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

sample226.0ms

Algorithm

intervals

Results

137.0ms	49×	body	2560	valid
53.0ms	94×	body	1280	valid
17.0ms	59×	body	640	valid
5.0ms	27×	body	320	valid
3.0ms	20×	body	160	valid
1.0ms	7×	body	80	valid

simplify474.0ms

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: 30.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.9b	(- x (tan x))
0.9b	(- 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:

7.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series53.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ (- x (sin x)) (- x (tan x)))
12.0ms	(- x (tan x))
13.0ms	(- x (sin x))

simplify64.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4864	1139
1	4864	1139

prune84.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	0	0
Picked	0	1	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:

0.1b	(* (pow x 4) -27/2800)
0.1b	(* x (* x 9/40))
0.1b	(* x 9/40)
17.3b	(+ (* 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:

7.0ms	(* (pow x 4) -27/2800)
5.0ms	(* x (* x 9/40))
3.0ms	(* x 9/40)
7.0ms	(+ (* x (* x 9/40)) (+ -1/2 (* (pow x 4) -27/2800)))

series14.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (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)
17.3b	(+ (+ (* 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))

series13.0ms

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))

simplify52.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4921	646
1	4921	646

prune94.0ms

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- x (tan x)) 3)
0.9b	(- x (tan x))
0.9b	(- x (sin x))
21.2b	(cbrt (pow (- x (tan x)) 3))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`cbrt-prod`
10×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
8×	`add-log-exp`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div` `flip3--` `flip--`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 82

Calls

4 calls:

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(pow (- x (tan x)) 3)
12.0ms	(- x (tan x))
5.0ms	(- x (sin x))
12.0ms	(cbrt (pow (- x (tan x)) 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5307	835

prune87.0ms

Filtered

58 candidates to 94 candidates (-62.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	94	3	97

Merged error: 0b

Counts

97 → 3

regimes72.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch39.0ms

Steps

Iters	Range		Point
11	2.45794352520559e-08	4.087206661276032e+16	0.028588739690112084
8	-89.31807550206912	-0.0022795926261585425	-0.02666523152166068

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	31
1	48	31

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.2s	1633×	body	2560	valid
1.7s	2748×	body	1280	valid
492.0ms	1853×	body	640	valid
171.0ms	947×	body	320	valid
60.0ms	478×	body	160	valid
26.0ms	341×	body	80	valid

Details

analyze1.4s

sample226.0ms

simplify474.0ms

prune4.0ms

localize10.0ms

rewrite20.0ms

series53.0ms

simplify64.0ms

prune84.0ms

localize9.0ms

rewrite24.0ms

series14.0ms

simplify55.0ms

prune103.0ms

localize9.0ms

rewrite22.0ms

series13.0ms

simplify52.0ms

prune94.0ms

localize12.0ms

rewrite17.0ms

series40.0ms

simplify44.0ms

prune87.0ms

regimes72.0ms

bsearch39.0ms

simplify2.0ms

end0.0ms

sample6.8s

Profiling