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

sample214.0ms

Algorithm

intervals

Results

138.0ms	43×	body	2560	valid
40.0ms	86×	body	1280	valid
14.0ms	58×	body	640	valid
7.0ms	37×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	18×	body	80	valid

simplify450.0ms

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: 25.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (sin x))
1.9b	(- x (tan x))

rewrite30.0ms

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))

series39.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (sin x))
21.0ms	(- x (tan x))

simplify62.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4864	1139
1	4864	1139

prune109.0ms

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
0.1b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
1.9b	(- x (sin x))
1.9b	(- x (tan x))

rewrite42.0ms

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	(pow (/ (- x (sin x)) (- x (tan x))) 3)
12.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
4.0ms	(- x (sin x))
3.0ms	(- x (tan x))

series50.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
14.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
5.0ms	(- x (sin x))
10.0ms	(- x (tan x))

simplify46.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5081	3368

prune158.0ms

Filtered

87 candidates to 198 candidates (-127.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	198	4	202

Merged error: 0.0b

Counts

202 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
0.2b	(/ (sin x) (cos x))
1.9b	(- x (sin x))
1.9b	(- x (/ (sin x) (cos x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
46×	`times-frac`
25×	`add-cube-cbrt`
22×	`difference-of-squares`
15×	`distribute-lft-out--`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `div-inv` `associate-/l/`
1×	`quot-tan` `div-sub`

Counts

4 → 113

Calls

4 calls:

12.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
4.0ms	(/ (sin x) (cos x))
3.0ms	(- x (sin x))
7.0ms	(- x (/ (sin x) (cos x)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
6.0ms	(/ (sin x) (cos x))
5.0ms	(- x (sin x))
11.0ms	(- x (/ (sin x) (cos x)))

simplify72.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4890	1869
1	4890	1869

prune107.0ms

Filtered

91 candidates to 125 candidates (-37.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	125	4	129

Merged error: 0.0b

Counts

129 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x 9/40))
0.1b	(* (pow x 4) -27/2800)
0.2b	(* x 9/40)
19.1b	(+ (* 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:

4.0ms	(* x (* x 9/40))
5.0ms	(* (pow x 4) -27/2800)
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:

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

simplify54.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4903	646
1	4903	646

prune105.0ms

Filtered

53 candidates to 86 candidates (-62.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

regimes84.0ms

Accuracy

100% (0.0b remaining)

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

bsearch38.0ms

Steps

Iters	Range		Point
7	0.00043222788164716514	0.027530255985715523	0.02423900971992383
10	-166313.48269314817	-2.0966605875303807e-05	-0.029101539732209875

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	45
1	61	45

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.8s	1547×	body	2560	valid
1.7s	2795×	body	1280	valid
474.0ms	1840×	body	640	valid
176.0ms	996×	body	320	valid
54.0ms	440×	body	160	valid
29.0ms	382×	body	80	valid

Details

analyze1.4s

sample214.0ms

simplify450.0ms

prune4.0ms

localize11.0ms

rewrite30.0ms

series39.0ms

simplify62.0ms

prune109.0ms

localize12.0ms

rewrite42.0ms

series50.0ms

simplify46.0ms

prune158.0ms

localize10.0ms

rewrite30.0ms

series37.0ms

simplify72.0ms

prune107.0ms

localize11.0ms

rewrite22.0ms

series14.0ms

simplify54.0ms

prune105.0ms

regimes84.0ms

bsearch38.0ms

simplify2.0ms

end0.0ms

sample6.4s

Profiling