Details

analyze484.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample44.0ms

Algorithm

intervals

Results

11.0ms	34×	body	2560	valid
9.0ms	165×	body	80	valid
8.0ms	30×	body	1280	valid
3.0ms	16×	body	640	valid
1.0ms	23×	body	80	nan
1.0ms	6×	body	320	valid
1.0ms	12×	body	80	invalid
0.0ms	4×	body	160	valid
0.0ms	1×	body	5120	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	17
1	27	17

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: 34.8b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.5b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.1b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod`
3×	`distribute-rgt-neg-in` `associate-r` `pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `associate-l` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv`

Counts

4 → 76

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* 3.0 a) c)
27.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4939	1209
1	4939	1209

prune161.0ms

Filtered

64 candidates to 88 candidates (-37.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	80	10	90

Merged error: 5.5b

Counts

90 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
2.8b	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
11.5b	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
24.9b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
34×	`times-frac`
32×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
11×	`add-cube-cbrt`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r*` `sqrt-prod` `add-log-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `distribute-rgt-neg-in` `flip--`
4×	`div-inv`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 119

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
14.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
12.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
3.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series128.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
45.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
54.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5002	2471

prune177.0ms

Filtered

84 candidates to 131 candidates (-56.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	132	9	141

Merged error: 5.4b

Counts

141 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
0.2b	(* 3.0 (* a c))
0.7b	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
24.9b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
21×	`times-frac`
18×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `distribute-lft-out--` `difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
7×	`associate-/r*`
5×	`distribute-rgt-neg-in`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`sqrt-div` `diff-log` `associate-/r/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `associate-r` `neg-log` `clear-num` `*-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

9.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
5.0ms	(* 3.0 (* a c))
7.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
5.0ms	(* 3.0 (* a c))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5482	1713

prune147.0ms

Filtered

72 candidates to 107 candidates (-48.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	106	10	116

Merged error: 5.3b

Counts

116 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (+ (sqrt (- (* b b) (* 3.0 (* a c)))) (neg b)) 3.0) a)
0.2b	(* 3.0 (* a c))
1.1b	(+ (sqrt (- (* b b) (* 3.0 (* a c)))) (neg b))
24.9b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
114×	`*-un-lft-identity`
63×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
26×	`distribute-lft-out`
19×	`associate-/l*`
14×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-rgt-neg-in`
10×	`pow1`
8×	`add-log-exp`
5×	`div-inv`
4×	`div-sub`
3×	`cbrt-undiv` `div-exp` `associate-l` `pow-prod-down` `prod-exp` `associate-/r*` `sqrt-prod` `cbrt-unprod`
2×	`neg-sub0` `associate-+r-` `sqrt-div` `unsub-neg` `sum-log`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `neg-log` `clear-num` `*-commutative` `flip--` `flip-+` `associate-/l/`

Counts

4 → 145

Calls

4 calls:

12.0ms	(/ (/ (+ (sqrt (- (* b b) (* 3.0 (* a c)))) (neg b)) 3.0) a)
5.0ms	(* 3.0 (* a c))
8.0ms	(+ (sqrt (- (* b b) (* 3.0 (* a c)))) (neg b))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (/ (+ (sqrt (- (* b b) (* 3.0 (* a c)))) (neg b)) 3.0) a)
3.0ms	(* 3.0 (* a c))
15.0ms	(+ (sqrt (- (* b b) (* 3.0 (* a c)))) (neg b))
17.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify64.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5116	3127

prune200.0ms

Filtered

104 candidates to 157 candidates (-51.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	157	10	167

Merged error: 5.3b

Counts

167 → 10

regimes579.0ms

Accuracy

93.6% (1.5b remaining)

Error of 6.9b against oracle of 5.4b and baseline of 29.1b

bsearch815.0ms

Steps

Iters	Range	Point
9	6.048260475595057e+67	5.120081681784899e+72	1.1734572876339935e+72
9	-3.467480227987288e-250	-8.635691079222375e-260	-8.870563017505624e-257
9	-1.7197635662839285e+80	-2.096644772178657e+73	-1.6931695005490156e+80

Iters

Range

Point

6.048260475595057e+67

5.120081681784899e+72

1.1734572876339935e+72

-3.467480227987288e-250

-8.635691079222375e-260

-8.870563017505624e-257

-1.7197635662839285e+80

-2.096644772178657e+73

-1.6931695005490156e+80

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	64
1	52	64

end0.0ms

analyze661.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample1.3s

Algorithm

intervals

Results

355.0ms	1104×	body	2560	valid
283.0ms	5119×	body	80	valid
232.0ms	904×	body	1280	valid
95.0ms	450×	body	640	valid
43.0ms	114×	body	5120	valid
35.0ms	694×	body	80	nan
29.0ms	192×	body	320	valid
21.0ms	384×	body	80	invalid
12.0ms	117×	body	160	valid

Details

analyze484.0ms

sample44.0ms

simplify3.0ms

prune13.0ms

localize10.0ms

rewrite28.0ms

series59.0ms

simplify57.0ms

prune161.0ms

localize12.0ms

rewrite43.0ms

series128.0ms

simplify49.0ms

prune177.0ms

localize11.0ms

rewrite27.0ms

series80.0ms

simplify50.0ms

prune147.0ms

localize12.0ms

rewrite34.0ms

series61.0ms

simplify64.0ms

prune200.0ms

regimes579.0ms

bsearch815.0ms

simplify1.0ms

end0.0ms

analyze661.0ms

sample1.3s

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