Details

analyze236.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

sample71.0ms

Algorithm

intervals

Results

30.0ms	57×	body	1280	valid
13.0ms	40×	body	640	valid
11.0ms	139×	body	80	valid
2.0ms	11×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	6×	body	80	overflowed
0.0ms	1×	body	640	invalid
0.0ms	4×	body	80	invalid
0.0ms	1×	body	160	invalid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5720	27

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 27.7b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (neg (* (- 1.0 eps) x)))
0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b	(* (- 1.0 eps) x)
2.2b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
77×	`exp-neg`
76×	`frac-times`
58×	`neg-sub0` `exp-diff`
40×	`associate-*l/`
38×	`associate-*r/`
30×	`flip3-+` `flip-+`
29×	`flip3--` `flip--`
19×	`un-div-inv`
15×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cube-cbrt` `associate-l`
8×	`pow1` `add-cbrt-cube` `add-log-exp`
7×	`add-exp-log`
6×	`exp-prod` `associate-r`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`distribute-lft-neg-in` `neg-mul-1` `sub-neg` `distribute-rgt-neg-in` `diff-log` `neg-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 159

Calls

4 calls:

3.0ms	(exp (neg (* (- 1.0 eps) x)))
12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
6.0ms	(* (- 1.0 eps) x)
17.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(exp (neg (* (- 1.0 eps) x)))
10.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
5.0ms	(* (- 1.0 eps) x)
50.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5017	6569

prune338.0ms

Filtered

92 candidates to 171 candidates (-85.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	170	2	172

Merged error: 0.6b

Counts

172 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (pow x 3) 0.6666666666666667)
6.4b	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-l`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-r` `prod-exp`
2×	`pow1` `sum-log` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `associate-+r-` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 45

Calls

2 calls:

5.0ms	(* (pow x 3) 0.6666666666666667)
7.0ms	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

series8.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(* (pow x 3) 0.6666666666666667)
4.0ms	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

simplify56.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4959	458
1	4959	458

prune71.0ms

Filtered

33 candidates to 51 candidates (-54.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	49	4	53

Merged error: 0.6b

Counts

53 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (* x (- (* x 0.6666666666666667) 1.0)))
0.0b	(* x (- (* x 0.6666666666666667) 1.0))
0.1b	(pow (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))) 3)
4.9b	(cbrt (pow (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))) 3))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1` `add-exp-log` `cbrt-prod` `add-cbrt-cube`
6×	`sub-neg` `unpow-prod-down` `cube-prod` `associate-r/` `associate-l*`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`cube-div` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `cbrt-div` `flip3--` `flip3-+` `unpow3` `*-commutative` `flip--` `flip-+` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

8.0ms	(* x (* x (- (* x 0.6666666666666667) 1.0)))
6.0ms	(* x (- (* x 0.6666666666666667) 1.0))
4.0ms	(pow (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))) 3)
4.0ms	(cbrt (pow (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))) 3))

series24.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* x (* x (- (* x 0.6666666666666667) 1.0)))
5.0ms	(* x (- (* x 0.6666666666666667) 1.0))
5.0ms	(pow (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))) 3)
4.0ms	(cbrt (pow (+ 2.0 (* x (* x (- (* x 0.6666666666666667) 1.0)))) 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5054	1421

prune130.0ms

Filtered

59 candidates to 106 candidates (-79.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	105	5	110

Merged error: 0.6b

Counts

110 → 5

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (* x x) (- (* x 8.0) 12.0))
10.0b	(cbrt (+ 8.0 (* (* x x) (- (* x 8.0) 12.0))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `*-un-lft-identity`
3×	`cbrt-prod` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `cbrt-div` `associate-*r/` `add-log-exp`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip3-+` `pow1/3` `associate-l` `*-commutative` `flip--` `flip-+` `unswap-sqr`

Counts

2 → 36

Calls

2 calls:

9.0ms	(* (* x x) (- (* x 8.0) 12.0))
3.0ms	(cbrt (+ 8.0 (* (* x x) (- (* x 8.0) 12.0))))

series18.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(* (* x x) (- (* x 8.0) 12.0))
11.0ms	(cbrt (+ 8.0 (* (* x x) (- (* x 8.0) 12.0))))

simplify48.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4935	622
1	4935	622

prune67.0ms

Filtered

31 candidates to 42 candidates (-35.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	42	5	47

Merged error: 0.6b

Counts

47 → 5

regimes118.0ms

Accuracy

99.5% (0.1b remaining)

Error of 1.0b against oracle of 0.9b and baseline of 16.7b

bsearch84.0ms

Steps

Iters	Range		Point
9	2.3483345582160555	396880.52369225153	454.9806945668749

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	426	49
1	426	49

end0.0ms

sample2.1s

Algorithm

intervals

Results

955.0ms	1750×	body	1280	valid
415.0ms	1223×	body	640	valid
326.0ms	4137×	body	80	valid
140.0ms	597×	body	320	valid
45.0ms	293×	body	160	valid
17.0ms	211×	body	80	invalid
15.0ms	197×	body	80	overflowed
6.0ms	12×	body	1280	invalid
5.0ms	13×	body	640	invalid
4.0ms	13×	body	320	invalid
1.0ms	3×	body	160	invalid

Details

analyze236.0ms

sample71.0ms

simplify44.0ms

prune8.0ms

localize20.0ms

rewrite49.0ms

series70.0ms

simplify87.0ms

prune338.0ms

localize9.0ms

rewrite13.0ms

series8.0ms

simplify56.0ms

prune71.0ms

localize11.0ms

rewrite25.0ms

series24.0ms

simplify43.0ms

prune130.0ms

localize8.0ms

rewrite12.0ms

series18.0ms

simplify48.0ms

prune67.0ms

regimes118.0ms

bsearch84.0ms

simplify8.0ms

end0.0ms

sample2.1s

Profiling