Details

sample32.0ms

Algorithm

intervals

Results

11.0ms	67×	body	1280	valid
6.0ms	56×	body	640	valid
2.0ms	28×	body	320	valid
2.0ms	84×	body	80	valid
2.0ms	90×	body	80	overflowed
1.0ms	21×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4

prune2.0ms

Filtered

1 candidates to 0 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: 42.5b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
6.2b	(- (exp x) 1.0)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 51

Calls

2 calls:

7.0ms	(/ (exp x) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)

series41.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	180	378
1	542	357
2	2210	354
3	5001	354

prune102.0ms

Filtered

57 candidates to 41 candidates (71.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	2	58

Merged error: 0.0b

Counts

58 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
0.3b	(* 1/12 x)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

7.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
3.0ms	(* 1/12 x)

series31.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
14.0ms	(* 1/12 x)

simplify57.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	148	149
1	534	137
2	2215	137
3	5001	137

prune44.0ms

Filtered

38 candidates to 24 candidates (63.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	38	2	40

Merged error: 0.0b

Counts

40 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (exp x))
0.0b	(/ (exp x) (- (pow (exp x) 3) (pow 1.0 3)))
0.0b	(* (/ (exp x) (- (pow (exp x) 3) (pow 1.0 3))) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0))))
6.0b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

273×	`add-sqr-sqrt`
154×	`*-un-lft-identity`
151×	`times-frac`
128×	`difference-of-squares`
96×	`unpow-prod-down` `cube-prod`
84×	`associate-l`
74×	`add-cube-cbrt`
64×	`sqr-pow`
40×	`distribute-lft-out--`
25×	`associate-/r*`
18×	`exp-prod`
13×	`pow1` `add-cbrt-cube`
9×	`add-exp-log`
8×	`difference-cubes`
6×	`associate-r` `add-log-exp`
5×	`pow-prod-down`
4×	`associate-/r/` `pow-sqr` `pow-prod-up`
3×	`flip3--` `swap-sqr` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `flip3-+` `associate-r/` `div-exp` `-commutative` `flip-+` `div-inv`
1×	`pow2` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `pow-plus` `diff-log` `associate-*l/` `clear-num`

Counts

4 → 291

Calls

4 calls:

6.0ms	(* (exp x) (exp x))
17.0ms	(/ (exp x) (- (pow (exp x) 3) (pow 1.0 3)))
35.0ms	(* (/ (exp x) (- (pow (exp x) 3) (pow 1.0 3))) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0))))
14.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series228.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (exp x) (exp x))
55.0ms	(/ (exp x) (- (pow (exp x) 3) (pow 1.0 3)))
122.0ms	(* (/ (exp x) (- (pow (exp x) 3) (pow 1.0 3))) (+ (* (exp x) (exp x)) (+ (* 1.0 1.0) (* (exp x) 1.0))))
37.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify66.0ms

Algorithm

egg-herbie

Counts

303 → 303

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1036	3625
1	5002	3468

prune667.0ms

Filtered

303 candidates to 179 candidates (59.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	302	1	303
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	302	3	305

Merged error: 0.0b

Counts

305 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2)
0.0b	(* (+ (* 1.0 (+ 1.0 (exp x))) (pow (exp x) 2)) (+ (pow (exp x) 3) (pow 1.0 3)))
0.0b	(* (/ (exp x) (- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1.0 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (exp x))) (pow (exp x) 2)) (+ (pow (exp x) 3) (pow 1.0 3))))
6.0b	(- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1.0 3) (pow 1.0 3)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
24×	`associate-l`
20×	`add-sqr-sqrt` `frac-times`
18×	`add-cube-cbrt` `flip3-+` `add-cbrt-cube` `flip-+`
16×	`add-exp-log`
15×	`times-frac`
14×	`associate-*r/`
12×	`pow1` `pow-prod-down`
10×	`associate-r`
7×	`unpow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `distribute-lft-out`
4×	`difference-cubes` `pow-pow` `cube-prod` `difference-of-squares`
3×	`pow-unpow` `exp-prod`
2×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r/` `*-commutative` `flip--`
1×	`pow-to-exp` `sub-neg` `diff-log` `pow-exp` `sum-cubes` `div-inv` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 130

Calls

4 calls:

3.0ms	(pow (exp x) 2)
24.0ms	(* (+ (* 1.0 (+ 1.0 (exp x))) (pow (exp x) 2)) (+ (pow (exp x) 3) (pow 1.0 3)))
36.0ms	(* (/ (exp x) (- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1.0 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (exp x))) (pow (exp x) 2)) (+ (pow (exp x) 3) (pow 1.0 3))))
10.0ms	(- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1.0 3) (pow 1.0 3)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (exp x) 2)
86.0ms	(* (+ (* 1.0 (+ 1.0 (exp x))) (pow (exp x) 2)) (+ (pow (exp x) 3) (pow 1.0 3)))
180.0ms	(* (/ (exp x) (- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1.0 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (exp x))) (pow (exp x) 2)) (+ (pow (exp x) 3) (pow 1.0 3))))
49.0ms	(- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1.0 3) (pow 1.0 3)))

simplify54.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	889	2733
1	5002	2397

prune460.0ms

Filtered

142 candidates to 105 candidates (73.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	143	2	145

Merged error: 0.0b

Counts

145 → 2

regimes37.0ms

Accuracy

98% (0.4b remaining)

Error of 0.9b against oracle of 0.5b and baseline of 22.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	36
1	47	36

end0.0ms

sample951.0ms

Algorithm

intervals

Results

415.0ms	2194×	body	1280	valid
189.0ms	1582×	body	640	valid
69.0ms	2995×	body	80	valid
65.0ms	796×	body	320	valid
53.0ms	2585×	body	80	overflowed
22.0ms	436×	body	160	valid