Details

sample212.0ms

Algorithm

intervals

Results

86.0ms	82×	body	2560	valid
59.0ms	104×	body	1280	valid
14.0ms	42×	body	640	valid
12.0ms	23×	body	1280	overflowed
6.0ms	327×	pre	80	true
4.0ms	5×	body	2560	overflowed
3.0ms	11×	body	640	overflowed
2.0ms	9×	body	320	valid
2.0ms	10×	body	320	overflowed
1.0ms	20×	body	80	overflowed
1.0ms	14×	body	80	valid
1.0ms	5×	body	160	valid
0.0ms	2×	body	160	overflowed

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4970	24
1	4970	24

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 60.2b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.5b	(- (exp (* b eps)) 1.0)
2.7b	(- (exp (* a eps)) 1.0)
3.5b	(- (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 (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series42.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (- (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)

simplify34.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5222	1190

prune142.0ms

Filtered

70 candidates to 88 candidates (-25.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	85	5	90

Merged error: 49.6b

Counts

90 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

3.5b	(- (exp (* (+ a b) eps)) 1.0)
7.1b	(* eps (* 1/6 (pow a 3)))
7.9b	(+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3))))
16.2b	(* (* eps eps) (+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
14×	`add-cbrt-cube`
11×	`pow1`
10×	`prod-exp`
9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt` `cbrt-unprod`
4×	`associate-r` `associate-l` `pow-prod-down`
2×	`flip3-+` `associate-r/` `-commutative` `flip-+`
1×	`+-commutative` `distribute-rgt-in` `pow-to-exp` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `pow-exp` `sum-log` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

4.0ms	(- (exp (* (+ a b) eps)) 1.0)
6.0ms	(* eps (* 1/6 (pow a 3)))
5.0ms	(+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3))))
11.0ms	(* (* eps eps) (+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3)))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (exp (* (+ a b) eps)) 1.0)
10.0ms	(* eps (* 1/6 (pow a 3)))
8.0ms	(+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3))))
22.0ms	(* (* eps eps) (+ (* a (* a 1/2)) (* eps (* 1/6 (pow a 3)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4963	1004
1	4963	1004

prune138.0ms

Filtered

52 candidates to 79 candidates (-51.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	77	7	84

Merged error: 48.8b

Counts

84 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

2.7b	(* (+ (* a eps) (* eps (* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a)))))) (- (exp (* b eps)) 1.0))
2.9b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* a eps) (* eps (* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a)))))) (- (exp (* b eps)) 1.0)))
3.5b	(- (exp (* (+ a b) eps)) 1.0)
7.4b	(* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
15×	`pow1`
13×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
10×	`associate-*r/`
8×	`frac-times` `flip3--` `associate-/r/` `flip--`
7×	`add-cube-cbrt` `flip3-+` `pow-prod-down` `flip-+`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l` `add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-*l/`
3×	`sub-neg`
2×	`*-commutative` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

9.0ms	(* (+ (* a eps) (* eps (* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a)))))) (- (exp (* b eps)) 1.0))
14.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* a eps) (* eps (* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a)))))) (- (exp (* b eps)) 1.0)))
6.0ms	(- (exp (* (+ a b) eps)) 1.0)
9.0ms	(* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (+ (* a eps) (* eps (* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a)))))) (- (exp (* b eps)) 1.0))
263.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* a eps) (* eps (* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a)))))) (- (exp (* b eps)) 1.0)))
13.0ms	(- (exp (* (+ a b) eps)) 1.0)
16.0ms	(* eps (* (* a a) (+ 1/2 (* (* eps 1/6) a))))

simplify50.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5071	3360

prune193.0ms

Filtered

84 candidates to 116 candidates (-38.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	119	4	123

Merged error: 0.0b

Counts

123 → 4

localize6.0ms

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))

simplify73.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4923	196
1	4923	196

prune21.0ms

Filtered

14 candidates to 22 candidates (-57.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	19	7	26

Merged error: 0.0b

Counts

26 → 7

regimes240.0ms

Accuracy

81.1% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 3.0b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	86
1	38	86

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.8s	2606×	body	2560	valid
1.9s	3411×	body	1280	valid
368.0ms	1095×	body	640	valid
307.0ms	717×	body	1280	overflowed
192.0ms	10070×	pre	80	true
119.0ms	403×	body	640	overflowed
103.0ms	152×	body	2560	overflowed
84.0ms	352×	body	320	valid
41.0ms	199×	body	320	overflowed
37.0ms	505×	body	80	overflowed
29.0ms	403×	body	80	valid
21.0ms	135×	body	160	valid
13.0ms	92×	body	160	overflowed

Details

sample212.0ms

simplify45.0ms

prune13.0ms

localize18.0ms

rewrite23.0ms

series42.0ms

simplify34.0ms

prune142.0ms

localize24.0ms

rewrite28.0ms

series54.0ms

simplify49.0ms

prune138.0ms

localize23.0ms

rewrite41.0ms

series321.0ms

simplify50.0ms

prune193.0ms

localize6.0ms

rewrite12.0ms

series3.0ms

simplify73.0ms

prune21.0ms

regimes240.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

sample6.5s

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