Details

sample189.0ms

Algorithm

intervals

Results

76.0ms	70×	body	2560	valid
65.0ms	120×	body	1280	valid
15.0ms	34×	body	640	valid
6.0ms	322×	pre	80	true
4.0ms	66×	body	80	overflowed
2.0ms	10×	body	320	valid
1.0ms	18×	body	80	valid
1.0ms	4×	body	160	valid

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: 59.5b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.9b	(- (exp (* b eps)) 1.0)
3.7b	(- (exp (* a eps)) 1.0)
5.7b	(- (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:

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

series41.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (- (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 (8.0ms)

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

prune150.0ms

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: 48.4b

Counts

89 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (* 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)))))
5.7b	(- (exp (* (+ a b) eps)) 1.0)
16.0b	(* (pow eps 2) (pow b 2))
18.7b	(* (pow eps 3) (pow b 3))

rewrite48.0ms

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

series678.0ms

Counts

4 → 12

Calls

4 calls:

648.0ms	(/ (* 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)))))
14.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* (pow eps 2) (pow b 2))
10.0ms	(* (pow eps 3) (pow b 3))

simplify46.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	848	1789
1	5001	1488

prune344.0ms

Filtered

96 candidates to 167 candidates (-74.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	171	3	174

Merged error: 0.1b

Counts

174 → 3

localize7.0ms

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:

13.0ms

(+ (/ 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

prune34.0ms

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: 0.1b

Counts

25 → 4

localize10.0ms

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)))

rewrite74.0ms

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:

32.0ms	(* (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)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
21.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
21.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
21.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify59.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (42.0ms)

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

prune266.0ms

Filtered

87 candidates to 171 candidates (-96.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	171	4	175

Merged error: 0.1b

Counts

175 → 4

regimes152.0ms

Accuracy

0% (3.2b 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

sample5.8s

Algorithm

intervals

Results

2.7s	2582×	body	2560	valid
1.9s	3412×	body	1280	valid
347.0ms	1067×	body	640	valid
192.0ms	10006×	pre	80	true
130.0ms	2001×	body	80	overflowed
84.0ms	358×	body	320	valid
30.0ms	453×	body	80	valid
19.0ms	133×	body	160	valid

Details

sample189.0ms

simplify96.0ms

prune4.0ms

localize18.0ms

rewrite23.0ms

series41.0ms

simplify41.0ms

prune150.0ms

localize26.0ms

rewrite48.0ms

series678.0ms

simplify46.0ms

prune344.0ms

localize7.0ms

rewrite13.0ms

series3.0ms

simplify66.0ms

prune34.0ms

localize10.0ms

rewrite74.0ms

series93.0ms

simplify59.0ms

prune266.0ms

regimes152.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.8s

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