Details

analyze664.0ms

Algorithm: search

sample48.0ms

Algorithm

intervals

Results

13.0ms	42×	body	2560	valid
10.0ms	151×	body	80	valid
7.0ms	29×	body	1280	valid
4.0ms	19×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	20×	body	80	nan
1.0ms	6×	body	320	valid
0.0ms	7×	body	80	invalid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

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: 35.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.6b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

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

series66.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5002	673

prune156.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 6.1b

Counts

83 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.8b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series132.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
59.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	646	2693
1	3163	2447
2	5003	2434

prune288.0ms

Filtered

111 candidates to 166 candidates (-49.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	166	9	175

Merged error: 6.0b

Counts

175 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 4.0 (/ 2.0 (* a c)))
0.8b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.6b	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

221×	`times-frac`
165×	`add-sqr-sqrt`
138×	`*-un-lft-identity`
103×	`add-exp-log`
96×	`add-cube-cbrt`
85×	`associate-r`
67×	`add-cbrt-cube`
54×	`div-exp`
32×	`cbrt-undiv`
26×	`associate-l` `prod-exp`
20×	`distribute-lft-out--` `difference-of-squares`
16×	`cbrt-unprod`
13×	`sqrt-prod` `div-inv`
10×	`distribute-rgt-neg-in`
8×	`associate-/r/` `add-log-exp` `unswap-sqr`
7×	`pow1` `associate-/r*`
5×	`flip3--` `flip--`
4×	`rec-exp` `1-exp`
3×	`associate-/l*`
2×	`sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 244

Calls

4 calls:

6.0ms	(/ 4.0 (/ 2.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
57.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 4.0 (/ 2.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1395	3426
1	5001	2945

prune441.0ms

Filtered

165 candidates to 256 candidates (-55.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	256	9	265

Merged error: 6.0b

Counts

265 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.6b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
45×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`associate-/r*`
10×	`distribute-lft-out` `add-log-exp`
9×	`associate-/r/`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `flip3-+` `flip-+` `div-inv`
3×	`rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 114

Calls

4 calls:

13.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	528	1585
1	2596	1372
2	5001	1305

prune127.0ms

Filtered

71 candidates to 126 candidates (-77.5%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	4	5
Picked	0	1	1
Done	0	3	3
Total	126	9	135

Merged error: 6.0b

Counts

135 → 9

regimes416.0ms

Accuracy

88.6% (3.1b remaining)

Error of 8.3b against oracle of 5.1b and baseline of 32.5b

bsearch546.0ms

Steps

Iters	Range	Point
8	1.1344596947434557e+44	1.7587978671157717e+47	6.803825997763841e+46
4	1.0383840758260193e-138	1.6537116651443586e-138	1.0527671810604839e-138
5	-2.4082024510636466e+117	-1.0457114575651237e+117	-2.334250401022177e+117

Iters

Range

Point

1.1344596947434557e+44

1.7587978671157717e+47

6.803825997763841e+46

1.0383840758260193e-138

1.6537116651443586e-138

1.0527671810604839e-138

-2.4082024510636466e+117

-1.0457114575651237e+117

-2.334250401022177e+117

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	28
1	48	28
2	48	28

end0.0ms

analyze454.0ms

Algorithm: search

sample1.3s

Algorithm

intervals

Results

346.0ms	1112×	body	2560	valid
262.0ms	5086×	body	80	valid
230.0ms	926×	body	1280	valid
87.0ms	438×	body	640	valid
37.0ms	96×	body	5120	valid
33.0ms	233×	body	320	valid
33.0ms	631×	body	80	nan
20.0ms	387×	body	80	invalid
11.0ms	109×	body	160	valid

Details

analyze664.0ms

sample48.0ms

simplify11.0ms

prune3.0ms

localize12.0ms

rewrite28.0ms

series66.0ms

simplify48.0ms

prune156.0ms

localize16.0ms

rewrite50.0ms

series132.0ms

simplify119.0ms

prune288.0ms

localize17.0ms

rewrite89.0ms

series78.0ms

simplify66.0ms

prune441.0ms

localize13.0ms

rewrite32.0ms

series73.0ms

simplify70.0ms

prune127.0ms

regimes416.0ms

bsearch546.0ms

simplify2.0ms

end0.0ms

analyze454.0ms

sample1.3s

Profiling