Details

analyze590.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample103.0ms

Algorithm

intervals

Results

10.0ms	43×	body	2560	valid
7.0ms	33×	body	1280	valid
6.0ms	154×	body	80	valid
2.0ms	11×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify502.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune12.0ms

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: 35.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
5.9b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
15.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b	(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 → 82

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
28.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5743	1403

prune134.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	86	8	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	8	95

Merged error: 6.8b

Counts

95 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

5.9b	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
11.1b	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
12.5b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
40×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l*`
10×	`associate-/r/`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `distribute-lft-out`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
3×	`distribute-frac-neg` `sqrt-prod`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `distribute-rgt-neg-out` `cbrt-unprod`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `sum-log` `flip--` `associate-/l/`

Counts

4 → 114

Calls

4 calls:

11.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
9.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
6.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
53.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify54.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4948	2297
1	4948	2297

prune134.0ms

Filtered

98 candidates to 126 candidates (-28.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	126	8	134

Merged error: 6.7b

Counts

134 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
2.6b	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
12.5b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
6.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
15.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5326	1109

prune102.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	81	10	91

Merged error: 6.7b

Counts

91 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
6.0b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
15.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

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 → 83

Calls

4 calls:

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

series54.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4984	1258
1	4984	1258

prune92.0ms

Filtered

69 candidates to 95 candidates (-37.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	95	10	105

Merged error: 6.7b

Counts

105 → 10

regimes295.0ms

Accuracy

94.1% (1.4b remaining)

Error of 6.9b against oracle of 5.5b and baseline of 29.7b

bsearch91.0ms

Steps

Iters	Range	Point
4	3.5617937693117017e+133	6.562429594890015e+133	3.62400602061036e+133
9	-3.2909318226539855e-237	-8.269694962573503e-244	-3.670160880532066e-242
9	-1.8969536448137758e+27	-1.6369092528199503e+18	-1.8605498001882586e+27

Iters

Range

Point

3.5617937693117017e+133

6.562429594890015e+133

3.62400602061036e+133

-3.2909318226539855e-237

-8.269694962573503e-244

-3.670160880532066e-242

-1.8969536448137758e+27

-1.6369092528199503e+18

-1.8605498001882586e+27

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	64
1	93	64

end0.0ms

sample1.6s

Algorithm

intervals

Results

266.0ms	1143×	body	2560	valid
198.0ms	5077×	body	80	valid
170.0ms	895×	body	1280	valid
65.0ms	440×	body	640	valid
33.0ms	113×	body	5120	valid
24.0ms	219×	body	320	valid
8.0ms	113×	body	160	valid

Details

analyze590.0ms

sample103.0ms

simplify502.0ms

prune12.0ms

localize12.0ms

rewrite30.0ms

series69.0ms

simplify55.0ms

prune134.0ms

localize16.0ms

rewrite34.0ms

series116.0ms

simplify54.0ms

prune134.0ms

localize11.0ms

rewrite22.0ms

series78.0ms

simplify49.0ms

prune102.0ms

localize12.0ms

rewrite33.0ms

series54.0ms

simplify39.0ms

prune92.0ms

regimes295.0ms

bsearch91.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling