Details

sample212.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 50.024426%

Guaranteed chance to sample good point: 75%

Results

90.0ms	82×	body	2560	valid
64.0ms	108×	body	1280	valid
9.0ms	28×	body	640	valid
9.0ms	21×	body	1280	overflowed
7.0ms	311×	pre	80	true
4.0ms	13×	body	640	overflowed
4.0ms	16×	body	320	valid
2.0ms	3×	body	2560	overflowed
1.0ms	18×	body	80	valid
1.0ms	14×	body	80	overflowed
1.0ms	4×	body	160	valid
0.0ms	3×	body	160	overflowed
0.0ms	1×	body	320	overflowed

simplify96.0ms

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

prune4.0ms

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: 59.3b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.0b	(- (exp (* b eps)) 1.0)
3.9b	(- (exp (* a eps)) 1.0)
5.4b	(- (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:

9.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
7.0ms	(- (exp (* (+ a b) eps)) 1.0)

series41.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
7.0ms	(- (exp (* b eps)) 1.0)
7.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune149.0ms

Filtered

66 candidates to 88 candidates (-33.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 49.6b

Counts

89 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

3.9b	(- (exp (* a eps)) 1.0)
5.4b	(- (exp (* (+ a b) eps)) 1.0)
9.8b	(* (pow eps 2) (pow b 2))
14.1b	(* (pow eps 3) (pow b 3))

rewrite30.0ms

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)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow eps 2) (pow b 2))
9.0ms	(* (pow eps 3) (pow b 3))

series36.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (exp (* a eps)) 1.0)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* (pow eps 2) (pow b 2))
10.0ms	(* (pow eps 3) (pow b 3))

simplify81.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (70.0ms)

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

prune286.0ms

Filtered

78 candidates to 150 candidates (-92.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	143	7	150
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	145	11	156

Merged error: 48.5b

Counts

156 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

3.1b	(/ (* 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)))))
3.9b	(- (exp (* a eps)) 1.0)
5.4b	(- (exp (* (+ a b) eps)) 1.0)
9.8b	(* (pow eps 2) (pow b 2))

rewrite38.0ms

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:

18.0ms	(/ (* 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)))))
3.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* (pow eps 2) (pow b 2))

series654.0ms

Counts

4 → 12

Calls

4 calls:

628.0ms	(/ (* 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)))))
7.0ms	(- (exp (* a eps)) 1.0)
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* (pow eps 2) (pow b 2))

simplify107.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	751	1535
1	4175	1257
2	5001	1253

prune257.0ms

Filtered

75 candidates to 122 candidates (-62.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	130	3	133

Merged error: 0.0b

Counts

133 → 3

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

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:

11.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify62.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	101	104
1	345	94
2	1153	91
3	2755	90
4	5001	90

prune23.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

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

regimes149.0ms

Accuracy

0% (3.5b 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

sample6.3s

Algorithm

intervals

sampling

Space saved by range analysis: 50.024426%

Space saved by search: 50.024426%

Guaranteed chance to sample good point: 75%

Results

2.7s	2553×	body	2560	valid
1.9s	3441×	body	1280	valid
346.0ms	1054×	body	640	valid
290.0ms	677×	body	1280	overflowed
212.0ms	9944×	pre	80	true
104.0ms	161×	body	2560	overflowed
94.0ms	347×	body	640	overflowed
78.0ms	342×	body	320	valid
37.0ms	485×	body	80	valid
34.0ms	507×	body	80	overflowed
31.0ms	162×	body	320	overflowed
18.0ms	125×	body	160	valid
12.0ms	90×	body	160	overflowed

Details

sample212.0ms

simplify96.0ms

prune4.0ms

localize16.0ms

rewrite25.0ms

series41.0ms

simplify42.0ms

prune149.0ms

localize27.0ms

rewrite30.0ms

series36.0ms

simplify81.0ms

prune286.0ms

localize25.0ms

rewrite38.0ms

series654.0ms

simplify107.0ms

prune257.0ms

localize4.0ms

rewrite11.0ms

series2.0ms

simplify62.0ms

prune23.0ms

regimes149.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.3s

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