Details

sample60.0ms

Algorithm

intervals

Results

10.0ms	192×	body	80	valid
9.0ms	30×	body	2560	valid
7.0ms	20×	body	640	valid
7.0ms	28×	body	1280	valid
5.0ms	98×	body	80	nan
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	5120	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 31.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

11.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
17.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	398	888
1	1466	803
2	5001	798

prune174.0ms

Filtered

89 candidates to 65 candidates (27.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	9	90

Merged error: 5.2b

Counts

90 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.2b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

16.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify92.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	463	989
1	2033	868
2	5001	860

prune160.0ms

Filtered

97 candidates to 63 candidates (35.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	98	8	106

Merged error: 5.2b

Counts

106 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
2.8b	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
10.6b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
52×	`times-frac`
51×	`add-exp-log`
30×	`add-cube-cbrt` `associate-l`
27×	`add-cbrt-cube`
20×	`prod-exp`
18×	`difference-of-squares`
16×	`div-exp`
13×	`distribute-lft-out`
12×	`sqrt-prod`
9×	`distribute-lft-out--`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1` `associate-r`
6×	`associate-/r*` `add-log-exp`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `associate-/l*`
3×	`div-inv`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 149

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
11.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series123.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
43.0ms	(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
58.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify118.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	758	2360
1	3752	2016
2	5001	1993

prune284.0ms

Filtered

161 candidates to 102 candidates (36.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	155	6	161
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	158	11	169

Merged error: 5.2b

Counts

169 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b	(- (* b b) (* 4.0 (* a c)))
14.1b	(/ (* 4.0 (* a c)) (* 2.0 a))
21.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

6.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series39.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(- (* b b) (* 4.0 (* a c)))
2.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify54.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	399	575
1	2213	498
2	5003	498

prune113.0ms

Filtered

79 candidates to 54 candidates (31.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	3	5	8
Picked	1	0	1
Done	0	2	2
Total	82	8	90

Merged error: 5.2b

Counts

90 → 8

regimes416.0ms

Accuracy

95% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.6b

bsearch119.0ms

Steps

Iters	Range		Point
10	4.2917270207488e+96	9.615152778888747e+106	2.3651486002630512e+104
10	7.430561088356834e-244	3.136616431968671e-232	1.108169573258626e-243
9	-1.3279209152234913e+54	-5.495259451600425e+45	-1.307112579275623e+54

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	24
1	43	24

end0.0ms

sample1.7s

Algorithm

intervals

Results

329.0ms	1055×	body	2560	valid
310.0ms	5776×	body	80	valid
245.0ms	971×	body	1280	valid
150.0ms	2855×	body	80	nan
87.0ms	439×	body	640	valid
45.0ms	122×	body	5120	valid
37.0ms	247×	body	320	valid
12.0ms	116×	body	160	valid

Details

sample60.0ms

simplify13.0ms

prune4.0ms

localize11.0ms

rewrite27.0ms

series58.0ms

simplify44.0ms

prune174.0ms

localize13.0ms

rewrite33.0ms

series65.0ms

simplify92.0ms

prune160.0ms

localize15.0ms

rewrite45.0ms

series123.0ms

simplify118.0ms

prune284.0ms

localize13.0ms

rewrite26.0ms

series39.0ms

simplify54.0ms

prune113.0ms

regimes416.0ms

bsearch119.0ms

simplify2.0ms

end0.0ms

sample1.7s

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