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

sample247.0ms

Algorithm

intervals

Results

158.0ms	47×	body	2560	valid
51.0ms	85×	body	1280	valid
17.0ms	59×	body	640	valid
7.0ms	36×	body	320	valid
3.0ms	18×	body	160	valid
1.0ms	11×	body	80	valid

simplify438.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	9
1	9	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: 31.2b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (sin x))
1.7b	(- x (tan x))

rewrite21.0ms

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 (sin x))
5.0ms	(- x (tan x))

series39.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify57.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5236	1127

prune81.0ms

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	(* x (* x 9/40))
0.1b	(* 27/2800 (pow x 4))
0.2b	(* x 9/40)
16.6b	(- (* x (* x 9/40)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

4.0ms	(* x (* x 9/40))
5.0ms	(* 27/2800 (pow x 4))
3.0ms	(* x 9/40)
7.0ms	(- (* x (* x 9/40)) (+ (* 27/2800 (pow x 4)) 1/2))

series18.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify46.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4939	656
1	4939	656

prune94.0ms

Filtered

52 candidates to 86 candidates (-65.4%)

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: 0.0b

Counts

89 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
1.7b	(- x (tan x))
1.7b	(- (* x x) (pow (sin x) 2))
15.4b	(/ (- (* x x) (pow (sin x) 2)) (+ x (sin x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
28×	`times-frac`
25×	`difference-of-squares`
19×	`add-cube-cbrt`
9×	`unpow-prod-down`
8×	`distribute-lft-out` `add-log-exp`
7×	`add-exp-log` `associate-/l*` `unpow2` `sqr-pow`
6×	`add-cbrt-cube`
5×	`pow1`
4×	`associate-/r*`
3×	`pow-unpow` `flip3--` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `div-sub` `div-exp` `pow-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out--`

Counts

4 → 102

Calls

4 calls:

2.0ms	(pow (sin x) 2)
3.0ms	(- x (tan x))
7.0ms	(- (* x x) (pow (sin x) 2))
11.0ms	(/ (- (* x x) (pow (sin x) 2)) (+ x (sin x)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow (sin x) 2)
10.0ms	(- x (tan x))
9.0ms	(- (* x x) (pow (sin x) 2))
13.0ms	(/ (- (* x x) (pow (sin x) 2)) (+ x (sin x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4931	1346
1	4931	1346

prune114.0ms

Filtered

76 candidates to 114 candidates (-50.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	114	3	117

Merged error: 0.0b

Counts

117 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (pow x 3) (pow (tan x) 3))
1.7b	(- (* x x) (pow (sin x) 2))
15.4b	(/ (- (* x x) (pow (sin x) 2)) (+ x (sin x)))
32.7b	(/ (- (pow x 3) (pow (tan x) 3)) (+ (* x x) (* (tan x) (+ x (tan x)))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
104×	`difference-of-squares`
103×	`times-frac`
66×	`unpow-prod-down`
60×	`cube-prod`
47×	`add-cube-cbrt`
46×	`sqr-pow`
32×	`associate-/l*`
25×	`distribute-lft-out--`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
7×	`associate-/r*`
6×	`unpow2`
5×	`difference-cubes`
4×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 224

Calls

4 calls:

12.0ms	(- (pow x 3) (pow (tan x) 3))
5.0ms	(- (* x x) (pow (sin x) 2))
11.0ms	(/ (- (* x x) (pow (sin x) 2)) (+ x (sin x)))
20.0ms	(/ (- (pow x 3) (pow (tan x) 3)) (+ (* x x) (* (tan x) (+ x (tan x)))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(- (pow x 3) (pow (tan x) 3))
9.0ms	(- (* x x) (pow (sin x) 2))
13.0ms	(/ (- (* x x) (pow (sin x) 2)) (+ x (sin x)))
43.0ms	(/ (- (pow x 3) (pow (tan x) 3)) (+ (* x x) (* (tan x) (+ x (tan x)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4952	5812
1	4952	5812

prune315.0ms

Filtered

134 candidates to 236 candidates (-76.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	236	3	239

Merged error: 0.0b

Counts

239 → 3

regimes75.0ms

Accuracy

100% (0.0b remaining)

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

bsearch62.0ms

Steps

Iters	Range		Point
10	3.533960664661459e-08	5117698.773793675	0.024876010453197765
10	-0.07380404989037599	-1.0970421424112894e-13	-0.023049000000213135

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	31
1	29	31

end0.0ms

analyze1.2s

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

sample6.8s

Algorithm

intervals

Results

4.2s	1651×	body	2560	valid
1.7s	2751×	body	1280	valid
498.0ms	1816×	body	640	valid
171.0ms	929×	body	320	valid
66.0ms	497×	body	160	valid
32.0ms	356×	body	80	valid

Details

analyze1.4s

sample247.0ms

simplify438.0ms

prune4.0ms

localize11.0ms

rewrite21.0ms

series39.0ms

simplify57.0ms

prune81.0ms

localize9.0ms

rewrite22.0ms

series18.0ms

simplify46.0ms

prune94.0ms

localize13.0ms

rewrite27.0ms

series36.0ms

simplify52.0ms

prune114.0ms

localize22.0ms

rewrite59.0ms

series85.0ms

simplify88.0ms

prune315.0ms

regimes75.0ms

bsearch62.0ms

simplify1.0ms

end0.0ms

analyze1.2s

sample6.8s

Profiling