Details

sample106.0ms

Algorithm

intervals

Results

33.0ms	56×	body	1280	valid
22.0ms	329×	body	80	valid
15.0ms	48×	body	640	valid
5.0ms	22×	body	320	valid
4.0ms	59×	body	80	overflowed
2.0ms	8×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (35.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune15.0ms

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: 31.1b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.0b	(* (+ 1.0 eps) x)
1.5b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

122×	`*-un-lft-identity`
106×	`times-frac`
94×	`add-sqr-sqrt`
36×	`add-cube-cbrt`
26×	`distribute-lft-out--`
17×	`difference-of-squares`
11×	`distribute-lft-out`
10×	`add-cbrt-cube` `associate-/l*`
8×	`add-exp-log`
6×	`pow1` `associate-/r*` `add-log-exp`
4×	`associate-l` `div-inv` `associate-/l/`
3×	`div-sub` `associate-r`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `associate-*l/` `clear-num` `flip--` `flip-+`
1×	`sub-neg` `distribute-rgt-out--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `sub-div` `associate--r-` `unswap-sqr`

Counts

4 → 137

Calls

4 calls:

11.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
11.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
6.0ms	(* (+ 1.0 eps) x)
145.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series90.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
12.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
5.0ms	(* (+ 1.0 eps) x)
61.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	689	1986
1	2265	1877
2	5002	1876

prune1.2s

Filtered

149 candidates to 109 candidates (26.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	148	3	151

Merged error: 0.9b

Counts

151 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
0.1b	(* 0.33333333333333337 (pow x 3))
5.8b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp` `unswap-sqr`
7×	`add-cbrt-cube`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`cube-mult` `sub-neg` `flip3--` `unpow3` `associate--l+` `sum-log` `flip--`

Counts

3 → 72

Calls

3 calls:

5.0ms	(* 0.5 (pow x 2))
6.0ms	(* 0.33333333333333337 (pow x 3))
7.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(* 0.5 (pow x 2))
4.0ms	(* 0.33333333333333337 (pow x 3))
5.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify45.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	281	367
1	1210	327
2	5001	314

prune220.0ms

Filtered

81 candidates to 48 candidates (40.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	79	5	84

Merged error: 0.9b

Counts

84 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
0.1b	(* 0.33333333333333337 (pow x 3))
5.8b	(+ (* 0.33333333333333337 (pow x 3)) (- 1.0 (* 0.5 (pow x 2))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp` `unswap-sqr`
7×	`add-cbrt-cube`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `associate-+r+` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod` `unpow2`
1×	`+-commutative` `cube-mult` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `unpow3` `flip-+`

Counts

3 → 73

Calls

3 calls:

5.0ms	(* 0.5 (pow x 2))
6.0ms	(* 0.33333333333333337 (pow x 3))
6.0ms	(+ (* 0.33333333333333337 (pow x 3)) (- 1.0 (* 0.5 (pow x 2))))

series12.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(* 0.5 (pow x 2))
4.0ms	(* 0.33333333333333337 (pow x 3))
5.0ms	(+ (* 0.33333333333333337 (pow x 3)) (- 1.0 (* 0.5 (pow x 2))))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	287	366
1	1198	326
2	5002	316

prune211.0ms

Filtered

82 candidates to 49 candidates (40.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	82	5	87

Merged error: 0.9b

Counts

87 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 0.33333333333333337 x) x)
0.7b	(cbrt x)
0.7b	(pow (cbrt x) 3)
5.8b	(- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log`
9×	`cbrt-prod` `add-cbrt-cube` `add-log-exp`
6×	`unpow-prod-down` `cube-prod`
3×	`pow-unpow` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow-pow` `pow1/3` `diff-log`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `associate-l` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (* 0.33333333333333337 x) x)
1.0ms	(cbrt x)
3.0ms	(pow (cbrt x) 3)
11.0ms	(- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 0.33333333333333337 x) x)
26.0ms	(cbrt x)
32.0ms	(pow (cbrt x) 3)
7.0ms	(- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2)))

simplify68.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	351	412
1	1878	356
2	5001	322

prune260.0ms

Filtered

85 candidates to 47 candidates (44.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	85	5	90

Merged error: 0.9b

Counts

90 → 5

regimes118.0ms

Accuracy

97.1% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.3b

bsearch168.0ms

Steps

Iters	Range		Point
9	5.042106407826366e-05	28.700163284045342	0.4483322262182013

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	26
1	41	26

end0.0ms

sample2.8s

Algorithm

intervals

Results

847.0ms	1696×	body	1280	valid
711.0ms	10267×	body	80	valid
413.0ms	1345×	body	640	valid
135.0ms	2000×	body	80	overflowed
132.0ms	620×	body	320	valid
46.0ms	341×	body	160	valid

Details

sample106.0ms

simplify36.0ms

prune15.0ms

localize17.0ms

rewrite180.0ms

series90.0ms

simplify68.0ms

prune1.2s

localize9.0ms

rewrite20.0ms

series12.0ms

simplify45.0ms

prune220.0ms

localize9.0ms

rewrite20.0ms

series12.0ms

simplify44.0ms

prune211.0ms

localize16.0ms

rewrite22.0ms

series69.0ms

simplify68.0ms

prune260.0ms

regimes118.0ms

bsearch168.0ms

simplify1.0ms

end0.0ms

sample2.8s

Profiling