Details

sample48.0ms

Algorithm

intervals

Results

12.0ms	37×	body	2560	valid
7.0ms	180×	body	80	valid
7.0ms	35×	body	1280	valid
4.0ms	110×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	5×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	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

localize11.0ms

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)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

483×	`add-sqr-sqrt`
330×	`associate-l` `prod-diff`
309×	`*-un-lft-identity`
229×	`add-cube-cbrt`
177×	`associate-r`
125×	`unswap-sqr`
75×	`swap-sqr`
65×	`*-commutative`
60×	`times-frac`
30×	`difference-of-squares`
28×	`distribute-lft-out`
24×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
15×	`fma-neg`
12×	`associate-/r*` `distribute-lft-out--`
10×	`fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `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 → 541

Calls

4 calls:

42.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
34.0ms	(- (* b b) (* (* 4.0 a) c))
35.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms	(- (* b b) (* (* 4.0 a) c))
86.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify209.0ms

Algorithm

egg-herbie

Counts

553 → 553

Iterations

Useful iterations: 2 (129.0ms)

Iter	Nodes	Cost
0	1442	9181
1	4892	6678
2	5001	6676

prune555.0ms

Filtered

553 candidates to 170 candidates (69.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	543	10	553
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	544	10	554

Merged error: 5.1b

Counts

554 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 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)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

450×	`add-sqr-sqrt`
330×	`prod-diff`
312×	`associate-l`
252×	`*-un-lft-identity`
208×	`add-cube-cbrt`
159×	`associate-r`
119×	`unswap-sqr`
75×	`swap-sqr`
59×	`*-commutative`
30×	`difference-of-squares`
24×	`sqrt-prod`
15×	`times-frac` `fma-neg`
12×	`distribute-lft-out--`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 485

Calls

4 calls:

42.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
32.0ms	(- (* b b) (* (* 4.0 a) c))
35.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
52.0ms	(- (* b b) (* (* 4.0 a) c))
86.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify177.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	1256	8241
1	3951	5763
2	5001	5758

prune480.0ms

Filtered

497 candidates to 142 candidates (71.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	494	3	497
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	497	10	507

Merged error: 5.1b

Counts

507 → 10

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)))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

665×	`add-sqr-sqrt`
607×	`*-un-lft-identity`
438×	`times-frac`
381×	`add-cube-cbrt`
376×	`associate-l`
330×	`prod-diff`
222×	`associate-r`
140×	`unswap-sqr`
100×	`distribute-lft-out`
80×	`*-commutative`
75×	`swap-sqr`
71×	`associate-/r*`
53×	`distribute-rgt-neg-in`
30×	`difference-of-squares`
28×	`associate-/r/`
25×	`add-exp-log`
24×	`sqrt-prod`
17×	`associate-/l*`
15×	`fma-neg`
13×	`add-cbrt-cube`
12×	`div-exp` `distribute-lft-out--`
10×	`fma-def` `add-log-exp`
6×	`pow1`
5×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `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-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `cbrt-unprod` `inv-pow`

Counts

4 → 761

Calls

4 calls:

56.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
34.0ms	(- (* b b) (* (* 4.0 a) c))
35.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series383.0ms

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))
88.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
85.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify157.0ms

Algorithm

egg-herbie

Counts

773 → 773

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	1992	12865
1	5001	10486

prune806.0ms

Filtered

773 candidates to 242 candidates (68.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	767	6	773
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	773	10	783

Merged error: 5.1b

Counts

783 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

37808×	`times-frac`
25764×	`*-un-lft-identity`
20820×	`add-sqr-sqrt`
16161×	`cbrt-prod`
13774×	`add-cube-cbrt`
5706×	`associate-l`
5553×	`associate-r`
4780×	`distribute-lft-out`
4724×	`unswap-sqr`
2481×	`swap-sqr`
2393×	`distribute-rgt-neg-in`
1456×	`*-commutative`
493×	`associate-/r/`
411×	`associate-/r*`
330×	`prod-diff`
233×	`div-inv`
200×	`flip3-+` `flip-+`
119×	`add-cbrt-cube`
110×	`associate-/l*`
85×	`cbrt-undiv`
38×	`cbrt-unprod`
36×	`add-exp-log`
30×	`difference-of-squares`
24×	`sqrt-prod`
20×	`associate-/l/`
18×	`div-exp`
15×	`fma-neg`
12×	`distribute-lft-out--`
10×	`fma-def` `add-log-exp`
6×	`prod-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `frac-2neg` `clear-num`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log`

Counts

4 → 13827

Calls

4 calls:

396.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (cbrt 1)))
34.0ms	(- (* b b) (* (* 4.0 a) c))
38.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (cbrt 1)))
55.0ms	(- (* b b) (* (* 4.0 a) c))
100.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.2s

Algorithm

egg-herbie

Counts

13839 → 13839

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	8549	440527

prune34.5s

Filtered

13839 candidates to 6689 candidates (51.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	13837	2	13839
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	13839	10	13849

Merged error: 5.1b

Counts

13849 → 10

regimes250.0ms

Accuracy

85.5% (4.2b remaining)

Error of 9.7b against oracle of 5.6b and baseline of 34.4b

bsearch136.0ms

Steps

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	19
1	41	19

end0.0ms

sample1.3s

Algorithm

intervals

Results

291.0ms	1098×	body	2560	valid
264.0ms	5797×	body	80	valid
195.0ms	885×	body	1280	valid
119.0ms	2780×	body	80	nan
77.0ms	464×	body	640	valid
37.0ms	116×	body	5120	valid
34.0ms	249×	body	320	valid
10.0ms	117×	body	160	valid