Details

analyze1.6s

Algorithm: search

sample203.0ms

Algorithm

intervals

Results

89.0ms	88×	body	2560	valid
55.0ms	97×	body	1280	valid
12.0ms	19×	body	1280	overflowed
12.0ms	39×	body	640	valid
6.0ms	308×	pre	80	true
5.0ms	8×	body	2560	overflowed
3.0ms	12×	body	320	valid
2.0ms	9×	body	640	overflowed
2.0ms	8×	body	320	overflowed
1.0ms	7×	body	160	valid
1.0ms	13×	body	80	valid
0.0ms	7×	body	80	overflowed
0.0ms	1×	body	160	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

prune198.0ms

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: 60.5b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.6b	(- (exp (* a eps)) 1.0)
4.2b	(- (exp (* b eps)) 1.0)
6.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite23.0ms

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
7.0ms	(- (exp (* a eps)) 1.0)
7.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify45.0ms

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: 50.0b

Counts

89 → 7

localize32.0ms

Local error

Found 4 expressions with local error:

4.2b	(/ (* 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)))))
6.1b	(- (exp (* (+ a b) eps)) 1.0)
17.1b	(* (pow eps 2) (pow b 2))
18.2b	(* (pow eps 3) (pow b 3))

rewrite50.0ms

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:

23.0ms	(/ (* 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))
10.0ms	(* (pow eps 3) (pow b 3))

series702.0ms

Counts

4 → 12

Calls

4 calls:

668.0ms	(/ (* 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)
7.0ms	(* (pow eps 2) (pow b 2))
10.0ms	(* (pow eps 3) (pow b 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	848	1789
1	5001	1488

prune368.0ms

Filtered

96 candidates to 167 candidates (-74.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	169	5	174

Merged error: 0.2b

Counts

174 → 5

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite13.0ms

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:

12.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify66.0ms

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	2755	90
4	5001	90

prune51.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	19	8	27

Merged error: 0.2b

Counts

27 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

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:

12.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
12.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
13.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
31.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
21.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
24.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
27.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))

simplify58.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	442	1931
1	1543	1682
2	5001	1499

prune275.0ms

Filtered

87 candidates to 171 candidates (-96.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	170	9	179

Merged error: 0.2b

Counts

179 → 9

regimes230.0ms

Accuracy

0% (3.3b 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

analyze1.6s

Algorithm: search

sample6.2s

Algorithm

intervals

Results

2.7s	2547×	body	2560	valid
1.9s	3378×	body	1280	valid
375.0ms	1118×	body	640	valid
281.0ms	659×	body	1280	overflowed
208.0ms	9680×	pre	80	true
116.0ms	174×	body	2560	overflowed
100.0ms	352×	body	640	overflowed
90.0ms	391×	body	320	valid
36.0ms	181×	body	320	overflowed
32.0ms	451×	body	80	valid
17.0ms	246×	body	80	overflowed
17.0ms	115×	body	160	valid
11.0ms	65×	body	160	overflowed
3.0ms	3×	body	2560	invalid

Details

analyze1.6s

sample203.0ms

simplify95.0ms

prune198.0ms

localize17.0ms

rewrite23.0ms

series42.0ms

simplify45.0ms

prune155.0ms

localize32.0ms

rewrite50.0ms

series702.0ms

simplify44.0ms

prune368.0ms

localize5.0ms

rewrite13.0ms

series3.0ms

simplify66.0ms

prune51.0ms

localize9.0ms

rewrite77.0ms

series94.0ms

simplify58.0ms

prune275.0ms

regimes230.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.6s

sample6.2s

Profiling