Details

analyze1.3s

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

sample217.0ms

Algorithm

intervals

Results

117.0ms	36×	body	2560	valid
63.0ms	105×	body	1280	valid
16.0ms	59×	body	640	valid
7.0ms	36×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	6×	body	80	valid

simplify445.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	1004	9
1	1004	9

prune5.0ms

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: 26.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.1b	(- x (sin x))
1.1b	(- x (tan x))

rewrite29.0ms

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:

17.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series38.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (sin x))
20.0ms	(- x (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5030	1137

prune111.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Merged error: 0.0b

Counts

88 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
0.0b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
1.1b	(- x (sin x))
1.1b	(- x (tan x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
62×	`unpow-prod-down` `cube-prod`
50×	`add-cube-cbrt`
42×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 186

Calls

4 calls:

11.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
10.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
3.0ms	(- x (sin x))
3.0ms	(- x (tan x))

series47.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
19.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
5.0ms	(- x (sin x))
10.0ms	(- x (tan x))

simplify72.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5151	3430

prune160.0ms

Filtered

88 candidates to 198 candidates (-125.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	198	5	203

Merged error: 0.0b

Counts

203 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x 9/40))
0.1b	(* x 9/40)
0.3b	(* (pow x 4) -27/2800)
21.8b	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
7×	`associate-r` `prod-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `unswap-sqr`
3×	`sum-log` `*-commutative`
2×	`sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 74

Calls

4 calls:

4.0ms	(* x (* x 9/40))
5.0ms	(* x 9/40)
5.0ms	(* (pow x 4) -27/2800)
7.0ms	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

series13.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* x (* x 9/40))
2.0ms	(* x 9/40)
4.0ms	(* (pow x 4) -27/2800)
5.0ms	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

simplify58.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4873	646
1	4873	646

prune124.0ms

Filtered

53 candidates to 86 candidates (-62.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	86	5	91

Merged error: 0.0b

Counts

91 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x 9/40))
0.1b	(* x 9/40)
0.3b	(* (pow x 4) -27/2800)
21.8b	(+ (+ (* x (* x 9/40)) -1/2) (* (pow x 4) -27/2800))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
7×	`associate-r` `prod-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `unswap-sqr`
3×	`sum-log` `*-commutative`
2×	`sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 74

Calls

4 calls:

4.0ms	(* x (* x 9/40))
3.0ms	(* x 9/40)
5.0ms	(* (pow x 4) -27/2800)
8.0ms	(+ (+ (* x (* x 9/40)) -1/2) (* (pow x 4) -27/2800))

series13.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* x (* x 9/40))
2.0ms	(* x 9/40)
3.0ms	(* (pow x 4) -27/2800)
5.0ms	(+ (+ (* x (* x 9/40)) -1/2) (* (pow x 4) -27/2800))

simplify58.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4901	646
1	4901	646

prune107.0ms

Filtered

53 candidates to 86 candidates (-62.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	86	5	91

Merged error: 0.0b

Counts

91 → 5

regimes95.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.1b

bsearch53.0ms

Steps

Iters	Range		Point
10	1.2213758715411944e-16	0.07100218025040958	0.029172484020573174
11	-4.478594567710113e+18	-0.0005181946935010989	-0.03304928005131623

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	110	34
1	110	34

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.0s	1583×	body	2560	valid
1.7s	2805×	body	1280	valid
493.0ms	1817×	body	640	valid
189.0ms	965×	body	320	valid
64.0ms	493×	body	160	valid
27.0ms	337×	body	80	valid

Details

analyze1.3s

sample217.0ms

simplify445.0ms

prune5.0ms

localize11.0ms

rewrite29.0ms

series38.0ms

simplify43.0ms

prune111.0ms

localize11.0ms

rewrite40.0ms

series47.0ms

simplify72.0ms

prune160.0ms

localize9.0ms

rewrite24.0ms

series13.0ms

simplify58.0ms

prune124.0ms

localize8.0ms

rewrite22.0ms

series13.0ms

simplify58.0ms

prune107.0ms

regimes95.0ms

bsearch53.0ms

simplify2.0ms

end0.0ms

sample6.6s

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