Details

sample46.0ms

Algorithm

intervals

Results

10.0ms	204×	body	80	valid
8.0ms	29×	body	2560	valid
6.0ms	26×	body	1280	valid
5.0ms	104×	body	80	nan
1.0ms	8×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	5120	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Filtered

1 candidates to 0 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: 30.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.8b	(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:

14.0ms	(/ (- (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)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune230.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	8	90

Merged error: 6.0b

Counts

90 → 8

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)))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.8b	(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:

14.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
45.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify62.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	469	991
1	2048	866
2	5002	857

prune216.0ms

Filtered

97 candidates to 65 candidates (67.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	97	8	105

Merged error: 5.9b

Counts

105 → 8

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)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.8b	(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:

13.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series320.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
52.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	533	1802
1	2544	1603
2	5002	1529

prune244.0ms

Filtered

137 candidates to 72 candidates (52.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	136	9	145

Merged error: 5.9b

Counts

145 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.1b	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
8.6b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
52×	`times-frac`
51×	`add-exp-log`
30×	`add-cube-cbrt` `associate-l`
27×	`add-cbrt-cube`
20×	`prod-exp` `difference-of-squares`
16×	`div-exp`
13×	`sqrt-prod` `distribute-lft-out`
10×	`distribute-lft-out--`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1` `associate-r`
6×	`associate-/r*` `add-log-exp`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `associate-/l*`
3×	`div-inv`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 152

Calls

4 calls:

7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
19.0ms	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
11.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series521.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
161.0ms	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
205.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify129.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	764	2421
1	3663	2067
2	5001	2044

prune345.0ms

Filtered

164 candidates to 105 candidates (64.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	163	10	173

Merged error: 5.9b

Counts

173 → 10

regimes213.0ms

Accuracy

88.8% (3.3b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 34.4b

bsearch190.0ms

Steps

Iters	Range	Point
8	4.1433580792185867e+68	2.4413096282015733e+73	1.8740434333082397e+73
6	-2.624118589682792e-285	-4.963115371856115e-286	-5.8227715998679075e-286
10	-1.779583628235151e+73	-1.8574760383643568e+59	-2.9600705709081314e+66

Iters

Range

Point

4.1433580792185867e+68

2.4413096282015733e+73

1.8740434333082397e+73

-2.624118589682792e-285

-4.963115371856115e-286

-5.8227715998679075e-286

-1.779583628235151e+73

-1.8574760383643568e+59

-2.9600705709081314e+66

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	31
1	48	31

end0.0ms

sample1.4s

Algorithm

intervals

Results

317.0ms	1086×	body	2560	valid
297.0ms	5782×	body	80	valid
200.0ms	872×	body	1280	valid
146.0ms	2973×	body	80	nan
91.0ms	479×	body	640	valid
39.0ms	105×	body	5120	valid
32.0ms	233×	body	320	valid
12.0ms	127×	body	160	valid

Details

sample46.0ms

simplify14.0ms

prune3.0ms

localize12.0ms

rewrite31.0ms

series289.0ms

simplify46.0ms

prune230.0ms

localize13.0ms

rewrite32.0ms

series294.0ms

simplify62.0ms

prune216.0ms

localize13.0ms

rewrite34.0ms

series320.0ms

simplify72.0ms

prune244.0ms

localize15.0ms

rewrite47.0ms

series521.0ms

simplify129.0ms

prune345.0ms

regimes213.0ms

bsearch190.0ms

simplify2.0ms

end0.0ms

sample1.4s

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