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

sample268.0ms

Algorithm

intervals

Results

169.0ms	55×	body	2560	valid
64.0ms	93×	body	1280	valid
15.0ms	57×	body	640	valid
6.0ms	31×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	7×	body	80	valid

simplify472.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

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: 35.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (tan x))
1.4b	(- x (sin x))

rewrite31.0ms

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:

18.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series38.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
11.0ms	(- x (tan x))
13.0ms	(- x (sin x))

simplify63.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4864	1139
1	4864	1139

prune97.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0.0b

Counts

88 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow x 4) -27/2800)
0.1b	(* x 9/40)
0.1b	(* x (* x 9/40))
14.6b	(+ (* 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)
3.0ms	(* x 9/40)
4.0ms	(* x (* 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)
2.0ms	(* x 9/40)
3.0ms	(* x (* x 9/40))
6.0ms	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

simplify56.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4903	646
1	4903	646

prune101.0ms

Filtered

53 candidates to 86 candidates (-62.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.2b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.4b	(- x (tan x))
1.4b	(- x (tan x))

rewrite43.0ms

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)))
28.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series61.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (sin x) (- x (tan x)))
30.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
10.0ms	(- x (tan x))
10.0ms	(- x (tan x))

simplify52.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5028	1430

prune91.0ms

Filtered

80 candidates to 103 candidates (-28.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	103	4	107

Merged error: 0.0b

Counts

107 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.2b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.4b	(- x (tan x))
1.4b	(- x (tan x))

rewrite43.0ms

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)))
28.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
3.0ms	(- x (tan x))

series62.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (sin x) (- x (tan x)))
32.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
10.0ms	(- x (tan x))
10.0ms	(- x (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5028	1430

prune117.0ms

Filtered

81 candidates to 103 candidates (-27.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	102	5	107

Merged error: 0.0b

Counts

107 → 5

regimes49.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.1b

bsearch37.0ms

Steps

Iters	Range		Point
10	2.494025445275307e-09	407.48051452230374	0.030174469617931295
8	-0.21125380283824044	-0.00015107894629750538	-0.028305308455860895

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	38
1	58	38

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.1s	1572×	body	2560	valid
1.7s	2796×	body	1280	valid
504.0ms	1894×	body	640	valid
165.0ms	930×	body	320	valid
58.0ms	464×	body	160	valid
26.0ms	344×	body	80	valid

Details

analyze1.4s

sample268.0ms

simplify472.0ms

prune4.0ms

localize10.0ms

rewrite31.0ms

series38.0ms

simplify63.0ms

prune97.0ms

localize9.0ms

rewrite22.0ms

series14.0ms

simplify56.0ms

prune101.0ms

localize9.0ms

rewrite43.0ms

series61.0ms

simplify52.0ms

prune91.0ms

localize12.0ms

rewrite43.0ms

series62.0ms

simplify48.0ms

prune117.0ms

regimes49.0ms

bsearch37.0ms

simplify2.0ms

end0.0ms

sample6.7s

Profiling