Details

analyze1.7s

Algorithm

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

sample195.0ms

Algorithm

intervals

Results

74.0ms	71×	body	2560	valid
72.0ms	123×	body	1280	valid
13.0ms	39×	body	640	valid
6.0ms	296×	pre	80	true
6.0ms	15×	body	1280	overflowed
3.0ms	5×	body	2560	overflowed
2.0ms	8×	body	640	overflowed
2.0ms	10×	body	320	valid
1.0ms	5×	body	320	overflowed
1.0ms	10×	body	80	valid
0.0ms	3×	body	160	valid
0.0ms	5×	body	80	overflowed
0.0ms	2×	body	160	overflowed

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4855	24
1	4855	24

prune14.0ms

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: 61.0b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (pow (exp b) eps) 1.0)
1.2b	(pow (exp a) eps)
1.7b	(pow (exp (+ a b)) eps)
1.9b	(pow (exp b) eps)

rewrite19.0ms

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 → 77

Calls

4 calls:

5.0ms	(- (pow (exp b) eps) 1.0)
3.0ms	(pow (exp a) eps)
5.0ms	(pow (exp (+ a b)) eps)
3.0ms	(pow (exp b) eps)

series43.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (pow (exp b) eps) 1.0)
9.0ms	(pow (exp a) eps)
13.0ms	(pow (exp (+ a b)) eps)
10.0ms	(pow (exp b) eps)

simplify53.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4952	645
1	4952	645

prune122.0ms

Filtered

65 candidates to 89 candidates (-36.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	88	3	91

Merged error: 50.5b

Counts

91 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (exp a) eps)
1.7b	(pow (exp (+ a b)) eps)
2.9b	(* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))))
6.4b	(* eps (/ (- (pow (exp (+ a b)) eps) 1.0) (* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))))))

rewrite50.0ms

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:

3.0ms	(pow (exp a) eps)
5.0ms	(pow (exp (+ a b)) eps)
13.0ms	(* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))))
24.0ms	(* eps (/ (- (pow (exp (+ a b)) eps) 1.0) (* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))))))

series733.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(pow (exp a) eps)
13.0ms	(pow (exp (+ a b)) eps)
52.0ms	(* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))))
657.0ms	(* eps (/ (- (pow (exp (+ a b)) eps) 1.0) (* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))))))

simplify57.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5011	2786

prune364.0ms

Filtered

93 candidates to 129 candidates (-38.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	11	129
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	119	13	132

Merged error: 49.1b

Counts

132 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (exp a) eps)
1.7b	(pow (exp (+ a b)) eps)
2.9b	(* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))))
6.0b	(/ (* eps (- (pow (exp (+ a b)) eps) 1.0)) (* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))))))

rewrite51.0ms

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:

3.0ms	(pow (exp a) eps)
5.0ms	(pow (exp (+ a b)) eps)
16.0ms	(* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))))
23.0ms	(/ (* eps (- (pow (exp (+ a b)) eps) 1.0)) (* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))))))

series736.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(pow (exp a) eps)
13.0ms	(pow (exp (+ a b)) eps)
56.0ms	(* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2)))))))
657.0ms	(/ (* eps (- (pow (exp (+ a b)) eps) 1.0)) (* (- (pow (exp a) eps) 1.0) (* eps (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4980	2698
1	4980	2698

prune298.0ms

Filtered

84 candidates to 123 candidates (-46.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	127	9	136

Merged error: 42.9b

Counts

136 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp a) eps) 1.0) (* 1 (/ (- (pow (exp (+ a b)) eps) 1.0) (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))))))
0.4b	(- (pow (exp (+ a b)) eps) 1.0)
1.2b	(pow (exp a) eps)
1.7b	(pow (exp (+ a b)) eps)

rewrite41.0ms

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 → 94

Calls

4 calls:

20.0ms	(/ (- (pow (exp a) eps) 1.0) (* 1 (/ (- (pow (exp (+ a b)) eps) 1.0) (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))))))
8.0ms	(- (pow (exp (+ a b)) eps) 1.0)
3.0ms	(pow (exp a) eps)
7.0ms	(pow (exp (+ a b)) eps)

series189.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (- (pow (exp a) eps) 1.0) (* 1 (/ (- (pow (exp (+ a b)) eps) 1.0) (+ b (+ (log 1) (* eps (* 1/2 (pow (log 1) 2))))))))
22.0ms	(- (pow (exp (+ a b)) eps) 1.0)
9.0ms	(pow (exp a) eps)
13.0ms	(pow (exp (+ a b)) eps)

simplify34.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5354	1948

prune200.0ms

Filtered

75 candidates to 106 candidates (-41.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	109	6	115

Merged error: 17.9b

Counts

115 → 6

regimes222.0ms

Accuracy

57.8% (6.7b remaining)

Error of 24.3b against oracle of 17.6b and baseline of 33.4b

bsearch234.0ms

Steps

Iters	Range		Point
5	2.438527547597832e+80	8.508792856655824e+80	4.597599401570338e+80
8	8.002968803683242e+68	3.202864112374286e+72	2.324937610672138e+71
6	66723551.0014271	368749633.8989153	92599213.53339611
6	-4.453858046020007e+29	-9.641372177129191e+28	-1.4111558736078662e+29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	64
1	85	64

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.8s	2632×	body	2560	valid
2.0s	3483×	body	1280	valid
333.0ms	996×	body	640	valid
275.0ms	649×	body	1280	overflowed
199.0ms	9650×	pre	80	true
98.0ms	154×	body	2560	overflowed
97.0ms	341×	body	640	overflowed
77.0ms	344×	body	320	valid
38.0ms	181×	body	320	overflowed
30.0ms	429×	body	80	valid
18.0ms	116×	body	160	valid
17.0ms	241×	body	80	overflowed
11.0ms	82×	body	160	overflowed
3.0ms	2×	body	2560	invalid

Details

analyze1.7s

sample195.0ms

simplify39.0ms

prune14.0ms

localize20.0ms

rewrite19.0ms

series43.0ms

simplify53.0ms

prune122.0ms

localize23.0ms

rewrite50.0ms

series733.0ms

simplify57.0ms

prune364.0ms

localize23.0ms

rewrite51.0ms

series736.0ms

simplify61.0ms

prune298.0ms

localize21.0ms

rewrite41.0ms

series189.0ms

simplify34.0ms

prune200.0ms

regimes222.0ms

bsearch234.0ms

simplify2.0ms

end0.0ms

sample6.2s

Profiling