Details

sample104.0ms

Algorithm

intervals

Results

25.0ms	60×	body	10240	exit
23.0ms	54×	body	1280	valid
17.0ms	299×	body	80	valid
15.0ms	44×	body	640	valid
4.0ms	22×	body	320	valid
1.0ms	11×	body	160	valid

simplify37.0ms

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

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 30.1b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.1b	(exp (* (- 1.0 eps) x))
0.1b	(exp (* (+ 1.0 eps) x))
3.0b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite407.0ms

Algorithm

rewrite-expression-head

Rules

1798×	`associate-/l*`
1679×	`add-sqr-sqrt`
1627×	`*-un-lft-identity`
1428×	`frac-sub`
1346×	`times-frac`
1134×	`associate-/l/`
937×	`add-cube-cbrt`
467×	`associate-/r*`
290×	`difference-of-squares`
175×	`distribute-lft-out`
163×	`distribute-lft-out--`
155×	`frac-2neg`
153×	`clear-num`
79×	`div-inv`
42×	`flip3-+` `flip-+`
36×	`flip3--` `flip--`
27×	`exp-prod`
14×	`add-log-exp`
9×	`associate-l`
7×	`add-exp-log` `sub-div`
6×	`associate-r` `add-cbrt-cube`
4×	`pow1` `exp-to-pow`
3×	`div-sub`
2×	`diff-log` `div-exp` `*-commutative` `rem-exp-log` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `distribute-rgt-out--` `sum-log` `associate--r-`

Counts

4 → 1564

Calls

4 calls:

17.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
7.0ms	(exp (* (- 1.0 eps) x))
6.0ms	(exp (* (+ 1.0 eps) x))
217.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series268.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
24.0ms	(exp (* (- 1.0 eps) x))
19.0ms	(exp (* (+ 1.0 eps) x))
181.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify577.0ms

Algorithm

egg-herbie

Counts

1576 → 1576

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5001	63135

prune4.4s

Filtered

1576 candidates to 933 candidates (40.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	1571	5	1576
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1572	5	1577

Merged error: 0.5b

Counts

1577 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (pow x 2))
0.1b	(* 0.33333333333333337 (pow x 3))
6.6b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
16×	`associate-r`
13×	`add-exp-log`
11×	`associate-l` `unswap-sqr`
9×	`add-cube-cbrt` `unpow-prod-down`
8×	`add-log-exp`
7×	`pow1` `add-cbrt-cube`
6×	`prod-exp` `distribute-lft-out--`
5×	`difference-of-squares` `sqr-pow`
4×	`distribute-lft-out`
3×	`unpow2`
2×	`pow-to-exp` `diff-log` `pow-prod-down` `pow-exp` `associate--l+` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `flip3--` `unpow3` `sum-log` `flip--`

Counts

3 → 81

Calls

3 calls:

6.0ms	(* 0.5 (pow x 2))
6.0ms	(* 0.33333333333333337 (pow x 3))
20.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series106.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* 0.5 (pow x 2))
37.0ms	(* 0.33333333333333337 (pow x 3))
44.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify53.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	298	475
1	1154	439
2	5001	422

prune154.0ms

Filtered

90 candidates to 53 candidates (41.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	88	7	95

Merged error: 0.5b

Counts

95 → 7

localize8.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (pow x 2) (- (* 0.33333333333333337 x) 0.5))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
9×	`associate-l`
8×	`*-un-lft-identity`
7×	`associate-r`
6×	`add-exp-log`
5×	`unswap-sqr`
4×	`add-cube-cbrt` `unpow-prod-down`
3×	`pow1` `prod-exp` `add-cbrt-cube`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/` `distribute-lft-out--` `unpow2` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `flip3--` `pow-prod-down` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `add-log-exp`

Counts

1 → 38

Calls

1 calls:

13.0ms

(* (pow x 2) (- (* 0.33333333333333337 x) 0.5))

series87.0ms

Counts

1 → 3

Calls

1 calls:

87.0ms

(* (pow x 2) (- (* 0.33333333333333337 x) 0.5))

simplify183.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	178	237
1	701	208
2	4975	208
3	5001	208

prune83.0ms

Filtered

41 candidates to 24 candidates (41.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	41	7	48

Merged error: 0.5b

Counts

48 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

6.6b	(- (+ (* (* (cbrt (* 0.33333333333333337 (pow x 3))) (cbrt (* 0.33333333333333337 (pow x 3)))) (cbrt (* 0.33333333333333337 (pow x 3)))) 1.0) (* 0.5 (pow x 2)))
41.9b	(cbrt (* 0.33333333333333337 (pow x 3)))
41.9b	(cbrt (* 0.33333333333333337 (pow x 3)))
41.9b	(cbrt (* 0.33333333333333337 (pow x 3)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

57×	`cbrt-prod`
43×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
24×	`associate-r`
19×	`associate-l`
16×	`add-cube-cbrt`
13×	`unpow-prod-down` `unswap-sqr`
9×	`add-log-exp`
8×	`distribute-lft-out--`
7×	`sqr-pow`
6×	`distribute-lft-out`
5×	`difference-of-squares`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3` `unpow3` `*-commutative`
2×	`diff-log` `associate--l+`
1×	`+-commutative` `sub-neg` `flip3--` `sum-log` `flip--` `unpow2`

Counts

4 → 109

Calls

4 calls:

145.0ms	(- (+ (* (* (cbrt (* 0.33333333333333337 (pow x 3))) (cbrt (* 0.33333333333333337 (pow x 3)))) (cbrt (* 0.33333333333333337 (pow x 3)))) 1.0) (* 0.5 (pow x 2)))
7.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
7.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
7.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (+ (* (* (cbrt (* 0.33333333333333337 (pow x 3))) (cbrt (* 0.33333333333333337 (pow x 3)))) (cbrt (* 0.33333333333333337 (pow x 3)))) 1.0) (* 0.5 (pow x 2)))
45.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
38.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
45.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))

simplify242.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 3 (228.0ms)

Iter	Nodes	Cost
0	259	1089
1	846	929
2	4815	844
3	5001	835

prune245.0ms

Filtered

121 candidates to 73 candidates (39.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	121	7	128

Merged error: 0.5b

Counts

128 → 7

regimes92.0ms

Accuracy

96.9% (0.5b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 17.0b

bsearch138.0ms

Steps

Iters	Range		Point
9	5.487422510167526e-06	1875.067688488174	210.23946370490975

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	27
1	45	27
2	45	27

end0.0ms

sample2.9s

Algorithm

intervals

Results

792.0ms	1873×	body	10240	exit
752.0ms	1690×	body	1280	valid
589.0ms	10220×	body	80	valid
326.0ms	1222×	body	640	valid
113.0ms	654×	body	320	valid
34.0ms	287×	body	160	valid