Details

sample46.0ms

Algorithm

intervals

Results

9.0ms	32×	body	1280	valid
8.0ms	34×	body	2560	valid
7.0ms	172×	body	80	valid
3.0ms	79×	body	80	nan
3.0ms	9×	body	5120	valid
2.0ms	16×	body	640	valid
1.0ms	9×	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	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	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: 35.6b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.2b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

139×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
60×	`times-frac`
42×	`unswap-sqr`
36×	`add-cube-cbrt`
30×	`difference-of-squares`
28×	`distribute-lft-out`
26×	`associate-l`
22×	`sqrt-prod`
18×	`associate-r`
14×	`distribute-rgt-neg-in`
12×	`associate-/r` `-commutative`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--`
6×	`swap-sqr`
5×	`pow1` `associate-/l*`
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` `cbrt-unprod` `div-inv`

Counts

4 → 174

Calls

4 calls:

45.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
23.0ms	(- (* b b) (* 4.0 (* a c)))
38.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms	(- (* b b) (* 4.0 (* a c)))
83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify80.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	626	2233
1	2470	2137
2	5002	2122

prune437.0ms

Filtered

186 candidates to 109 candidates (58.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	177	9	186
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	178	9	187

Merged error: 6.1b

Counts

187 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.2b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
58×	`associate-r`
49×	`unswap-sqr`
40×	`add-cube-cbrt` `times-frac`
36×	`frac-times` `associate-/r*`
31×	`associate-l`
30×	`difference-of-squares`
23×	`add-exp-log`
22×	`sqrt-prod`
20×	`flip3-+` `flip-+`
18×	`associate-*r/`
13×	`*-commutative` `add-cbrt-cube`
10×	`prod-exp` `associate-/l*` `add-log-exp`
8×	`distribute-lft-out--`
7×	`pow1`
6×	`swap-sqr`
4×	`div-exp` `clear-num` `cbrt-unprod` `distribute-lft-out`
3×	`frac-2neg` `un-div-inv`
2×	`cbrt-undiv` `rec-exp` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `neg-log` `div-inv`

Counts

4 → 208

Calls

4 calls:

57.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
23.0ms	(- (* b b) (* 4.0 (* a c)))
35.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
27.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
48.0ms	(- (* b b) (* 4.0 (* a c)))
83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify52.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	937	2753
1	5001	2560

prune536.0ms

Filtered

220 candidates to 138 candidates (62.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	216	4	220
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	221	8	229

Merged error: 6.1b

Counts

229 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* (cbrt 1) (cbrt 1))) (/ (* 2.0 a) (cbrt 1)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.2b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite814.0ms

Algorithm

rewrite-expression-head

Rules

8508×	`times-frac`
7528×	`add-sqr-sqrt`
5171×	`cbrt-prod`
4757×	`*-un-lft-identity`
3973×	`associate-r`
3351×	`add-cube-cbrt`
2926×	`unswap-sqr`
1902×	`associate-l`
699×	`swap-sqr`
586×	`*-commutative`
156×	`distribute-lft-out`
113×	`add-cbrt-cube`
82×	`associate-/r*`
78×	`distribute-rgt-neg-in`
69×	`associate-/l*`
59×	`div-inv`
57×	`cbrt-unprod`
54×	`cbrt-undiv`
40×	`add-exp-log`
30×	`difference-of-squares`
22×	`sqrt-prod`
21×	`associate-/r/`
15×	`div-exp`
12×	`prod-exp`
10×	`add-log-exp`
8×	`distribute-lft-out--`
5×	`pow1`
2×	`flip3--` `frac-2neg` `flip3-+` `sqrt-div` `associate-*l/` `clear-num` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log`

Counts

4 → 4617

Calls

4 calls:

170.0ms	(/ (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* (cbrt 1) (cbrt 1))) (/ (* 2.0 a) (cbrt 1)))
25.0ms	(- (* b b) (* 4.0 (* a c)))
34.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* (cbrt 1) (cbrt 1))) (/ (* 2.0 a) (cbrt 1)))
46.0ms	(- (* b b) (* 4.0 (* a c)))
76.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Algorithm

egg-herbie

Counts

4629 → 4629

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5001	128233

prune13.7s

Filtered

4629 candidates to 2727 candidates (58.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	4627	2	4629
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	4629	8	4637

Merged error: 6.1b

Counts

4637 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
14.2b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

143×	`add-sqr-sqrt`
54×	`unswap-sqr`
45×	`difference-of-squares`
44×	`sqrt-prod`
38×	`*-un-lft-identity`
14×	`associate-l`
12×	`distribute-lft-out--`
10×	`add-log-exp`
9×	`swap-sqr` `*-commutative`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `flip3-+` `diff-log` `neg-log` `flip-+`

Counts

4 → 116

Calls

4 calls:

27.0ms	(- (* b b) (* 4.0 (* a c)))
122.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
24.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* 4.0 (* a c)))
84.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
281.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	321	1283
1	1182	1168
2	5001	1163

prune398.0ms

Filtered

128 candidates to 75 candidates (58.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	128	8	136

Merged error: 6.1b

Counts

136 → 8

regimes239.0ms

Accuracy

84.9% (4.3b remaining)

Error of 9.7b against oracle of 5.4b and baseline of 33.8b

bsearch90.0ms

Steps

Iters	Range		Point
4	2.7062129888597453e-95	4.861630376334293e-95	3.8681552371770574e-95
9	-1.8864815038392082e+94	-1.5243980513895428e+89	-9.911609721462535e+93

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	21
1	41	21

end0.0ms

sample1.2s

Algorithm

intervals

Results

244.0ms	1052×	body	2560	valid
237.0ms	5820×	body	80	valid
171.0ms	891×	body	1280	valid
107.0ms	2865×	body	80	nan
69.0ms	469×	body	640	valid
32.0ms	111×	body	5120	valid
29.0ms	235×	body	320	valid
9.0ms	122×	body	160	valid