Details

sample47.0ms

Algorithm

intervals

Results

9.0ms	37×	body	2560	valid
7.0ms	180×	body	80	valid
7.0ms	35×	body	1280	valid
4.0ms	14×	body	640	valid
4.0ms	110×	body	80	nan
1.0ms	4×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	5×	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

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: 33.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.8b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

139×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
60×	`times-frac`
42×	`unswap-sqr`
36×	`add-cube-cbrt`
30×	`difference-of-squares`
28×	`distribute-lft-out`
26×	`associate-l`
22×	`sqrt-prod`
18×	`associate-r`
14×	`distribute-rgt-neg-in`
12×	`associate-/r` `-commutative`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--`
6×	`swap-sqr`
5×	`pow1` `associate-/l*`
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` `cbrt-unprod` `div-inv`

Counts

4 → 174

Calls

4 calls:

42.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
22.0ms	(- (* b b) (* 4.0 (* a c)))
35.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify73.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	619	2234
1	2404	2137
2	5002	2122

prune312.0ms

Filtered

186 candidates to 109 candidates (41.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	178	8	186
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	178	9	187

Merged error: 5.0b

Counts

187 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.8b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

438×	`times-frac`
406×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
188×	`add-cube-cbrt`
100×	`distribute-lft-out`
72×	`associate-l`
71×	`associate-/r*`
63×	`associate-r`
57×	`unswap-sqr`
50×	`distribute-rgt-neg-in`
30×	`difference-of-squares`
28×	`associate-/r/`
27×	`*-commutative`
25×	`add-exp-log`
22×	`sqrt-prod`
17×	`associate-/l*`
13×	`add-cbrt-cube`
12×	`div-exp`
10×	`add-log-exp`
8×	`distribute-lft-out--`
6×	`pow1` `swap-sqr`
5×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv`
3×	`rec-exp` `1-exp` `prod-exp` `clear-num` `remove-double-div`
2×	`flip3--` `frac-2neg` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `cbrt-unprod` `inv-pow`

Counts

4 → 394

Calls

4 calls:

54.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.0ms	(- (* b b) (* 4.0 (* a c)))
32.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series356.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
50.0ms	(- (* b b) (* 4.0 (* a c)))
83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
78.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify86.0ms

Algorithm

egg-herbie

Counts

406 → 406

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1171	5915
1	5001	5447

prune507.0ms

Filtered

406 candidates to 170 candidates (58.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	401	5	406
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	406	9	415

Merged error: 5.0b

Counts

415 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.8b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
44×	`sqrt-prod`
36×	`unswap-sqr`
30×	`*-un-lft-identity` `difference-of-squares`
12×	`add-log-exp`
8×	`associate-l` `distribute-lft-out--`
6×	`pow1` `add-cube-cbrt` `swap-sqr` `*-commutative`
4×	`add-exp-log` `sqrt-div` `sum-log` `add-cbrt-cube` `distribute-lft-out`
2×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 98

Calls

4 calls:

33.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
36.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
26.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
82.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify129.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	283	1030
1	946	988
2	3709	972
3	5001	960

prune275.0ms

Filtered

110 candidates to 72 candidates (34.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	110	9	119

Merged error: 5.0b

Counts

119 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.8b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
44×	`sqrt-prod`
36×	`unswap-sqr`
30×	`*-un-lft-identity` `difference-of-squares`
12×	`add-log-exp`
8×	`associate-l` `distribute-lft-out--`
6×	`pow1` `add-cube-cbrt` `swap-sqr` `*-commutative`
4×	`add-exp-log` `sqrt-div` `sum-log` `add-cbrt-cube` `distribute-lft-out`
2×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 98

Calls

4 calls:

35.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
34.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
23.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
98.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify125.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	283	1030
1	946	988
2	3709	972
3	5001	960

prune299.0ms

Filtered

110 candidates to 72 candidates (34.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	110	9	119

Merged error: 5.0b

Counts

119 → 9

regimes282.0ms

Accuracy

85.3% (4.3b remaining)

Error of 9.7b against oracle of 5.5b and baseline of 34.4b

bsearch113.0ms

Steps

Iters	Range		Point
9	2.9593950748212843e-63	2.4702945119117623e-58	1.301803315389237e-62
8	-8.122802074996069e+81	-2.6359676868927157e+78	-8.403193116555128e+80

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	15
1	33	15

end0.0ms

sample1.2s

Algorithm

intervals

Results

272.0ms	1098×	body	2560	valid
248.0ms	5797×	body	80	valid
175.0ms	885×	body	1280	valid
107.0ms	2780×	body	80	nan
72.0ms	464×	body	640	valid
34.0ms	116×	body	5120	valid
29.0ms	249×	body	320	valid
9.0ms	117×	body	160	valid