Details

analyze231.0ms

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

31.0ms	57×	body	1280	valid
12.0ms	38×	body	640	valid
10.0ms	132×	body	80	valid
4.0ms	18×	body	320	valid
2.0ms	11×	body	160	valid
1.0ms	14×	body	80	invalid
1.0ms	2×	body	640	invalid
0.0ms	4×	body	80	overflowed

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5720	27

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 29.1b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b	(+ 1.0 (/ 1.0 eps))
2.0b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
80×	`exp-neg` `frac-times`
60×	`neg-sub0` `exp-diff`
40×	`associate-r/` `associate-l/`
31×	`flip3--` `flip3-+` `flip--` `flip-+`
20×	`un-div-inv`
17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`associate-l`
8×	`pow1` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`add-exp-log` `associate-r`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `sub-neg` `times-frac` `diff-log` `sum-log` `distribute-lft-out--`

Counts

4 → 162

Calls

4 calls:

14.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
6.0ms	(+ 1.0 (/ 1.0 eps))
17.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x))))
9.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
3.0ms	(+ 1.0 (/ 1.0 eps))
43.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5081	6879

prune357.0ms

Filtered

93 candidates to 174 candidates (-87.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	171	3	174
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	173	3	176

Merged error: 0.3b

Counts

176 → 3

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
5.2b	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (* x x))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
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-l` `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:

6.0ms	(* 0.6666666666666667 (pow x 3))
7.0ms	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (* x x))))

series8.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify26.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5306	451

prune68.0ms

Filtered

32 candidates to 51 candidates (-59.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	50	4	54

Merged error: 0.3b

Counts

54 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (* x (- (* 0.6666666666666667 x) 1.0)))
0.0b	(pow (+ 2.0 (* x (* x (- (* 0.6666666666666667 x) 1.0)))) 3)
0.1b	(* x (- (* 0.6666666666666667 x) 1.0))
3.3b	(cbrt (pow (+ 2.0 (* x (* x (- (* 0.6666666666666667 x) 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 (- (* 0.6666666666666667 x) 1.0)))
4.0ms	(pow (+ 2.0 (* x (* x (- (* 0.6666666666666667 x) 1.0)))) 3)
6.0ms	(* x (- (* 0.6666666666666667 x) 1.0))
4.0ms	(cbrt (pow (+ 2.0 (* x (* x (- (* 0.6666666666666667 x) 1.0)))) 3))

series20.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* x (* x (- (* 0.6666666666666667 x) 1.0)))
4.0ms	(pow (+ 2.0 (* x (* x (- (* 0.6666666666666667 x) 1.0)))) 3)
5.0ms	(* x (- (* 0.6666666666666667 x) 1.0))
4.0ms	(cbrt (pow (+ 2.0 (* x (* x (- (* 0.6666666666666667 x) 1.0)))) 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5054	1421

prune134.0ms

Filtered

67 candidates to 106 candidates (-58.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	106	4	110

Merged error: 0.3b

Counts

110 → 4

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* x x) (- (* x 8.0) 12.0))
9.7b	(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:

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

series16.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(* (* x x) (- (* x 8.0) 12.0))
9.0ms	(cbrt (+ 8.0 (* (* x x) (- (* x 8.0) 12.0))))

simplify45.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4935	622
1	4935	622

prune64.0ms

Filtered

31 candidates to 42 candidates (-35.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	42	4	46

Merged error: 0.3b

Counts

46 → 4

regimes99.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.6b

bsearch66.0ms

Steps

Iters	Range		Point
8	0.4945291466315318	19437.217628884515	280.86223002821583

simplify12.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	653	77
1	653	77

end0.0ms

sample2.1s

Algorithm

intervals

Results

938.0ms	1751×	body	1280	valid
426.0ms	1252×	body	640	valid
318.0ms	4096×	body	80	valid
135.0ms	594×	body	320	valid
46.0ms	307×	body	160	valid
17.0ms	218×	body	80	invalid
14.0ms	190×	body	80	overflowed
6.0ms	12×	body	1280	invalid
4.0ms	11×	body	640	invalid
3.0ms	10×	body	320	invalid
1.0ms	3×	body	160	invalid

Details

analyze231.0ms

sample71.0ms

simplify43.0ms

prune13.0ms

localize17.0ms

rewrite62.0ms

series66.0ms

simplify90.0ms

prune357.0ms

localize9.0ms

rewrite14.0ms

series8.0ms

simplify26.0ms

prune68.0ms

localize11.0ms

rewrite25.0ms

series20.0ms

simplify43.0ms

prune134.0ms

localize8.0ms

rewrite12.0ms

series16.0ms

simplify45.0ms

prune64.0ms

regimes99.0ms

bsearch66.0ms

simplify12.0ms

end0.0ms

sample2.1s

Profiling