Details

sample52.0ms

Algorithm

intervals

Results

10.0ms	200×	body	80	valid
9.0ms	30×	body	2560	valid
7.0ms	104×	body	80	nan
6.0ms	24×	body	1280	valid
3.0ms	16×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	9
1	65	9
2	121	9
3	151	9
4	160	9
5	164	9
6	164	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: 34.5b

Counts

2 → 1

localize12.0ms

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)))
1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

16.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series286.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms	(- (* b b) (* 4.0 (* a c)))
76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify82.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	590	3305
1	2101	2212
2	5002	2128

prune310.0ms

Filtered

169 candidates to 89 candidates (52.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	160	9	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	9	170

Merged error: 6.5b

Counts

170 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

16.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
6.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
48.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify90.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	656	3422
1	2594	2238
2	5001	2193

prune301.0ms

Filtered

177 candidates to 90 candidates (50.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	178	8	186

Merged error: 6.5b

Counts

186 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt b)
0.6b	(cbrt b)
21.0b	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--` `fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt b)
1.0ms	(cbrt b)
1.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series578.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt b)
183.0ms	(cbrt b)
142.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify91.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	214	411
1	699	373
2	2823	356
3	5001	352

prune223.0ms

Filtered

65 candidates to 58 candidates (89.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	64	9	73

Merged error: 6.5b

Counts

73 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt b)
0.6b	(cbrt b)
21.0b	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--` `fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt b)
1.0ms	(cbrt b)
1.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series571.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt b)
187.0ms	(cbrt b)
134.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify91.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	214	411
1	699	373
2	2823	356
3	5001	352

prune220.0ms

Filtered

65 candidates to 58 candidates (89.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	64	10	74

Merged error: 6.5b

Counts

74 → 10

regimes438.0ms

Accuracy

83.3% (5.0b remaining)

Error of 11.1b against oracle of 6.1b and baseline of 36.0b

bsearch219.0ms

Steps

Iters	Range		Point
6	6.333441064762502e+69	2.6854631551896503e+70	2.6627070202833933e+70
5	-1.482547241207331e-101	-6.742792119201738e-102	-1.0320808747865978e-101
8	-8.810326546476336e-23	-4.169997451253584e-26	-1.0154709195266253e-23
8	-9.838482322929929	-0.0014803844373699059	-0.0015046342707181791

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	37
1	50	37

end0.0ms

sample1.4s

Algorithm

intervals

Results

314.0ms	1082×	body	2560	valid
293.0ms	5819×	body	80	valid
224.0ms	889×	body	1280	valid
141.0ms	2916×	body	80	nan
83.0ms	445×	body	640	valid
39.0ms	106×	body	5120	valid
33.0ms	233×	body	320	valid
12.0ms	127×	body	160	valid