Details

sample100.0ms

Algorithm

intervals

Results

32.0ms	330×	body	80	valid
22.0ms	42×	body	1280	valid
13.0ms	36×	body	640	valid
5.0ms	22×	body	320	valid
5.0ms	57×	body	80	overflowed
2.0ms	12×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5151	27

prune12.0ms

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: 26.3b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b	(exp (neg (* (- 1.0 eps) x)))
0.0b	(exp (neg (* (+ 1.0 eps) x)))
2.4b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
78×	`exp-neg`
76×	`frac-times`
59×	`neg-sub0` `exp-diff`
38×	`associate-r/` `associate-l/`
30×	`flip3-+` `flip-+`
28×	`flip3--` `flip--`
19×	`un-div-inv`
12×	`exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-cbrt-cube`
5×	`add-exp-log`
4×	`associate-l` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 155

Calls

4 calls:

13.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
4.0ms	(exp (neg (* (- 1.0 eps) x)))
3.0ms	(exp (neg (* (+ 1.0 eps) x)))
22.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
6.0ms	(exp (neg (* (- 1.0 eps) x)))
7.0ms	(exp (neg (* (+ 1.0 eps) x)))
53.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify89.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4954	6555
1	4954	6555

prune370.0ms

Filtered

92 candidates to 167 candidates (-81.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	167	2	169

Merged error: 0.3b

Counts

169 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(* 0.6666666666666667 (pow x 3))
7.0b	(+ (* 0.6666666666666667 (pow x 3)) (- 2.0 (* 1.0 (* x x))))

rewrite15.0ms

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` `associate-+r+` `sum-log` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 46

Calls

2 calls:

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

series9.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify21.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5048	458

prune75.0ms

Filtered

32 candidates to 52 candidates (-62.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	51	3	54

Merged error: 0.3b

Counts

54 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (* x (- (* 0.6666666666666667 x) 1.0)))
0.0b	(* x (- (* 0.6666666666666667 x) 1.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

9.0ms	(* x (* x (- (* 0.6666666666666667 x) 1.0)))
7.0ms	(* x (- (* 0.6666666666666667 x) 1.0))

series14.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(* x (* x (- (* 0.6666666666666667 x) 1.0)))
6.0ms	(* x (- (* 0.6666666666666667 x) 1.0))

simplify27.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4973	552
1	4973	552

prune64.0ms

Filtered

35 candidates to 58 candidates (-65.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	58	3	61

Merged error: 0.3b

Counts

61 → 3

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)
0.0b	(* x (- (* 0.6666666666666667 x) 1.0))
3.7b	(cbrt (pow (+ 2.0 (* x (* x (- (* 0.6666666666666667 x) 1.0)))) 3))

rewrite27.0ms

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`
10×	`distribute-rgt-in` `distribute-lft-in`
6×	`sub-neg` `unpow-prod-down` `cube-prod` `associate-r/` `associate-l*`
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 → 100

Calls

4 calls:

9.0ms	(* x (* x (- (* 0.6666666666666667 x) 1.0)))
4.0ms	(pow (+ 2.0 (* x (* x (- (* 0.6666666666666667 x) 1.0)))) 3)
7.0ms	(* x (- (* 0.6666666666666667 x) 1.0))
4.0ms	(cbrt (pow (+ 2.0 (* x (* x (- (* 0.6666666666666667 x) 1.0)))) 3))

series26.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* x (* x (- (* 0.6666666666666667 x) 1.0)))
5.0ms	(pow (+ 2.0 (* x (* x (- (* 0.6666666666666667 x) 1.0)))) 3)
8.0ms	(* x (- (* 0.6666666666666667 x) 1.0))
5.0ms	(cbrt (pow (+ 2.0 (* x (* x (- (* 0.6666666666666667 x) 1.0)))) 3))

simplify38.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5027	1483

prune140.0ms

Filtered

66 candidates to 112 candidates (-69.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	112	3	115

Merged error: 0.3b

Counts

115 → 3

regimes106.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 17.1b

bsearch93.0ms

Steps

Iters	Range		Point
9	0.0012906900159990226	483.8343007553032	223.69169998523014

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	45
1	47	45

end0.0ms

sample3.1s

Algorithm

intervals

Results

875.0ms	10220×	body	80	valid
867.0ms	1632×	body	1280	valid
433.0ms	1235×	body	640	valid
165.0ms	1963×	body	80	overflowed
160.0ms	613×	body	320	valid
56.0ms	331×	body	160	valid

Details

sample100.0ms

simplify37.0ms

prune12.0ms

localize18.0ms

rewrite54.0ms

series77.0ms

simplify89.0ms

prune370.0ms

localize10.0ms

rewrite15.0ms

series9.0ms

simplify21.0ms

prune75.0ms

localize8.0ms

rewrite17.0ms

series14.0ms

simplify27.0ms

prune64.0ms

localize11.0ms

rewrite27.0ms

series26.0ms

simplify38.0ms

prune140.0ms

regimes106.0ms

bsearch93.0ms

simplify1.0ms

end0.0ms

sample3.1s

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