Details

analyze1.4s

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

sample168.0ms

Algorithm

intervals

Results

85.0ms	46×	body	2560	valid
42.0ms	86×	body	1280	valid
15.0ms	54×	body	640	valid
7.0ms	40×	body	320	valid
3.0ms	23×	body	160	valid
1.0ms	7×	body	80	valid

simplify462.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	1004	9
1	1004	9

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: 28.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.5b	(- x (tan x))
1.6b	(- x (sin x))

rewrite20.0ms

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)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series56.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
30.0ms	(- x (tan x))
13.0ms	(- x (sin x))

simplify62.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4864	1139
1	4864	1139

prune87.0ms

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: 0.0b

Counts

88 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
1.2b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.5b	(- x (tan x))
1.5b	(- x (tan x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 91

Calls

4 calls:

6.0ms	(/ (sin x) (- x (tan x)))
30.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series65.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ (sin x) (- x (tan x)))
33.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
10.0ms	(- x (tan x))
10.0ms	(- x (tan x))

simplify49.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5028	1430

prune91.0ms

Filtered

80 candidates to 103 candidates (-28.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	103	3	106

Merged error: 0.0b

Counts

106 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow x 4) -27/2800)
0.1b	(* x (* x 9/40))
0.1b	(* x 9/40)
16.6b	(+ (* 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-+r+` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 74

Calls

4 calls:

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

series14.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4903	646
1	4903	646

prune103.0ms

Filtered

53 candidates to 86 candidates (-62.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	86	3	89

Merged error: 0b

Counts

89 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow x 4) -27/2800)
0.1b	(* x (* x 9/40))
0.1b	(* x 9/40)
16.6b	(+ (+ (* 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:

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

series14.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify51.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4921	646
1	4921	646

prune93.0ms

Filtered

53 candidates to 86 candidates (-62.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	86	3	89

Merged error: 0b

Counts

89 → 3

regimes41.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch38.0ms

Steps

Iters	Range		Point
9	1.4566916963608107e-06	1328.8357353907656	0.02270592306163545
8	-0.33859120317188024	-0.000650630938788985	-0.03420339012678163

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	36
1	56	36

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.9s	1589×	body	2560	valid
1.7s	2793×	body	1280	valid
513.0ms	1869×	body	640	valid
179.0ms	942×	body	320	valid
64.0ms	495×	body	160	valid
29.0ms	312×	body	80	valid

Details

analyze1.4s

sample168.0ms

simplify462.0ms

prune4.0ms

localize10.0ms

rewrite20.0ms

series56.0ms

simplify62.0ms

prune87.0ms

localize9.0ms

rewrite45.0ms

series65.0ms

simplify49.0ms

prune91.0ms

localize12.0ms

rewrite22.0ms

series14.0ms

simplify55.0ms

prune103.0ms

localize9.0ms

rewrite22.0ms

series14.0ms

simplify51.0ms

prune93.0ms

regimes41.0ms

bsearch38.0ms

simplify2.0ms

end0.0ms

sample6.5s

Profiling