Details

sample44.0ms

Algorithm

intervals

Results

8.0ms	203×	body	80	valid
6.0ms	31×	body	1280	valid
6.0ms	23×	body	2560	valid
5.0ms	17×	body	640	valid
3.0ms	79×	body	80	nan
1.0ms	4×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 32.9b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

1094×	`add-sqr-sqrt`
580×	`prod-diff`
482×	`*-un-lft-identity`
330×	`add-cube-cbrt`
318×	`associate-r`
307×	`unswap-sqr`
256×	`sqrt-prod`
231×	`associate-l`
208×	`difference-of-squares`
105×	`swap-sqr`
97×	`*-commutative`
92×	`distribute-rgt-neg-in`
84×	`times-frac`
78×	`distribute-lft-neg-in`
76×	`distribute-lft-out--`
26×	`neg-mul-1`
25×	`fma-neg`
12×	`associate-/r*`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `sqrt-div` `div-sub` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`

Counts

4 → 817

Calls

4 calls:

61.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
34.0ms	(- (* b b) (* 4.0 (* a c)))
42.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
78.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify188.0ms

Algorithm

egg-herbie

Counts

829 → 829

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1939	20317
1	5002	15499

prune906.0ms

Filtered

829 candidates to 208 candidates (25.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	820	9	829
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	821	9	830

Merged error: 6.4b

Counts

830 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

1474×	`add-sqr-sqrt`
822×	`*-un-lft-identity`
606×	`times-frac`
580×	`prod-diff`
524×	`add-cube-cbrt`
381×	`associate-r`
328×	`unswap-sqr`
295×	`associate-l`
292×	`sqrt-prod`
280×	`difference-of-squares`
148×	`distribute-lft-out--`
128×	`distribute-rgt-neg-in`
118×	`*-commutative`
105×	`swap-sqr`
97×	`associate-/r*`
78×	`distribute-lft-neg-in`
30×	`associate-/r/`
26×	`neg-mul-1`
25×	`add-exp-log` `fma-neg`
17×	`associate-/l*`
13×	`add-cbrt-cube`
12×	`div-exp`
10×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `clear-num` `remove-double-div`
2×	`sub-neg` `frac-2neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `neg-log` `cbrt-unprod` `inv-pow`

Counts

4 → 1108

Calls

4 calls:

63.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
32.0ms	(- (* b b) (* 4.0 (* a c)))
45.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
78.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify252.0ms

Algorithm

egg-herbie

Counts

1120 → 1120

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2566	25667
1	5002	21550

prune1.5s

Filtered

1120 candidates to 347 candidates (31.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1116	4	1120
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	1121	8	1129

Merged error: 6.3b

Counts

1129 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite394.0ms

Algorithm

rewrite-expression-head

Rules

2949×	`times-frac`
2728×	`add-sqr-sqrt`
1962×	`*-un-lft-identity`
1366×	`add-cube-cbrt`
580×	`prod-diff`
549×	`associate-r`
462×	`associate-l`
430×	`difference-of-squares`
384×	`unswap-sqr`
367×	`sqrt-prod`
298×	`distribute-lft-out--`
203×	`distribute-rgt-neg-in`
174×	`*-commutative`
105×	`swap-sqr`
95×	`associate-/r/`
87×	`add-exp-log`
78×	`distribute-lft-neg-in`
70×	`div-inv`
58×	`div-exp`
46×	`associate-/r` `associate-/l`
44×	`flip3--` `flip--`
26×	`neg-mul-1`
25×	`fma-neg` `add-cbrt-cube`
18×	`associate-/l/`
15×	`rec-exp` `1-exp`
13×	`cbrt-undiv`
12×	`prod-exp`
10×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `diff-log` `clear-num`
2×	`sub-neg` `sqrt-div` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 1918

Calls

4 calls:

79.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
35.0ms	(- (* b b) (* 4.0 (* a c)))
41.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
45.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
78.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify425.0ms

Algorithm

egg-herbie

Counts

1930 → 1930

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5001	47869

prune4.5s

Filtered

1930 candidates to 917 candidates (47.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1927	3	1930
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	1929	9	1938

Merged error: 6.3b

Counts

1938 → 9

localize34.0ms

Local error

Found 4 expressions with local error:

22.8b	(cbrt (- (* b b) (* 4.0 (* a c))))
22.8b	(cbrt (- (* b b) (* 4.0 (* a c))))
22.8b	(cbrt (- (* b b) (* 4.0 (* a c))))
62.3b	(fma (- (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) (sqrt (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c)))))) (* (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

142×	`add-sqr-sqrt`
66×	`cbrt-prod`
54×	`unswap-sqr`
45×	`difference-of-squares`
31×	`*-un-lft-identity`
12×	`associate-l` `distribute-lft-out--`
9×	`swap-sqr` `*-commutative`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
1×	`fma-udef`

Counts

4 → 112

Calls

4 calls:

23.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
28.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
23.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
1.0ms	(fma (- (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) (sqrt (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c)))))) (* (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))))))

series480.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
99.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
97.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
185.0ms	(fma (- (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) (sqrt (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c)))))) (* (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))))))

simplify109.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	282	1660
1	824	1525
2	3212	1487
3	5001	1446

prune572.0ms

Filtered

124 candidates to 82 candidates (66.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	124	9	133

Merged error: 6.3b

Counts

133 → 9

regimes195.0ms

Accuracy

84.5% (4.4b remaining)

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

bsearch136.0ms

Steps

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	14
1	34	14

end0.0ms

sample1.2s

Algorithm

intervals

Results

266.0ms	1063×	body	2560	valid
247.0ms	5846×	body	80	valid
169.0ms	849×	body	1280	valid
110.0ms	2863×	body	80	nan
74.0ms	463×	body	640	valid
31.0ms	105×	body	5120	valid
27.0ms	231×	body	320	valid
10.0ms	126×	body	160	valid