Details

sample249.0ms

Algorithm

intervals

Results

200.0ms	31×	body	2560	valid
12.0ms	197×	body	80	valid
7.0ms	32×	body	1280	valid
5.0ms	100×	body	80	nan
2.0ms	10×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify447.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	12
1	29	12

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 32.0b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

9.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
8.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5242	1411

prune152.0ms

Filtered

70 candidates to 96 candidates (-37.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	85	11	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	11	97

Merged error: 5.0b

Counts

97 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

16.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4958	1243
1	4958	1243

prune123.0ms

Filtered

69 candidates to 97 candidates (-40.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	97	11	108

Merged error: 5.0b

Counts

108 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

13.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5159	3292

prune162.0ms

Filtered

101 candidates to 174 candidates (-72.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	171	3	174
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	173	12	185

Merged error: 4.9b

Counts

185 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.1b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0b	(/ (* a (neg c)) a)
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
3×	`times-frac` `associate-/r*` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `sqrt-div` `div-exp` `flip--`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `distribute-frac-neg` `prod-exp` `clear-num` `sum-log` `distribute-rgt-neg-out` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 61

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms	(/ (* a (neg c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0ms	(/ (* a (neg c)) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4999	638
1	4999	638

prune73.0ms

Filtered

56 candidates to 73 candidates (-30.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	1	8	9
Picked	1	0	1
Done	1	1	2
Total	74	11	85

Merged error: 4.9b

Counts

85 → 11

regimes373.0ms

Accuracy

95.5% (1.3b remaining)

Error of 7.1b against oracle of 5.8b and baseline of 34.1b

bsearch99.0ms

Steps

Iters	Range	Point
7	4.3615889733450486e+108	1.0500909612496576e+110	3.150777270375896e+109
10	-1.4997779361889431e-248	-2.395781245667215e-266	-2.05318444838937e-250
8	-3.07876034479492e+94	-2.6562780769531156e+90	-1.887155650852303e+94

Iters

Range

Point

4.3615889733450486e+108

1.0500909612496576e+110

3.150777270375896e+109

-1.4997779361889431e-248

-2.395781245667215e-266

-2.05318444838937e-250

-3.07876034479492e+94

-2.6562780769531156e+90

-1.887155650852303e+94

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	55
1	42	55

end0.0ms

sample1.5s

Algorithm

intervals

Results

291.0ms	1076×	body	2560	valid
281.0ms	5900×	body	80	valid
200.0ms	885×	body	1280	valid
129.0ms	2905×	body	80	nan
79.0ms	455×	body	640	valid
32.0ms	99×	body	5120	valid
30.0ms	218×	body	320	valid
11.0ms	129×	body	160	valid

Details

sample249.0ms

simplify447.0ms

prune13.0ms

localize22.0ms

rewrite30.0ms

series63.0ms

simplify56.0ms

prune152.0ms

localize10.0ms

rewrite32.0ms

series53.0ms

simplify62.0ms

prune123.0ms

localize13.0ms

rewrite35.0ms

series66.0ms

simplify67.0ms

prune162.0ms

localize12.0ms

rewrite19.0ms

series35.0ms

simplify50.0ms

prune73.0ms

regimes373.0ms

bsearch99.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling