Details

sample33.0ms

Algorithm

intervals

Results

14.0ms	277×	body	80	valid
4.0ms	82×	body	80	nan

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	18
1	80	18
2	143	18
3	177	18
4	189	18
5	193	18
6	193	18

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: 16.1b

Counts

2 → 1

localize127.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

659×	`add-sqr-sqrt`
289×	`sqrt-prod`
270×	`prod-diff`
265×	`*-un-lft-identity`
216×	`unswap-sqr`
182×	`difference-of-squares`
113×	`add-cube-cbrt`
108×	`associate-l`
89×	`distribute-rgt-neg-in`
87×	`distribute-lft-neg-in`
74×	`distribute-lft-out--`
36×	`swap-sqr` `*-commutative`
29×	`neg-mul-1`
12×	`add-log-exp`
10×	`fma-def` `fma-neg`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 403

Calls

4 calls:

34.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify144.0ms

Algorithm

egg-herbie

Counts

415 → 415

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	733	12242
1	2067	9625
2	5001	9326

prune551.0ms

Filtered

415 candidates to 122 candidates (29.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	407	8	415
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	408	8	416

Merged error: 6.4b

Counts

416 → 8

localize133.0ms

Local error

Found 4 expressions with local error:

20.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
20.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
20.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
20.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

188×	`add-sqr-sqrt`
96×	`cbrt-prod`
72×	`unswap-sqr`
60×	`difference-of-squares`
56×	`*-un-lft-identity`
36×	`associate-l`
24×	`distribute-lft-out--`
12×	`swap-sqr` `*-commutative`
8×	`add-cube-cbrt` `cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`

Counts

4 → 144

Calls

4 calls:

23.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
27.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
104.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
109.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
105.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	234	1592
1	647	1548
2	2322	1540
3	5001	1540

prune772.0ms

Filtered

156 candidates to 92 candidates (59.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	156	8	164

Merged error: 6.4b

Counts

164 → 8

localize133.0ms

Local error

Found 4 expressions with local error:

20.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
20.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
20.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
30.4b	(+ (- (fabs (cbrt (- (* b b) (* (* 4.0 a) c))))) (fabs (* (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

145×	`add-sqr-sqrt`
72×	`cbrt-prod`
54×	`unswap-sqr`
50×	`*-un-lft-identity`
45×	`difference-of-squares`
27×	`associate-l`
18×	`distribute-lft-out--`
10×	`add-cube-cbrt` `fma-def`
9×	`swap-sqr` `*-commutative`
8×	`add-log-exp`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `distribute-rgt-neg-in` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `flip3--` `pow1/3` `flip--`
2×	`sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `flip-+`

Counts

4 → 135

Calls

4 calls:

25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(+ (- (fabs (cbrt (- (* b b) (* (* 4.0 a) c))))) (fabs (* (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))

series307.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
100.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
103.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(+ (- (fabs (cbrt (- (* b b) (* (* 4.0 a) c))))) (fabs (* (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))

simplify116.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	316	1720
1	936	1398
2	3302	1224
3	5001	1224

prune611.0ms

Filtered

147 candidates to 92 candidates (62.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	147	8	155

Merged error: 6.4b

Counts

155 → 8

localize123.0ms

Local error

Found 4 expressions with local error:

19.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
96×	`sqrt-prod`
72×	`unswap-sqr`
60×	`difference-of-squares`
56×	`*-un-lft-identity`
36×	`associate-l`
24×	`distribute-lft-out--`
12×	`swap-sqr` `*-commutative`
8×	`pow1` `add-cube-cbrt` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`

Counts

4 → 152

Calls

4 calls:

45.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify83.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	212	1500
1	630	1480
2	2277	1476
3	5001	1444

prune436.0ms

Filtered

164 candidates to 92 candidates (56.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	164	8	172

Merged error: 6.4b

Counts

172 → 8

regimes196.0ms

Accuracy

89.7% (1.2b remaining)

Error of 9.0b against oracle of 7.8b and baseline of 19.7b

bsearch199.0ms

Steps

Iters	Range		Point
7	8.175350185103435e+71	1.3253879264775672e+74	1.2930490387792999e+74
10	-2.7851241427016145e+159	-9.354797223898085e+144	-1.339770324042421e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	89
1	62	89

end0.0ms

sample840.0ms

Algorithm

intervals

Results

446.0ms	8703×	body	80	valid
146.0ms	2983×	body	80	nan