Details

sample274.0ms

Algorithm

intervals

Results

8.0ms	203×	body	80	valid
5.0ms	31×	body	1280	valid
4.0ms	23×	body	2560	valid
2.0ms	79×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune4.0ms

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: 32.9b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

10.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune247.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 6.2b

Counts

104 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.4b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
155.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
191.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	730	2960
1	3200	2803
2	5001	2783

prune494.0ms

Filtered

199 candidates to 148 candidates (74.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	193	6	199
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	199	9	208

Merged error: 6.1b

Counts

208 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ (* (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))) a)
3.1b	(* (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

245×	`times-frac`
227×	`add-sqr-sqrt`
136×	`*-un-lft-identity`
104×	`add-cube-cbrt`
103×	`sqrt-prod`
98×	`associate-r`
96×	`add-exp-log`
54×	`add-cbrt-cube`
49×	`div-exp`
33×	`associate-l`
25×	`cbrt-undiv`
24×	`prod-exp` `difference-of-squares`
20×	`unswap-sqr`
12×	`cbrt-unprod` `distribute-lft-out--`
8×	`pow1`
6×	`rec-exp` `sqrt-div` `1-exp` `div-inv`
4×	`add-log-exp`
3×	`flip3--` `associate-/r*` `associate-/r/` `flip--` `associate-/l/`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

4 → 251

Calls

4 calls:

28.0ms	(/ (* (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))) a)
72.0ms	(* (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (* (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))) a)
134.0ms	(* (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

263 → 263

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1294	4893
1	5002	4272

prune599.0ms

Filtered

263 candidates to 150 candidates (57.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	262	1	263
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	263	9	272

Merged error: 6.1b

Counts

272 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
1.8b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
549×	`add-sqr-sqrt`
450×	`*-un-lft-identity`
352×	`add-cube-cbrt`
98×	`difference-of-squares`
74×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 440

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
27.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
135.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
170.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify94.0ms

Algorithm

egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1571	7389
1	5002	6821

prune1.0s

Filtered

452 candidates to 301 candidates (66.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	449	3	452
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	452	9	461

Merged error: 6.1b

Counts

461 → 9

regimes192.0ms

Accuracy

92.1% (1.9b remaining)

Error of 7.3b against oracle of 5.4b and baseline of 29.5b

bsearch78.0ms

Steps

Iters	Range	Point
9	4.546949039871578e+116	7.0067478635952275e+121	3.7562991673264556e+118
4	2.7062129888597453e-95	4.861630376334293e-95	2.7444235711350233e-95
2	-1.0790742320216938e+148	-9.881700095519823e+147	-9.995330373606963e+147

Iters

Range

Point

4.546949039871578e+116

7.0067478635952275e+121

3.7562991673264556e+118

2.7062129888597453e-95

4.861630376334293e-95

2.7444235711350233e-95

-1.0790742320216938e+148

-9.881700095519823e+147

-9.995330373606963e+147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	20
1	36	20

end0.0ms

sample982.0ms

Algorithm

intervals

Results

206.0ms	1063×	body	2560	valid
195.0ms	5848×	body	80	valid
130.0ms	850×	body	1280	valid
88.0ms	2860×	body	80	nan
58.0ms	465×	body	640	valid
25.0ms	105×	body	5120	valid
21.0ms	234×	body	320	valid
7.0ms	120×	body	160	valid