Details

sample82.0ms

Algorithm

intervals

Results

23.0ms	56×	body	1280	valid
19.0ms	293×	body	80	valid
13.0ms	50×	body	640	valid
5.0ms	29×	body	320	valid
3.0ms	56×	body	80	overflowed
1.0ms	10×	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (- 1.0 eps) x))
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
2.7b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
106×	`times-frac`
90×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
26×	`distribute-lft-out--`
17×	`difference-of-squares`
10×	`distribute-lft-out` `associate-/l*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`add-exp-log` `associate-/r*`
4×	`pow1` `div-inv` `associate-/l/`
3×	`div-sub`
2×	`cbrt-undiv` `flip3--` `exp-to-pow` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--`
1×	`sub-neg` `exp-prod` `distribute-rgt-out--` `flip3-+` `frac-sub` `flip-+` `rem-exp-log` `sub-div` `associate--r-`

Counts

4 → 127

Calls

4 calls:

3.0ms	(exp (* (- 1.0 eps) x))
21.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
26.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
225.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series291.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(exp (* (- 1.0 eps) x))
45.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
44.0ms	(/ (- (/ 1.0 eps) 1.0) (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))

simplify56.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	617	1951
1	1860	1845
2	5001	1835

prune429.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 0.33333333333333337 (pow x 3)) 1.0)
0.1b	(* 0.33333333333333337 (pow x 3))
5.6b	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

4.0ms	(+ (* 0.33333333333333337 (pow x 3)) 1.0)
7.0ms	(* 0.33333333333333337 (pow x 3))
26.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(+ (* 0.33333333333333337 (pow x 3)) 1.0)
37.0ms	(* 0.33333333333333337 (pow x 3))
44.0ms	(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify38.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	251	336
1	1024	311
2	5002	307

prune162.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

5.6b	(- (+ (* (* (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)))
42.2b	(cbrt (* 0.33333333333333337 (pow x 3)))
42.2b	(cbrt (* 0.33333333333333337 (pow x 3)))
42.2b	(cbrt (* 0.33333333333333337 (pow x 3)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `pow1/3`
2×	`diff-log`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

4 → 41

Calls

4 calls:

106.0ms	(- (+ (* (* (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)))
2.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
2.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
2.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))

series191.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (+ (* (* (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)))
37.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
43.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
39.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))

simplify71.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	133	470
1	483	391
2	2177	346
3	5001	327

prune184.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

42.2b	(cbrt (* 0.33333333333333337 (pow x 3)))
42.2b	(cbrt (* 0.33333333333333337 (pow x 3)))
42.2b	(cbrt (* 0.33333333333333337 (pow x 3)))
42.2b	(cbrt (* 0.33333333333333337 (pow x 3)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 36

Calls

4 calls:

2.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
2.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
2.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
2.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
37.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
42.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))
37.0ms	(cbrt (* 0.33333333333333337 (pow x 3)))

simplify121.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	36	192
1	79	164
2	121	156
3	217	156
4	760	156
5	2444	156
6	5001	156

prune210.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes69.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 17.0b

bsearch132.0ms

Steps

Iters	Range		Point
9	0.7889543571722019	588165898.4936482	251.67631196577193

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	56
1	55	56

end0.0ms

sample2.2s

Algorithm

intervals

Results

729.0ms	1672×	body	1280	valid
572.0ms	10038×	body	80	valid
326.0ms	1253×	body	640	valid
115.0ms	660×	body	320	valid
106.0ms	1972×	body	80	overflowed
34.0ms	317×	body	160	valid