Details

analyze624.0ms

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

sample40.0ms

Algorithm

intervals

Results

8.0ms	173×	body	80	valid
6.0ms	21×	body	2560	valid
5.0ms	25×	body	1280	valid
4.0ms	24×	body	640	valid
1.0ms	7×	body	80	invalid
1.0ms	22×	body	80	nan
1.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify508.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

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: 32.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b	(- (* b_2 b_2) (* a c))
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

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:

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

series62.0ms

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)))

simplify54.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5743	1403

prune151.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	82	12	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	12	95

Merged error: 6.3b

Counts

95 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
2.3b	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
12.1b	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
38×	`*-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*`
6×	`div-inv` `distribute-lft-out` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
3×	`distribute-frac-neg` `sqrt-prod`
2×	`flip3--` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `distribute-rgt-neg-out` `flip--` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 113

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
10.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series109.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
48.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4932	2261
1	4932	2261

prune143.0ms

Filtered

96 candidates to 125 candidates (-30.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	127	10	137

Merged error: 6.1b

Counts

137 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b	(- (* b_2 b_2) (* a c))
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

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:

14.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (- (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))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4984	1258
1	4984	1258

prune115.0ms

Filtered

70 candidates to 95 candidates (-35.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	95	10	105

Merged error: 6.1b

Counts

105 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b	(- (* b_2 b_2) (* a c))
20.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
3×	`cbrt-prod` `flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `distribute-lft-out--`

Counts

4 → 51

Calls

4 calls:

1.0ms	(cbrt a)
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt a)
12.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5009	625

prune63.0ms

Filtered

48 candidates to 63 candidates (-31.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	62	11	73

Merged error: 6.1b

Counts

73 → 11

regimes368.0ms

Accuracy

82.4% (4.8b remaining)

Error of 10.5b against oracle of 5.7b and baseline of 33.0b

bsearch49.0ms

Steps

Iters	Range		Point
8	5.593748050341432e-124	2.6687142615248723e-119	5.740357605763107e-120
7	-6.538741830662118e+71	-1.9624505345410408e+70	-1.0226793514904988e+71

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	38
1	66	38

end0.0ms

sample1.1s

Algorithm

intervals

Results

272.0ms	1023×	body	2560	valid
237.0ms	5194×	body	80	valid
181.0ms	865×	body	1280	valid
82.0ms	455×	body	640	valid
35.0ms	111×	body	5120	valid
32.0ms	741×	body	80	nan
29.0ms	235×	body	320	valid
11.0ms	233×	body	80	invalid
10.0ms	117×	body	160	valid

Details

analyze624.0ms

sample40.0ms

simplify508.0ms

prune12.0ms

localize11.0ms

rewrite47.0ms

series62.0ms

simplify54.0ms

prune151.0ms

localize13.0ms

rewrite32.0ms

series109.0ms

simplify68.0ms

prune143.0ms

localize13.0ms

rewrite31.0ms

series55.0ms

simplify40.0ms

prune115.0ms

localize14.0ms

rewrite18.0ms

series57.0ms

simplify42.0ms

prune63.0ms

regimes368.0ms

bsearch49.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling