Details

sample291.0ms

Algorithm

intervals

Results

8.0ms	179×	body	80	valid
7.0ms	41×	body	1280	valid
5.0ms	24×	body	2560	valid
4.0ms	111×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

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: 35.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `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×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

14.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5002	2063

prune316.0ms

Filtered

183 candidates to 97 candidates (53.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	173	10	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	10	184

Merged error: 6.4b

Counts

184 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.4b	(- (* b_2 b_2) (* a c))
1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `associate-r`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

17.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
4.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
35.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify79.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	609	2985
1	2334	1993
2	5002	1940

prune271.0ms

Filtered

181 candidates to 96 candidates (53.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	181	10	191

Merged error: 6.4b

Counts

191 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))
13.3b	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
57×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
24×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1/2`
15×	`swap-sqr`
10×	`fma-neg` `prod-diff`
9×	`flip3--` `associate-r` `associate-l` `pow-prod-up` `flip--` `unswap-sqr`
8×	`add-log-exp`
6×	`add-exp-log` `distribute-lft-neg-in` `distribute-rgt-neg-in` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
2×	`neg-mul-1` `rem-sqrt-square` `diff-log` `associate-r/` `associate-l/`
1×	`associate--l-` `pow2` `neg-sub0` `sub-neg` `pow-plus` `sqrt-unprod` `neg-log` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `difference-of-squares`

Counts

4 → 156

Calls

4 calls:

18.0ms	(* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))
68.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	383	1788
1	1547	1498
2	5001	1387

prune297.0ms

Filtered

168 candidates to 96 candidates (57.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	168	10	178

Merged error: 6.4b

Counts

178 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt a)
0.5b	(cbrt a)
1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `pow1/3` `sqrt-div` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 133

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
10.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt a)
175.0ms	(cbrt a)
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	405	2447
1	1280	1575
2	5001	1488

prune234.0ms

Filtered

145 candidates to 77 candidates (53.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	145	10	155

Merged error: 6.4b

Counts

155 → 10

regimes233.0ms

Accuracy

82.3% (4.9b remaining)

Error of 10.4b against oracle of 5.5b and baseline of 33.1b

bsearch94.0ms

Steps

Iters	Range		Point
8	2.8028278488416225e+79	7.17624026241226e+82	7.042361471685654e+82
9	-1.3800529096284603e-81	-1.8960304733955153e-90	-2.91890913136631e-83

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	15
1	34	15

end0.0ms

sample1.1s

Algorithm

intervals

Results

228.0ms	1055×	body	2560	valid
214.0ms	5922×	body	80	valid
155.0ms	896×	body	1280	valid
101.0ms	3037×	body	80	nan
58.0ms	423×	body	640	valid
25.0ms	96×	body	5120	valid
21.0ms	212×	body	320	valid
8.0ms	113×	body	160	valid