Details

sample197.0ms

Algorithm

intervals

Results

92.0ms	90×	body	2560	valid
54.0ms	100×	body	1280	valid
12.0ms	39×	body	640	valid
12.0ms	132×	body	80	overflowed
6.0ms	388×	pre	80	true
1.0ms	6×	body	320	valid
1.0ms	20×	body	80	valid
0.0ms	1×	body	160	valid

simplify95.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.7b	(- (exp (* a eps)) 1.0)
3.3b	(- (exp (* b eps)) 1.0)
5.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite43.0ms

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:

28.0ms	(* (- (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)

series167.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
39.0ms	(- (exp (* a eps)) 1.0)
32.0ms	(- (exp (* b eps)) 1.0)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune360.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 56.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (sqrt (exp (* a eps))) (sqrt 1.0)) (- (exp (* b eps)) 1.0))
2.7b	(- (sqrt (exp (* a eps))) (sqrt 1.0))
3.3b	(- (exp (* b eps)) 1.0)
5.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
12×	`sqrt-prod`
11×	`difference-of-squares`
10×	`add-log-exp`
9×	`flip3--` `associate-l` `flip--`
7×	`distribute-lft-out--`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`sub-neg` `associate-r`
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 → 84

Calls

4 calls:

42.0ms	(* (- (sqrt (exp (* a eps))) (sqrt 1.0)) (- (exp (* b eps)) 1.0))
8.0ms	(- (sqrt (exp (* a eps))) (sqrt 1.0))
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series243.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (- (sqrt (exp (* a eps))) (sqrt 1.0)) (- (exp (* b eps)) 1.0))
56.0ms	(- (sqrt (exp (* a eps))) (sqrt 1.0))
38.0ms	(- (exp (* b eps)) 1.0)
48.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	359	935
1	1522	863
2	5003	863

prune441.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 56.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* (+ (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0))) (- (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0)))) (- (exp (* b eps)) 1.0))
2.8b	(- (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0)))
3.3b	(- (exp (* b eps)) 1.0)
5.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
28×	`frac-times`
24×	`sqrt-prod`
21×	`flip3--` `flip--`
17×	`*-un-lft-identity`
14×	`associate-*l/`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
8×	`associate-*r/`
6×	`distribute-lft-out--`
5×	`add-cube-cbrt` `sub-neg` `associate-r`
3×	`diff-log` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`associate-l` `*-commutative`

Counts

4 → 102

Calls

4 calls:

101.0ms	(* (* (+ (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0))) (- (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0)))) (- (exp (* b eps)) 1.0))
16.0ms	(- (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0)))
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series463.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(* (* (+ (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0))) (- (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0)))) (- (exp (* b eps)) 1.0))
113.0ms	(- (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0)))
37.0ms	(- (exp (* b eps)) 1.0)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify97.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	665	2113
1	3774	1773
2	5001	1773

prune635.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 56.0b

localize30.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0)))
2.8b	(- (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0)))
3.3b	(- (exp (* b eps)) 1.0)
5.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

48×	`sqrt-prod`
44×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `difference-of-squares`
12×	`add-log-exp`
8×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--`

Counts

4 → 76

Calls

4 calls:

13.0ms	(- (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0)))
16.0ms	(- (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0)))
4.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series304.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0)))
110.0ms	(- (sqrt (sqrt (exp (* a eps)))) (sqrt (sqrt 1.0)))
36.0ms	(- (exp (* b eps)) 1.0)
47.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	260	890
1	719	839
2	2178	834
3	5002	831

prune442.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 55.5b

regimes414.0ms

Accuracy

29.3% (1.9b remaining)

Error of 58.7b against oracle of 56.8b and baseline of 59.4b

bsearch289.0ms

Steps

Iters	Range		Point
8	2.5395121883065248e-24	5.7880101574957725e-21	2.5756149971396786e-24
9	-3.125122124602746e+43	-3.596465999237397e+36	-3.6563033602620086e+36

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	105
1	79	105

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.1s	2952×	body	2560	valid
1.8s	3335×	body	1280	valid
270.0ms	882×	body	640	valid
228.0ms	4271×	body	80	overflowed
188.0ms	12272×	pre	80	true
43.0ms	211×	body	320	valid
33.0ms	575×	body	80	valid
6.0ms	46×	body	160	valid