Details

sample187.0ms

Algorithm

intervals

Results

77.0ms	74×	body	2560	valid
63.0ms	120×	body	1280	valid
10.0ms	31×	body	640	valid
7.0ms	328×	pre	80	true
6.0ms	12×	body	320	valid
5.0ms	72×	body	80	overflowed
1.0ms	14×	body	80	valid
1.0ms	5×	body	160	valid

simplify92.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	245	13
3	697	13
4	3463	13
5	5001	13

prune3.0ms

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: 60.4b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
3.9b	(- (exp (* a eps)) 1.0)
4.6b	(- (exp (* b eps)) 1.0)
6.9b	(- (exp (* (+ a b) eps)) 1.0)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

17.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series295.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
35.0ms	(- (exp (* a eps)) 1.0)
30.0ms	(- (exp (* b eps)) 1.0)
44.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	488	957
1	2299	794
2	5001	789

prune268.0ms

Filtered

85 candidates to 63 candidates (74.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	3	86

Merged error: 0.0b

Counts

86 → 3

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

12.0ms

(+ (/ 1 b) (/ 1 a))

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

(+ (/ 1 b) (/ 1 a))

simplify68.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	101	104
1	345	94
2	1153	91
3	2775	90
4	5001	90

prune42.0ms

Filtered

22 candidates to 14 candidates (63.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	19	6	25

Merged error: 0.0b

Counts

25 → 6

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.5b	(cbrt (+ (/ 1 b) (/ 1 a)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
114×	`cbrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`times-frac`
37×	`add-sqr-sqrt`
33×	`cbrt-div` `swap-sqr`
29×	`add-cube-cbrt`
13×	`associate-r` `associate-l`
11×	`pow1` `flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-l/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 159

Calls

4 calls:

33.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
11.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
12.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
12.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
80.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
80.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
81.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify65.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	389	1813
1	1557	1563
2	5001	1403

prune269.0ms

Filtered

171 candidates to 87 candidates (50.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	171	6	177

Merged error: 0.0b

Counts

177 → 6

localize4.0ms

Local error

Found 1 expressions with local error:

11.5b

(/ (+ b a) (* b a))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `associate-/l/` `distribute-lft-out`
1×	`pow1` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 25

Calls

1 calls:

6.0ms

(/ (+ b a) (* b a))

series37.0ms

Counts

1 → 3

Calls

1 calls:

37.0ms

(/ (+ b a) (* b a))

simplify47.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	145	134
1	519	113
2	2023	113
3	5001	113

prune33.0ms

Filtered

28 candidates to 19 candidates (67.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	3	3
Picked	1	0	1
Done	1	1	2
Total	29	5	34

Merged error: 0b

Counts

34 → 5

regimes76.0ms

Accuracy

0% (3.6b remaining)

Error of 3.6b against oracle of 0.1b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.6s	2526×	body	2560	valid
1.9s	3391×	body	1280	valid
362.0ms	1105×	body	640	valid
206.0ms	9937×	pre	80	true
129.0ms	1935×	body	80	overflowed
78.0ms	351×	body	320	valid
33.0ms	486×	body	80	valid
21.0ms	143×	body	160	valid