Details

analyze442.0ms

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

sample43.0ms

Algorithm

intervals

Results

11.0ms	37×	body	2560	valid
8.0ms	162×	body	80	valid
8.0ms	33×	body	1280	valid
1.0ms	9×	body	320	valid
1.0ms	6×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	21×	body	80	nan
1.0ms	6×	body	160	valid
1.0ms	10×	body	80	invalid

simplify176.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (174.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune11.0ms

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: 36.0b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.2b	(- (* b b) (* (* 3.0 a) c))
1.6b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

14.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5899	1226

prune164.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	10	81
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 5.1b

Counts

83 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 3.0 (* a c)))
4.7b	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
9.4b	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
23.2b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

4.0ms	(- (* b b) (* 3.0 (* a c)))
16.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
13.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series122.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 3.0 (* a c)))
44.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
56.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify68.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4975	2392
1	4975	2392

prune205.0ms

Filtered

79 candidates to 125 candidates (-58.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	127	8	135

Merged error: 5.0b

Counts

135 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
0.6b	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
1.2b	(- (* b b) (* 3.0 (* a c)))
23.2b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `associate-r` `neg-log` `*-commutative`

Counts

4 → 61

Calls

4 calls:

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

series43.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
8.0ms	(- (* b b) (* 3.0 (* a c)))
16.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4956	873
1	4956	873

prune108.0ms

Filtered

51 candidates to 73 candidates (-43.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	72	9	81

Merged error: 5.0b

Counts

81 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
1.2b	(- (* b b) (* 3.0 (* a c)))
1.6b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
23.2b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 58

Calls

4 calls:

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
8.0ms	(- (* b b) (* 3.0 (* a c)))
14.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
16.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify41.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4938	809
1	4938	809

prune82.0ms

Filtered

49 candidates to 70 candidates (-42.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	69	10	79

Merged error: 5.0b

Counts

79 → 10

regimes233.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.9b against oracle of 5.8b and baseline of 29.9b

bsearch104.0ms

Steps

Iters	Range	Point
10	8.286226964197923e+119	2.3696295735334822e+135	2.3537684395445924e+133
9	-2.9150056974912156e-236	-2.197353997123338e-244	-3.707273886473642e-240
9	-2.589905260909067e+161	-1.0544072467496106e+154	-1.1992264276379268e+154

Iters

Range

Point

8.286226964197923e+119

2.3696295735334822e+135

2.3537684395445924e+133

-2.9150056974912156e-236

-2.197353997123338e-244

-3.707273886473642e-240

-2.589905260909067e+161

-1.0544072467496106e+154

-1.1992264276379268e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	115	65
1	115	65

end0.0ms

sample1.2s

Algorithm

intervals

Results

320.0ms	1088×	body	2560	valid
264.0ms	5130×	body	80	valid
219.0ms	892×	body	1280	valid
85.0ms	445×	body	640	valid
37.0ms	97×	body	5120	valid
33.0ms	236×	body	320	valid
33.0ms	689×	body	80	nan
19.0ms	386×	body	80	invalid
11.0ms	112×	body	160	valid

Details

analyze442.0ms

sample43.0ms

simplify176.0ms

prune11.0ms

localize10.0ms

rewrite32.0ms

series63.0ms

simplify53.0ms

prune164.0ms

localize12.0ms

rewrite41.0ms

series122.0ms

simplify68.0ms

prune205.0ms

localize13.0ms

rewrite23.0ms

series43.0ms

simplify46.0ms

prune108.0ms

localize11.0ms

rewrite21.0ms

series42.0ms

simplify41.0ms

prune82.0ms

regimes233.0ms

bsearch104.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling