Details

sample424.0ms

Algorithm

intervals

Results

172.0ms	80×	body	2560	valid
121.0ms	107×	body	1280	valid
24.0ms	22×	body	1280	overflowed
22.0ms	34×	body	640	valid
12.0ms	325×	pre	80	true
8.0ms	6×	body	2560	overflowed
6.0ms	6×	body	160	overflowed
5.0ms	8×	body	640	overflowed
4.0ms	10×	body	320	valid
4.0ms	20×	body	80	overflowed
3.0ms	7×	body	320	overflowed
3.0ms	19×	body	80	valid
2.0ms	6×	body	160	valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4855	24
1	4855	24

prune29.0ms

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: 58.6b

Counts

2 → 2

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (exp a) eps)
0.7b	(pow (exp (+ a b)) eps)
0.7b	(pow (exp b) eps)
0.8b	(- (pow (exp b) eps) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`add-cube-cbrt` `pow-pow`
11×	`unpow-prod-down`
10×	`exp-prod`
9×	`pow-unpow`
7×	`pow1`
6×	`add-log-exp`
4×	`add-exp-log` `add-cbrt-cube` `sqr-pow`
3×	`pow-to-exp` `pow-exp` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `exp-sum` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 78

Calls

4 calls:

6.0ms	(pow (exp a) eps)
10.0ms	(pow (exp (+ a b)) eps)
6.0ms	(pow (exp b) eps)
10.0ms	(- (pow (exp b) eps) 1.0)

series69.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (exp a) eps)
24.0ms	(pow (exp (+ a b)) eps)
15.0ms	(pow (exp b) eps)
18.0ms	(- (pow (exp b) eps) 1.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4952	647
1	4952	647

prune251.0ms

Filtered

65 candidates to 90 candidates (-38.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	88	4	92

Merged error: 51.0b

Counts

92 → 4

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (exp a) eps)
0.7b	(pow (exp (+ a b)) eps)
1.3b	(* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (* eps (* 1/2 (pow (log 1) 2))) (log 1)))))
3.6b	(* eps (/ (- (pow (exp (+ a b)) eps) 1.0) (* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (* eps (* 1/2 (pow (log 1) 2))) (log 1)))))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`add-exp-log` `add-cbrt-cube`
20×	`-un-lft-identity` `associate-r*`
17×	`associate-*r/`
14×	`add-cube-cbrt`
13×	`pow1`
10×	`associate-l` `prod-exp` `cbrt-unprod`
9×	`unpow-prod-down` `pow-pow`
8×	`frac-times` `associate-/r/`
7×	`exp-prod` `times-frac`
6×	`pow-unpow` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`
4×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-*l/` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `div-exp`
2×	`pow-to-exp` `pow-exp` `*-commutative` `distribute-lft-out--`
1×	`exp-sum` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

6.0ms	(pow (exp a) eps)
9.0ms	(pow (exp (+ a b)) eps)
28.0ms	(* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (* eps (* 1/2 (pow (log 1) 2))) (log 1)))))
57.0ms	(* eps (/ (- (pow (exp (+ a b)) eps) 1.0) (* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (* eps (* 1/2 (pow (log 1) 2))) (log 1)))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (exp a) eps)
24.0ms	(pow (exp (+ a b)) eps)
107.0ms	(* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (* eps (* 1/2 (pow (log 1) 2))) (log 1)))))
1.2s	(* eps (/ (- (pow (exp (+ a b)) eps) 1.0) (* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (* eps (* 1/2 (pow (log 1) 2))) (log 1)))))))

simplify108.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5020	2786

prune696.0ms

Filtered

93 candidates to 129 candidates (-38.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	9	129
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	122	11	133

Merged error: 49.8b

Counts

133 → 11

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (exp a) eps)
0.7b	(pow (exp (+ a b)) eps)
1.3b	(* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (* eps (* 1/2 (pow (log 1) 2))) (log 1)))))
3.5b	(/ (* eps (- (pow (exp (+ a b)) eps) 1.0)) (* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (* eps (* 1/2 (pow (log 1) 2))) (log 1))))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log` `add-cbrt-cube`
18×	`associate-*r/`
16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1` `add-cube-cbrt`
9×	`pow-pow`
8×	`frac-times` `unpow-prod-down` `associate-/r/`
7×	`exp-prod` `flip3--` `associate-l` `flip--`
6×	`cbrt-undiv` `pow-unpow` `flip3-+` `div-exp` `flip-+`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `add-log-exp`
3×	`pow-prod-down` `difference-of-squares` `sqr-pow`
2×	`pow-to-exp` `pow-exp` `associate-/l/`
1×	`frac-2neg` `times-frac` `associate-r` `exp-sum` `clear-num` `associate-/r` `-commutative` `div-inv` `distribute-lft-out` `associate-/l*` `distribute-lft-out--`

Counts

4 → 111

Calls

4 calls:

6.0ms	(pow (exp a) eps)
11.0ms	(pow (exp (+ a b)) eps)
33.0ms	(* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (* eps (* 1/2 (pow (log 1) 2))) (log 1)))))
54.0ms	(/ (* eps (- (pow (exp (+ a b)) eps) 1.0)) (* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (* eps (* 1/2 (pow (log 1) 2))) (log 1))))))

series1.4s

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (exp a) eps)
24.0ms	(pow (exp (+ a b)) eps)
97.0ms	(* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (* eps (* 1/2 (pow (log 1) 2))) (log 1)))))
1.3s	(/ (* eps (- (pow (exp (+ a b)) eps) 1.0)) (* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (* eps (* 1/2 (pow (log 1) 2))) (log 1))))))

simplify114.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4984	2698
1	4984	2698

prune584.0ms

Filtered

84 candidates to 123 candidates (-46.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	125	9	134

Merged error: 46.3b

Counts

134 → 9

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (pow (exp a) eps) 1.0) (* 1 (/ (- (pow (exp (+ a b)) eps) 1.0) (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))))))
0.2b	(- (pow (exp (+ a b)) eps) 1.0)
0.2b	(pow (exp a) eps)
0.7b	(pow (exp (+ a b)) eps)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`add-cube-cbrt`
10×	`unpow-prod-down`
9×	`pow-pow` `difference-of-squares`
7×	`exp-prod` `times-frac` `div-exp` `associate-/l*`
6×	`pow1` `pow-unpow` `add-log-exp`
5×	`sqr-pow`
4×	`cbrt-undiv` `prod-exp`
3×	`distribute-lft-out--`
2×	`pow-to-exp` `flip3--` `1-exp` `pow-exp` `flip--` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `exp-sum` `clear-num` `associate-/r` `associate-/r/` `div-inv` `distribute-lft-out`

Counts

4 → 95

Calls

4 calls:

41.0ms	(/ (- (pow (exp a) eps) 1.0) (* 1 (/ (- (pow (exp (+ a b)) eps) 1.0) (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))))))
16.0ms	(- (pow (exp (+ a b)) eps) 1.0)
6.0ms	(pow (exp a) eps)
11.0ms	(pow (exp (+ a b)) eps)

series356.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(/ (- (pow (exp a) eps) 1.0) (* 1 (/ (- (pow (exp (+ a b)) eps) 1.0) (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))))))
46.0ms	(- (pow (exp (+ a b)) eps) 1.0)
16.0ms	(pow (exp a) eps)
23.0ms	(pow (exp (+ a b)) eps)

simplify62.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5354	1950

prune384.0ms

Filtered

75 candidates to 107 candidates (-42.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	111	5	116

Merged error: 14.7b

Counts

116 → 5

regimes675.0ms

Accuracy

50.9% (8.0b remaining)

Error of 25.3b against oracle of 17.3b and baseline of 33.6b

bsearch321.0ms

Steps

Iters	Range		Point
9	1.601522318771203e+21	3.9263931897675755e+27	1.6259980530357452e+21
9	-9.633748705117338e+117	-1.126437604418301e+112	-1.1449809168537672e+112

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	55
1	63	55

end0.0ms

sample11.0s

Algorithm

intervals

Results

4.6s	2575×	body	2560	valid
3.4s	3397×	body	1280	valid
667.0ms	1110×	body	640	valid
517.0ms	683×	body	1280	overflowed
327.0ms	10027×	pre	80	true
189.0ms	358×	body	640	overflowed
175.0ms	158×	body	2560	overflowed
137.0ms	330×	body	320	valid
73.0ms	199×	body	320	overflowed
68.0ms	529×	body	80	overflowed
61.0ms	465×	body	80	valid
34.0ms	127×	body	160	valid
24.0ms	96×	body	160	overflowed

Details

sample424.0ms

simplify68.0ms

prune29.0ms

localize35.0ms

rewrite35.0ms

series69.0ms

simplify76.0ms

prune251.0ms

localize48.0ms

rewrite108.0ms

series1.3s

simplify108.0ms

prune696.0ms

localize43.0ms

rewrite112.0ms

series1.4s

simplify114.0ms

prune584.0ms

localize46.0ms

rewrite80.0ms

series356.0ms

simplify62.0ms

prune384.0ms

regimes675.0ms

bsearch321.0ms

simplify3.0ms

end0.0ms

sample11.0s

Profiling