Details

analyze452.0ms

Algorithm: search

sample40.0ms

Algorithm

intervals

Results

10.0ms	36×	body	2560	valid
9.0ms	174×	body	80	valid
5.0ms	23×	body	1280	valid
2.0ms	8×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	22×	body	80	nan
1.0ms	13×	body	80	invalid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	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

prune3.0ms

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: 31.7b

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))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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:

12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

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

prune170.0ms

Filtered

65 candidates to 89 candidates (-36.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	11	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	11	90

Merged error: 5.8b

Counts

90 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

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

series57.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
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))))

simplify57.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	463	989
1	2033	868
2	5001	860

prune140.0ms

Filtered

65 candidates to 97 candidates (-49.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	99	9	108

Merged error: 5.8b

Counts

108 → 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)))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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)))))))
4.0ms	(- (* 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))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 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)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify69.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (53.0ms)

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

prune152.0ms

Filtered

73 candidates to 137 candidates (-87.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	137	9	146

Merged error: 5.7b

Counts

146 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
6.0b	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

7.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	418	881
1	1485	823
2	5002	813

prune119.0ms

Filtered

68 candidates to 88 candidates (-29.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	88	9	97

Merged error: 5.7b

Counts

97 → 9

regimes290.0ms

Accuracy

89.4% (3.0b remaining)

Error of 8.2b against oracle of 5.2b and baseline of 33.6b

bsearch610.0ms

Steps

Iters	Range	Point
6	1.0476386085400234e+93	1.0859656323896043e+94	1.0644737218171245e+94
7	-3.351688645837212e-255	-9.99389634772289e-257	-3.3094635341804666e-255
8	-9.299072479203935e+26	-4.6017937658753755e+22	-3.615529685338681e+24

Iters

Range

Point

1.0476386085400234e+93

1.0859656323896043e+94

1.0644737218171245e+94

-3.351688645837212e-255

-9.99389634772289e-257

-3.3094635341804666e-255

-9.299072479203935e+26

-4.6017937658753755e+22

-3.615529685338681e+24

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	32
1	46	32

end0.0ms

analyze444.0ms

Algorithm: search

sample1.2s

Algorithm

intervals

Results

319.0ms	1061×	body	2560	valid
277.0ms	5157×	body	80	valid
212.0ms	870×	body	1280	valid
91.0ms	455×	body	640	valid
36.0ms	100×	body	5120	valid
35.0ms	718×	body	80	nan
34.0ms	232×	body	320	valid
18.0ms	354×	body	80	invalid
12.0ms	125×	body	160	valid

Details

analyze452.0ms

sample40.0ms

simplify12.0ms

prune3.0ms

localize11.0ms

rewrite31.0ms

series55.0ms

simplify47.0ms

prune170.0ms

localize13.0ms

rewrite32.0ms

series57.0ms

simplify57.0ms

prune140.0ms

localize13.0ms

rewrite31.0ms

series69.0ms

simplify69.0ms

prune152.0ms

localize12.0ms

rewrite32.0ms

series76.0ms

simplify45.0ms

prune119.0ms

regimes290.0ms

bsearch610.0ms

simplify2.0ms

end0.0ms

analyze444.0ms

sample1.2s

Profiling