.0ms	1309×	body	640	valid
164.0ms	4280×	body	80	valid
80.0ms	597×	body	320	valid
25.0ms	296×	body	160	valid

Details

sample318.0ms

simplify15.0ms

prune3.0ms

localize10.0ms

rewrite45.0ms

series207.0ms

simplify44.0ms

prune224.0ms

localize12.0ms

rewrite11.0ms

series72.0ms

simplify62.0ms

prune166.0ms

localize12.0ms

rewrite44.0ms

series362.0ms

simplify123.0ms

prune411.0ms

localize14.0ms

rewrite56.0ms

series321.0ms

simplify136.0ms

prune441.0ms

regimes182.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample991.0ms

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