Details

sample46.0ms

Algorithm

intervals

Results

11.0ms	192×	body	80	valid
9.0ms	36×	body	2560	valid
5.0ms	26×	body	1280	valid
3.0ms	83×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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 (0.0%)

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: 31.0b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.5b	(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:

41.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
22.0ms	(- (* b b) (* 4.0 (* a c)))
36.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series339.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
54.0ms	(- (* b b) (* 4.0 (* a c)))
88.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
80.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify77.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	619	2233
1	2404	2137
2	5002	2122

prune346.0ms

Filtered

186 candidates to 109 candidates (58.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	177	9	186
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	177	10	187

Merged error: 4.4b

Counts

187 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite158.0ms

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)))))))
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))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
53.0ms	(- (* b b) (* 4.0 (* a c)))
88.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
82.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify86.0ms

Algorithm

egg-herbie

Counts

406 → 406

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1171	5915
1	5001	5447

prune530.0ms

Filtered

406 candidates to 171 candidates (42.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	400	6	406
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	406	10	416

Merged error: 4.3b

Counts

416 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 2.0) (/ a (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

681×	`times-frac`
481×	`*-un-lft-identity`
380×	`add-sqr-sqrt`
289×	`add-cube-cbrt`
88×	`distribute-lft-out`
44×	`distribute-rgt-neg-in`
39×	`associate-/r/`
37×	`div-inv`
36×	`unswap-sqr`
30×	`difference-of-squares`
29×	`associate-/r*`
26×	`add-exp-log`
22×	`sqrt-prod`
19×	`associate-/l*`
16×	`div-exp` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
10×	`add-log-exp`
9×	`associate-/l/`
8×	`cbrt-undiv` `associate-l` `distribute-lft-out--`
6×	`swap-sqr` `*-commutative`
5×	`pow1`
3×	`frac-2neg` `clear-num`
2×	`rec-exp` `flip3--` `sqrt-div` `1-exp` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log`

Counts

4 → 429

Calls

4 calls:

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

series378.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (/ 1 2.0) (/ a (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
53.0ms	(- (* b b) (* 4.0 (* a c)))
86.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
81.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify111.0ms

Algorithm

egg-herbie

Counts

441 → 441

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1672	7957
1	5001	7482

prune668.0ms

Filtered

441 candidates to 208 candidates (47.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	440	1	441
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	441	10	451

Merged error: 4.3b

Counts

451 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
0.2b	(* (/ (cbrt 1) (/ a (cbrt 1))) (/ (cbrt 1) (/ 2.0 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite752.0ms

Algorithm

rewrite-expression-head

Rules

1767×	`times-frac`
1605×	`*-un-lft-identity`
1530×	`add-sqr-sqrt`
1365×	`associate-/r*`
1047×	`add-cube-cbrt`
930×	`frac-times`
808×	`cbrt-prod`
392×	`associate-/l*`
232×	`distribute-lft-out`
156×	`associate-l`
141×	`associate-r`
134×	`unswap-sqr`
127×	`add-cbrt-cube`
116×	`distribute-rgt-neg-in`
106×	`associate-/r/`
92×	`cbrt-undiv`
77×	`div-inv`
66×	`clear-num`
65×	`frac-2neg`
40×	`add-exp-log`
39×	`flip3-+` `flip-+`
35×	`cbrt-unprod`
31×	`associate-*l/`
30×	`associate-*r/` `difference-of-squares`
22×	`sqrt-prod`
18×	`div-exp`
10×	`add-log-exp`
9×	`prod-exp`
8×	`distribute-lft-out--`
7×	`pow1` `*-commutative`
6×	`swap-sqr`
2×	`flip3--` `sqrt-div` `sum-log` `un-div-inv` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `neg-log`

Counts

4 → 1513

Calls

4 calls:

22.0ms	(- (* b b) (* 4.0 (* a c)))
304.0ms	(* (/ (cbrt 1) (/ a (cbrt 1))) (/ (cbrt 1) (/ 2.0 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))))
32.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* 4.0 (* a c)))
156.0ms	(* (/ (cbrt 1) (/ a (cbrt 1))) (/ (cbrt 1) (/ 2.0 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))))
85.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
82.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify338.0ms

Algorithm

egg-herbie

Counts

1525 → 1525

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5001	36357

prune4.6s

Filtered

1525 candidates to 1057 candidates (69.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	1525	0	1525
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	1525	10	1535

Merged error: 4.3b

Counts

1535 → 10

regimes274.0ms

Accuracy

83.1% (4.7b remaining)

Error of 10.5b against oracle of 5.8b and baseline of 33.3b

bsearch113.0ms

Steps

Iters	Range		Point
6	5.170278655164064e-52	2.1804079894200568e-51	1.2688336265881624e-51
10	-2.7851241427016145e+159	-9.354797223898085e+144	-6.311729910477647e+146

simplify2.0ms

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

261.0ms	1031×	body	2560	valid
248.0ms	5955×	body	80	valid
167.0ms	853×	body	1280	valid
116.0ms	2987×	body	80	nan
76.0ms	462×	body	640	valid
26.0ms	222×	body	320	valid
26.0ms	86×	body	5120	valid
8.0ms	102×	body	160	valid