Details

analyze445.0ms

Algorithm: search

sample45.0ms

Algorithm

intervals

Results

9.0ms	29×	body	1280	valid
9.0ms	31×	body	2560	valid
8.0ms	161×	body	80	valid
3.0ms	15×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	4×	body	5120	valid
1.0ms	26×	body	80	nan
0.0ms	10×	body	80	invalid
0.0ms	4×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune4.0ms

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: 32.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

11.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	398	888
1	1466	803
2	5001	798

prune162.0ms

Filtered

65 candidates to 89 candidates (-36.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	9	90

Merged error: 4.6b

Counts

90 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

12.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify67.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	538	1801
1	2573	1602
2	5002	1528

prune154.0ms

Filtered

73 candidates to 137 candidates (-87.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	5	2	7
Picked	1	0	1
Done	0	1	1
Total	139	7	146

Merged error: 4.6b

Counts

146 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

1.9b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.2b	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
16.1b	(- (pow b 2) (pow b 2))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`unpow-prod-down`
19×	`add-exp-log`
16×	`difference-of-squares`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--` `add-log-exp`
8×	`distribute-lft-out--`
7×	`div-exp`
5×	`pow1` `associate-/l/`
4×	`cbrt-undiv` `prod-exp`
3×	`flip3-+` `times-frac` `associate-/r*` `sqrt-prod` `flip-+`
2×	`frac-times` `flip3--` `sqrt-div` `associate-*r/` `sum-log` `flip--` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `rec-exp` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `+-inverses` `diff-log` `1-exp` `neg-log` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 107

Calls

4 calls:

7.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
7.0ms	(- (pow b 2) (pow b 2))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series33.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
1.0ms	(- (pow b 2) (pow b 2))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify200.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (190.0ms)

Iter	Nodes	Cost
0	590	777
1	3981	571
2	5002	555

prune200.0ms

Filtered

79 candidates to 119 candidates (-50.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	118	8	126

Merged error: 4.6b

Counts

126 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.9b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

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-/r*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 69

Calls

4 calls:

10.0ms	(/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify42.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	374	757
1	1550	658
2	5002	645

prune100.0ms

Filtered

60 candidates to 81 candidates (-35.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	81	8	89

Merged error: 4.6b

Counts

89 → 8

regimes327.0ms

Accuracy

95% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.6b

bsearch642.0ms

Steps

Iters	Range	Point
9	1.4890696065677669e+56	2.670383127192816e+62	8.507949512374696e+61
4	3.4350767417723785e-237	5.70701445617709e-237	3.4936871713412144e-237
8	-1.5025131698978002e+154	-5.606218013898765e+150	-1.294421671741153e+152

Iters

Range

Point

1.4890696065677669e+56

2.670383127192816e+62

8.507949512374696e+61

3.4350767417723785e-237

5.70701445617709e-237

3.4936871713412144e-237

-1.5025131698978002e+154

-5.606218013898765e+150

-1.294421671741153e+152

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	24
1	40	24

end0.0ms

analyze448.0ms

Algorithm: search

sample1.2s

Algorithm

intervals

Results

310.0ms	1073×	body	2560	valid
270.0ms	5127×	body	80	valid
212.0ms	870×	body	1280	valid
89.0ms	445×	body	640	valid
41.0ms	111×	body	5120	valid
36.0ms	252×	body	320	valid
36.0ms	692×	body	80	nan
18.0ms	353×	body	80	invalid
12.0ms	122×	body	160	valid

Details

analyze445.0ms

sample45.0ms

simplify12.0ms

prune4.0ms

localize11.0ms

rewrite27.0ms

series59.0ms

simplify43.0ms

prune162.0ms

localize13.0ms

rewrite34.0ms

series72.0ms

simplify67.0ms

prune154.0ms

localize18.0ms

rewrite43.0ms

series33.0ms

simplify200.0ms

prune200.0ms

localize12.0ms

rewrite25.0ms

series89.0ms

simplify42.0ms

prune100.0ms

regimes327.0ms

bsearch642.0ms

simplify1.0ms

end0.0ms

analyze448.0ms

sample1.2s

Profiling