Details

sample6.0s

Algorithm

intervals

sampling

Space saved by range analysis: 51.928123%

Space saved by search: 50.097597%

Guaranteed chance to sample good point: 0%

Results

80.0ms	73×	body	2560	valid
62.0ms	115×	body	1280	valid
11.0ms	27×	body	1280	overflowed
11.0ms	33×	body	640	valid
6.0ms	315×	pre	80	true
4.0ms	16×	body	640	overflowed
4.0ms	6×	body	2560	overflowed
2.0ms	10×	body	320	valid
2.0ms	22×	body	80	valid
1.0ms	4×	body	320	overflowed
0.0ms	3×	body	160	valid
0.0ms	2×	body	160	overflowed
0.0ms	4×	body	80	overflowed

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

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: 58.3b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.1b	(- (exp (* b eps)) 1.0)
2.2b	(- (exp (* a eps)) 1.0)
3.3b	(- (exp (* (+ a b) eps)) 1.0)

rewrite22.0ms

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

series40.0ms

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)

simplify41.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

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

prune155.0ms

Filtered

66 candidates to 88 candidates (-33.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	7	89

Merged error: 47.1b

Counts

89 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
3.3b	(- (exp (* (+ a b) eps)) 1.0)
12.5b	(* (pow eps 2) (pow b 2))
14.2b	(* (pow eps 3) (pow b 3))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
40×	`add-exp-log`
32×	`unswap-sqr`
28×	`unpow-prod-down`
22×	`prod-exp`
20×	`associate-r` `associate-l` `add-cbrt-cube` `sqr-pow`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`associate-/r/`
6×	`cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`cube-mult` `unpow3` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 155

Calls

4 calls:

21.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
4.0ms	(- (exp (* (+ a b) eps)) 1.0)
7.0ms	(* (pow eps 2) (pow b 2))
9.0ms	(* (pow eps 3) (pow b 3))

series660.0ms

Counts

4 → 12

Calls

4 calls:

626.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
18.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* (pow eps 2) (pow b 2))
10.0ms	(* (pow eps 3) (pow b 3))

simplify42.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	848	1843
1	5001	1499

prune347.0ms

Filtered

96 candidates to 167 candidates (-74.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	171	3	174

Merged error: 0.1b

Counts

174 → 3

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

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))

series3.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify63.0ms

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

prune37.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	20	5	25

Merged error: 0.1b

Counts

25 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

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:

30.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
11.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
11.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
11.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
24.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
20.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
20.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	442	1931
1	1535	1682
2	5002	1499

prune260.0ms

Filtered

87 candidates to 171 candidates (-96.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	170	6	176

Merged error: 0.1b

Counts

176 → 6

regimes174.0ms

Accuracy

0% (3.4b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample11.8s

Algorithm

intervals

sampling

Space saved by range analysis: 51.928123%

Space saved by search: 50.097597%

Guaranteed chance to sample good point: 0%

Results

2.7s	2561×	body	2560	valid
1.9s	3433×	body	1280	valid
361.0ms	1084×	body	640	valid
276.0ms	672×	body	1280	overflowed
211.0ms	9626×	pre	80	true
109.0ms	390×	body	640	overflowed
90.0ms	140×	body	2560	overflowed
78.0ms	337×	body	320	valid
40.0ms	203×	body	320	overflowed
32.0ms	462×	body	80	valid
18.0ms	123×	body	160	valid
10.0ms	79×	body	160	overflowed
10.0ms	140×	body	80	overflowed
2.0ms	2×	body	2560	invalid

Details

sample6.0s

simplify95.0ms

prune4.0ms

localize18.0ms

rewrite22.0ms

series40.0ms

simplify41.0ms

prune155.0ms

localize30.0ms

rewrite46.0ms

series660.0ms

simplify42.0ms

prune347.0ms

localize4.0ms

rewrite12.0ms

series3.0ms

simplify63.0ms

prune37.0ms

localize8.0ms

rewrite71.0ms

series90.0ms

simplify57.0ms

prune260.0ms

regimes174.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample11.8s

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