Details

sample204.0ms

Algorithm

intervals

Results

92.0ms	83×	body	2560	valid
70.0ms	119×	body	1280	valid
10.0ms	31×	body	640	valid
7.0ms	330×	pre	80	true
5.0ms	74×	body	80	overflowed
2.0ms	9×	body	320	valid
1.0ms	10×	body	80	valid
1.0ms	4×	body	160	valid

simplify95.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 61.6b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.4b	(- (exp (* b eps)) 1.0)
5.4b	(- (exp (* a eps)) 1.0)
6.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times`
3×	`diff-log`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

10.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series162.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
31.0ms	(- (exp (* b eps)) 1.0)
36.0ms	(- (exp (* a eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	346	733
1	1449	673
2	5001	673

prune281.0ms

Filtered

88 candidates to 66 candidates (75.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 49.5b

Counts

89 → 5

localize32.0ms

Local error

Found 4 expressions with local error:

5.4b	(- (exp (* a eps)) 1.0)
6.5b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow eps 2) (pow b 2))
15.3b	(* (pow eps 3) (pow b 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`*-un-lft-identity` `prod-exp`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube` `add-log-exp`
4×	`pow1`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 138

Calls

4 calls:

4.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(* (pow eps 2) (pow b 2))
11.0ms	(* (pow eps 3) (pow b 3))

series177.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (exp (* a eps)) 1.0)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)
31.0ms	(* (pow eps 2) (pow b 2))
65.0ms	(* (pow eps 3) (pow b 3))

simplify82.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	460	772
1	2092	679
2	5001	636

prune480.0ms

Filtered

150 candidates to 78 candidates (52.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	148	7	155

Merged error: 48.8b

Counts

155 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

4.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
5.4b	(- (exp (* a eps)) 1.0)
6.5b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow eps 2) (pow b 2))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

22.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
4.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(* (pow eps 2) (pow b 2))

series1.4s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
36.0ms	(- (exp (* a eps)) 1.0)
45.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* (pow eps 2) (pow b 2))

simplify109.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	751	1571
1	4183	1256
2	5002	1252

prune433.0ms

Filtered

122 candidates to 75 candidates (61.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	126	3	129

Merged error: 0.0b

Counts

129 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite17.0ms

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:

16.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify65.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (26.0ms)

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

prune26.0ms

Filtered

22 candidates to 14 candidates (63.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	21	4	25

Merged error: 0.0b

Counts

25 → 4

regimes69.0ms

Accuracy

0% (3.1b remaining)

Error of 3.5b against oracle of 0.4b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.8s	2580×	body	2560	valid
1.9s	3399×	body	1280	valid
368.0ms	1099×	body	640	valid
209.0ms	10024×	pre	80	true
136.0ms	2022×	body	80	overflowed
74.0ms	324×	body	320	valid
34.0ms	468×	body	80	valid
20.0ms	132×	body	160	valid