Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	203×	body	80	valid
5.0ms	31×	body	1280	valid
5.0ms	23×	body	2560	valid
2.0ms	79×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7

prune2.0ms

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: 32.9b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

587×	`add-sqr-sqrt`
380×	`prod-diff`
326×	`*-un-lft-identity`
210×	`add-cube-cbrt`
192×	`sqrt-prod`
132×	`associate-l`
130×	`difference-of-squares`
112×	`unswap-sqr`
84×	`associate-r`
68×	`distribute-rgt-neg-in`
63×	`distribute-lft-neg-in` `swap-sqr`
58×	`distribute-lft-out--`
52×	`*-commutative`
25×	`fma-neg`
21×	`neg-mul-1` `times-frac`
10×	`add-log-exp`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`associate--l-` `neg-sub0` `sub-neg` `sqrt-div` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 533

Calls

4 calls:

42.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
19.0ms	(- (* b_2 b_2) (* a c))
28.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
29.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify167.0ms

Algorithm

egg-herbie

Counts

545 → 545

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	1166	10954
1	3713	7708
2	5001	7703

prune536.0ms

Filtered

545 candidates to 140 candidates (25.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	534	11	545
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	535	11	546

Merged error: 6.3b

Counts

546 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

685×	`add-sqr-sqrt`
425×	`*-un-lft-identity`
380×	`prod-diff`
272×	`add-cube-cbrt`
201×	`sqrt-prod`
165×	`times-frac`
148×	`difference-of-squares`
132×	`associate-l`
112×	`unswap-sqr`
84×	`associate-r`
77×	`distribute-rgt-neg-in`
76×	`distribute-lft-out--`
63×	`distribute-lft-neg-in` `swap-sqr`
52×	`*-commutative`
34×	`associate-/r*`
25×	`fma-neg`
21×	`neg-mul-1` `associate-/r/`
15×	`add-exp-log`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--` `associate-/l*`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `clear-num`
2×	`sub-neg` `rec-exp` `frac-2neg` `sqrt-div` `1-exp` `remove-double-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `neg-log` `inv-pow`

Counts

4 → 632

Calls

4 calls:

35.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
19.0ms	(- (* b_2 b_2) (* a c))
28.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
28.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
32.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify119.0ms

Algorithm

egg-herbie

Counts

644 → 644

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1396	12500
1	5001	9072

prune630.0ms

Filtered

644 candidates to 175 candidates (27.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	640	4	644
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	646	9	655

Merged error: 6.3b

Counts

655 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

587×	`add-sqr-sqrt`
380×	`prod-diff`
326×	`*-un-lft-identity`
210×	`add-cube-cbrt`
192×	`sqrt-prod`
132×	`associate-l`
130×	`difference-of-squares`
112×	`unswap-sqr`
84×	`associate-r`
68×	`distribute-rgt-neg-in`
63×	`distribute-lft-neg-in` `swap-sqr`
58×	`distribute-lft-out--`
52×	`*-commutative`
25×	`fma-neg`
21×	`neg-mul-1` `times-frac`
10×	`add-log-exp`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`associate--l-` `neg-sub0` `sub-neg` `sqrt-div` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 533

Calls

4 calls:

38.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
22.0ms	(- (* b_2 b_2) (* a c))
28.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
29.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify167.0ms

Algorithm

egg-herbie

Counts

545 → 545

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	1166	10954
1	3713	7708
2	5001	7703

prune460.0ms

Filtered

545 candidates to 135 candidates (24.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	545	0	545
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	545	9	554

Merged error: 6.3b

Counts

554 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

685×	`add-sqr-sqrt`
425×	`*-un-lft-identity`
380×	`prod-diff`
272×	`add-cube-cbrt`
201×	`sqrt-prod`
165×	`times-frac`
148×	`difference-of-squares`
132×	`associate-l`
112×	`unswap-sqr`
84×	`associate-r`
77×	`distribute-rgt-neg-in`
76×	`distribute-lft-out--`
63×	`distribute-lft-neg-in` `swap-sqr`
52×	`*-commutative`
34×	`associate-/r*`
25×	`fma-neg`
21×	`neg-mul-1` `associate-/r/`
15×	`add-exp-log`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--` `associate-/l*`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `clear-num`
2×	`sub-neg` `rec-exp` `frac-2neg` `sqrt-div` `1-exp` `remove-double-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `neg-log` `inv-pow`

Counts

4 → 632

Calls

4 calls:

32.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
22.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
32.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify121.0ms

Algorithm

egg-herbie

Counts

644 → 644

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1396	12500
1	5001	9072

prune638.0ms

Filtered

644 candidates to 176 candidates (27.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	643	1	644
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	644	9	653

Merged error: 6.3b

Counts

653 → 9

regimes215.0ms

Accuracy

84.7% (4.3b remaining)

Error of 9.8b against oracle of 5.4b and baseline of 33.7b

bsearch96.0ms

Steps

Iters	Range		Point
9	4.546949039871578e+116	7.0067478635952275e+121	2.12330831537073e+121
10	-1.0320842654441656e-69	-6.354733239957269e-82	-8.480118384731098e-73

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	11
1	25	11

end0.0ms

sample1.0s

Algorithm

intervals

Results

220.0ms	1063×	body	2560	valid
199.0ms	5848×	body	80	valid
143.0ms	850×	body	1280	valid
95.0ms	2860×	body	80	nan
62.0ms	465×	body	640	valid
26.0ms	105×	body	5120	valid
23.0ms	234×	body	320	valid
8.0ms	120×	body	160	valid