Details

sample103.0ms

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
1.0ms	8×	body	160	valid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (34.0ms)

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

prune13.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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

localize19.0ms

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))

rewrite171.0ms

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:

13.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
10.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
6.0ms	(* (+ 1.0 eps) x)
137.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series283.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
42.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
27.0ms	(* (+ 1.0 eps) x)
172.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (46.0ms)

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

prune604.0ms

Filtered

149 candidates to 109 candidates (73.2%)

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)))

rewrite22.0ms

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

series102.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* 0.5 (pow x 2))
35.0ms	(* 0.33333333333333337 (pow x 3))
38.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify43.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (37.0ms)

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

prune219.0ms

Filtered

81 candidates to 48 candidates (59.3%)

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))))

rewrite18.0ms

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

series103.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* 0.5 (pow x 2))
36.0ms	(* 0.33333333333333337 (pow x 3))
42.0ms	(+ (* 0.33333333333333337 (pow x 3)) (- 1.0 (* 0.5 (pow x 2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

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

prune211.0ms

Filtered

82 candidates to 49 candidates (59.8%)

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

localize13.0ms

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)))

rewrite23.0ms

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:

4.0ms	(* (* 0.33333333333333337 x) x)
1.0ms	(cbrt x)
3.0ms	(pow (cbrt x) 3)
13.0ms	(- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (* 0.33333333333333337 x) x)
93.0ms	(cbrt x)
139.0ms	(pow (cbrt x) 3)
52.0ms	(- (+ (* (* (* 0.33333333333333337 x) x) (pow (cbrt x) 3)) 1.0) (* 0.5 (pow x 2)))

simplify69.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	311	379
1	1784	317
2	5003	303

prune221.0ms

Filtered

85 candidates to 49 candidates (57.6%)

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

regimes119.0ms

Accuracy

97.1% (0.5b remaining)

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

bsearch152.0ms

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

sample2.7s

Algorithm

intervals

Results

840.0ms	1696×	body	1280	valid
697.0ms	10267×	body	80	valid
405.0ms	1345×	body	640	valid
134.0ms	2000×	body	80	overflowed
128.0ms	620×	body	320	valid
45.0ms	341×	body	160	valid

Details

sample103.0ms

simplify35.0ms

prune13.0ms

localize19.0ms

rewrite171.0ms

series283.0ms

simplify66.0ms

prune604.0ms

localize9.0ms

rewrite22.0ms

series102.0ms

simplify43.0ms

prune219.0ms

localize9.0ms

rewrite18.0ms

series103.0ms

simplify47.0ms

prune211.0ms

localize13.0ms

rewrite23.0ms

series312.0ms

simplify69.0ms

prune221.0ms

regimes119.0ms

bsearch152.0ms

simplify1.0ms

end0.0ms

sample2.7s

Profiling