Details

sample190.0ms

Algorithm

intervals

Results

79.0ms	70×	body	2560	valid
70.0ms	122×	body	1280	valid
11.0ms	35×	body	640	valid
7.0ms	317×	pre	80	true
4.0ms	61×	body	80	overflowed
1.0ms	19×	body	80	valid
1.0ms	5×	body	320	valid
1.0ms	5×	body	160	valid

simplify103.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	258	13
3	766	13
4	3895	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: 59.1b

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)))
2.5b	(- (exp (* b eps)) 1.0)
4.3b	(- (exp (* a eps)) 1.0)
5.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
10×	`flip3--` `flip--` `add-log-exp`
9×	`fma-neg`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
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 → 117

Calls

4 calls:

17.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* a eps)) 1.0)
8.0ms	(- (exp (* (+ a b) eps)) 1.0)

series324.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
32.0ms	(- (exp (* b eps)) 1.0)
36.0ms	(- (exp (* a eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify84.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	608	1462
1	2778	1079
2	5002	1072

prune357.0ms

Filtered

129 candidates to 86 candidates (66.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	126	3	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	3	130

Merged error: 0.0b

Counts

130 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

13.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify74.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	107	112
1	368	101
2	1274	98
3	3144	98
4	5001	98

prune74.0ms

Filtered

37 candidates to 28 candidates (75.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	35	5	40

Merged error: 0.0b

Counts

40 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
0.6b	(cbrt (/ 1 b))
0.6b	(cbrt (/ 1 b))
0.6b	(cbrt (/ 1 b))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

119×	`cbrt-prod`
97×	`add-sqr-sqrt`
79×	`times-frac`
67×	`*-un-lft-identity`
57×	`add-cube-cbrt`
18×	`swap-sqr`
16×	`associate-r` `associate-l` `unswap-sqr`
11×	`pow1`
9×	`pow1/3` `div-inv`
7×	`cbrt-div`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 161

Calls

4 calls:

12.0ms	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
2.0ms	(cbrt (/ 1 b))
2.0ms	(cbrt (/ 1 b))
3.0ms	(cbrt (/ 1 b))

series727.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (cbrt (/ 1 b)) (cbrt (/ 1 b)))
173.0ms	(cbrt (/ 1 b))
181.0ms	(cbrt (/ 1 b))
175.0ms	(cbrt (/ 1 b))

simplify53.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	223	1172
1	902	1064
2	5001	904

prune293.0ms

Filtered

173 candidates to 104 candidates (60.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	173	5	178

Merged error: 0.0b

Counts

178 → 5

localize4.0ms

Local error

Found 1 expressions with local error:

15.7b

(/ (+ 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` `expm1-log1p-u` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

7.0ms

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

series39.0ms

Counts

1 → 3

Calls

1 calls:

39.0ms

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

simplify50.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	149	142
1	531	120
2	2110	120
3	5001	120

prune37.0ms

Filtered

30 candidates to 21 candidates (70.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	0	2	2
Picked	0	1	1
Done	1	1	2
Total	30	5	35

Merged error: 0.0b

Counts

35 → 5

regimes75.0ms

Accuracy

0% (3.4b remaining)

Error of 3.5b against oracle of 0.1b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.7s	2579×	body	2560	valid
1.9s	3406×	body	1280	valid
366.0ms	1092×	body	640	valid
204.0ms	10044×	pre	80	true
136.0ms	2042×	body	80	overflowed
76.0ms	340×	body	320	valid
32.0ms	470×	body	80	valid
17.0ms	115×	body	160	valid