Details

sample44.0ms

Algorithm

intervals

Results

10.0ms	39×	body	2560	valid
8.0ms	180×	body	80	valid
6.0ms	30×	body	1280	valid
4.0ms	100×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune2.0ms

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: 33.1b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.6b	(- (* b b) (* (* 3.0 a) c))
1.0b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

8.0ms	(* (* 3.0 a) c)
6.0ms	(- (* b b) (* (* 3.0 a) c))
13.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
48.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
96.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune174.0ms

Filtered

72 candidates to 52 candidates (72.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	65	7	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	8	73

Merged error: 11.5b

Counts

73 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.8b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.1b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
17.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
16.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
147.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
183.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify119.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	647	2692
1	3076	2439
2	5001	2426

prune431.0ms

Filtered

166 candidates to 111 candidates (66.9%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	154	12	166
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	155	19	174

Merged error: 10.8b

Counts

174 → 19

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.7b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
9.0b	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
22.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
15.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
150.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
184.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify125.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	702	2050
1	4419	1582
2	5001	1541

prune330.0ms

Filtered

128 candidates to 86 candidates (67.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	6	11	17
Picked	1	0	1
Done	1	0	1
Total	128	19	147

Merged error: 10.3b

Counts

147 → 19

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.6b	(/ a (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
9.0b	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 136

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(/ a (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
11.0ms	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
83.0ms	(/ a (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
180.0ms	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify77.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	587	2060
1	2730	1822
2	5002	1805

prune348.0ms

Filtered

148 candidates to 106 candidates (71.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	8	10	18
Picked	1	0	1
Done	0	0	0
Total	154	13	167

Merged error: 6.5b

Counts

167 → 13

regimes256.0ms

Accuracy

94.5% (1.3b remaining)

Error of 7.8b against oracle of 6.5b and baseline of 29.9b

bsearch224.0ms

Steps

Iters	Range	Point
9	1.8873296595059161e+93	4.185563559022972e+102	8.94616693053734e+97
10	-3.652053439877918e-139	-3.418741215203259e-151	-3.478360471345321e-151
10	-1.218044689452388e+116	-9.206374310818687e+98	-1.1961650247121335e+116

Iters

Range

Point

1.8873296595059161e+93

4.185563559022972e+102

8.94616693053734e+97

-3.652053439877918e-139

-3.418741215203259e-151

-3.478360471345321e-151

-1.218044689452388e+116

-9.206374310818687e+98

-1.1961650247121335e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	42
1	52	42

end0.0ms

sample1.3s

Algorithm

intervals

Results

271.0ms	5853×	body	80	valid
267.0ms	1018×	body	2560	valid
195.0ms	920×	body	1280	valid
133.0ms	2973×	body	80	nan
80.0ms	457×	body	640	valid
33.0ms	105×	body	5120	valid
30.0ms	236×	body	320	valid
9.0ms	100×	body	160	valid

Details

sample44.0ms

simplify11.0ms

prune2.0ms

localize20.0ms

rewrite35.0ms

series239.0ms

simplify45.0ms

prune174.0ms

localize14.0ms

rewrite51.0ms

series479.0ms

simplify119.0ms

prune431.0ms

localize19.0ms

rewrite48.0ms

series484.0ms

simplify125.0ms

prune330.0ms

localize14.0ms

rewrite45.0ms

series407.0ms

simplify77.0ms

prune348.0ms

regimes256.0ms

bsearch224.0ms

simplify2.0ms

end0.0ms

sample1.3s

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