Details

sample77.0ms

Algorithm

intervals

Results

24.0ms	56×	body	1280	valid
18.0ms	314×	body	80	valid
9.0ms	33×	body	640	valid
3.0ms	21×	body	320	valid
3.0ms	59×	body	80	overflowed
1.0ms	8×	body	160	valid

simplify36.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b	(exp (* (- 1.0 eps) x))
0.0b	(exp (* (+ 1.0 eps) x))
2.2b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
94×	`times-frac`
81×	`add-sqr-sqrt`
26×	`distribute-lft-out--`
25×	`add-cube-cbrt`
17×	`difference-of-squares`
14×	`add-log-exp`
6×	`add-cbrt-cube` `distribute-lft-out` `associate-/l*`
5×	`add-exp-log`
4×	`pow1` `exp-to-pow`
3×	`div-sub` `associate-/r*` `div-inv`
2×	`exp-prod` `flip3--` `diff-log` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `distribute-rgt-out--` `frac-2neg` `div-exp` `clear-num` `sum-log` `frac-sub` `sub-div` `associate--r-`

Counts

4 → 105

Calls

4 calls:

43.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
8.0ms	(exp (* (- 1.0 eps) x))
6.0ms	(exp (* (+ 1.0 eps) x))
288.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series242.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
18.0ms	(exp (* (- 1.0 eps) x))
16.0ms	(exp (* (+ 1.0 eps) x))
164.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	506	1621
1	1440	1536
2	5002	1520

prune349.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 33

Calls

1 calls:

35.0ms

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

series74.0ms

Counts

1 → 3

Calls

1 calls:

74.0ms

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

simplify163.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	158	214
1	638	189
2	4553	189
3	5001	189

prune69.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b	(exp (* x (- 1.0 eps)))
0.0b	(exp (* (+ 1.0 eps) x))
2.2b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* x (- 1.0 eps)))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite481.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
94×	`times-frac`
81×	`add-sqr-sqrt`
26×	`distribute-lft-out--`
25×	`add-cube-cbrt`
17×	`difference-of-squares`
12×	`add-log-exp`
6×	`add-cbrt-cube` `distribute-lft-out` `associate-/l*`
5×	`add-exp-log`
4×	`pow1` `exp-sum`
3×	`sub-neg` `exp-to-pow` `div-sub` `associate-/r*` `div-inv`
2×	`distribute-rgt-in` `exp-prod` `flip3--` `distribute-lft-in` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-out--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `sub-div` `associate--r-`

Counts

4 → 108

Calls

4 calls:

43.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
6.0ms	(exp (* x (- 1.0 eps)))
6.0ms	(exp (* (+ 1.0 eps) x))
418.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* x (- 1.0 eps)))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series235.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
11.0ms	(exp (* x (- 1.0 eps)))
22.0ms	(exp (* (+ 1.0 eps) x))
162.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* x (- 1.0 eps)))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	514	1641
1	1446	1557
2	5001	1541

prune333.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (+ 1.0 eps) x))
0.0b	(exp (* (+ 1.0 eps) x))
0.0b	(exp (* (+ 1.0 eps) x))
3.9b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* x (- 1.0 eps)))) 2.0) (/ (/ (/ (- (/ 1.0 eps) 1.0) (* (cbrt (exp (* (+ 1.0 eps) x))) (cbrt (exp (* (+ 1.0 eps) x))))) (cbrt (exp (* (+ 1.0 eps) x)))) 2.0))

rewrite848.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-sqr-sqrt`
81×	`times-frac`
45×	`*-un-lft-identity`
18×	`add-log-exp` `difference-of-squares`
10×	`add-cube-cbrt` `distribute-lft-out--`
6×	`cbrt-prod` `exp-to-pow`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`exp-prod` `div-sub` `sum-log` `rem-exp-log` `distribute-lft-out`
2×	`div-inv`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `frac-sub` `flip--` `sub-div` `associate--r-`

Counts

4 → 77

Calls

4 calls:

6.0ms	(exp (* (+ 1.0 eps) x))
6.0ms	(exp (* (+ 1.0 eps) x))
6.0ms	(exp (* (+ 1.0 eps) x))
826.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* x (- 1.0 eps)))) 2.0) (/ (/ (/ (- (/ 1.0 eps) 1.0) (* (cbrt (exp (* (+ 1.0 eps) x))) (cbrt (exp (* (+ 1.0 eps) x))))) (cbrt (exp (* (+ 1.0 eps) x)))) 2.0))

series223.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(exp (* (+ 1.0 eps) x))
16.0ms	(exp (* (+ 1.0 eps) x))
17.0ms	(exp (* (+ 1.0 eps) x))
168.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* x (- 1.0 eps)))) 2.0) (/ (/ (/ (- (/ 1.0 eps) 1.0) (* (cbrt (exp (* (+ 1.0 eps) x))) (cbrt (exp (* (+ 1.0 eps) x))))) (cbrt (exp (* (+ 1.0 eps) x)))) 2.0))

simplify93.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	373	2114
1	932	1965
2	3591	1913
3	5001	1913

prune471.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

95.9% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.8b

bsearch154.0ms

Steps

Iters	Range		Point
10	9.155891339580972e-07	611368.3395468491	9.62605629459005

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	33
1	41	33

end0.0ms

sample2.3s

Algorithm

intervals

Results

745.0ms	1671×	body	1280	valid
584.0ms	9986×	body	80	valid
327.0ms	1257×	body	640	valid
113.0ms	637×	body	320	valid
113.0ms	1893×	body	80	overflowed
40.0ms	361×	body	160	valid