Details

sample290.0ms

Algorithm

intervals

Results

9.0ms	200×	body	80	valid
8.0ms	30×	body	2560	valid
7.0ms	104×	body	80	nan
5.0ms	24×	body	1280	valid
3.0ms	16×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify16.0ms

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: 34.5b

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))))
23.2b	(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)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (50.0ms)

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

prune320.0ms

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: 6.5b

Counts

184 → 10

localize10.0ms

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))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

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:

18.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
34.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify81.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (58.0ms)

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

prune275.0ms

Filtered

181 candidates to 96 candidates (53.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	182	9	191

Merged error: 6.5b

Counts

191 → 9

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)))))
8.9b	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite39.0ms

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:

19.0ms	(* (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)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))
71.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	382	1788
1	1546	1498
2	5002	1387

prune303.0ms

Filtered

168 candidates to 96 candidates (57.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	168	9	177

Merged error: 6.5b

Counts

177 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
5.5b	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
21.1b	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

91×	`prod-diff`
75×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
68×	`add-cube-cbrt` `log-prod` `exp-sum`
37×	`sqrt-prod`
31×	`distribute-rgt-neg-in`
30×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`neg-mul-1` `add-log-exp`
7×	`pow1`
6×	`exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log` `log-pow` `difference-of-squares`
2×	`sub-neg` `log-div` `sqrt-pow1` `pow1/2` `exp-diff` `distribute-lft-out--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `neg-log` `rem-exp-log`

Counts

4 → 178

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
17.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
66.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	535	4477
1	1473	2268
2	5002	2146

prune243.0ms

Filtered

190 candidates to 82 candidates (43.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	190	9	199

Merged error: 6.5b

Counts

199 → 9

regimes232.0ms

Accuracy

86.6% (3.6b remaining)

Error of 9.6b against oracle of 6.0b and baseline of 33.1b

bsearch145.0ms

Steps

Iters	Range	Point
6	6.333441064762502e+69	2.6854631551896503e+70	2.6627070202833933e+70
8	-3.207872221154417e-308	6.068018528671512e-305	-1.5917437502612807e-308
9	-1.1385716878983627e+38	-7.767129419132542e+28	-1.2077125772538958e+29

Iters

Range

Point

6.333441064762502e+69

2.6854631551896503e+70

2.6627070202833933e+70

-3.207872221154417e-308

6.068018528671512e-305

-1.5917437502612807e-308

-1.1385716878983627e+38

-7.767129419132542e+28

-1.2077125772538958e+29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	44	24
2	44	24

end0.0ms

sample1.2s

Algorithm

intervals

Results

269.0ms	1082×	body	2560	valid
256.0ms	5823×	body	80	valid
177.0ms	889×	body	1280	valid
122.0ms	2907×	body	80	nan
70.0ms	442×	body	640	valid
32.0ms	107×	body	5120	valid
28.0ms	239×	body	320	valid
10.0ms	120×	body	160	valid