Details

sample41.0ms

Algorithm

intervals

Results

9.0ms	191×	body	80	valid
9.0ms	39×	body	2560	valid
3.0ms	19×	body	1280	valid
3.0ms	82×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	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: 29.8b

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))
0.2b	(- (* 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))))

rewrite261.0ms

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:

65.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
36.0ms	(- (* b b) (* 4.0 (* a c)))
44.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify202.0ms

Algorithm

egg-herbie

Counts

829 → 829

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	1932	20316
1	5001	15481

prune695.0ms

Filtered

829 candidates to 206 candidates (24.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	819	10	829
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	820	10	830

Merged error: 4.4b

Counts

830 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
0.2b	(/ 1 (/ (* 2.0 a) (- (- 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))))

rewrite291.0ms

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:

38.0ms	(- (* b b) (* 4.0 (* a c)))
66.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
47.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series331.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b b) (* 4.0 (* a c)))
120.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
79.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify271.0ms

Algorithm

egg-herbie

Counts

1120 → 1120

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	2559	25667
1	5001	21115

prune1.2s

Filtered

1120 candidates to 346 candidates (30.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	1115	5	1120
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	1121	9	1130

Merged error: 4.3b

Counts

1130 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
0.2b	(- (* 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))))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

1017×	`add-sqr-sqrt`
580×	`prod-diff`
421×	`*-un-lft-identity`
305×	`add-cube-cbrt`
299×	`unswap-sqr`
294×	`associate-r`
247×	`sqrt-prod`
207×	`associate-l`
190×	`difference-of-squares`
105×	`swap-sqr`
89×	`*-commutative`
83×	`distribute-rgt-neg-in`
78×	`distribute-lft-neg-in`
58×	`distribute-lft-out--`
26×	`neg-mul-1`
25×	`fma-neg`
21×	`times-frac`
10×	`add-log-exp`
7×	`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×	`associate--l-` `neg-sub0` `sub-neg` `sqrt-div` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 743

Calls

4 calls:

64.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
35.0ms	(- (* b b) (* 4.0 (* a c)))
49.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
50.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
47.0ms	(- (* b b) (* 4.0 (* a c)))
84.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
81.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify177.0ms

Algorithm

egg-herbie

Counts

755 → 755

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1652	18955
1	5001	13833

prune764.0ms

Filtered

755 candidates to 170 candidates (22.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	752	3	755
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	755	9	764

Merged error: 4.3b

Counts

764 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
0.9b	(- (- b) (sqrt (+ (fma b b (- (* (cbrt c) (* 4.0 (* a (* (cbrt c) (cbrt c))))))) (* (* 4.0 (* a (* (cbrt c) (cbrt c)))) (+ (- (cbrt c)) (cbrt c))))))
3.7b	(* (* 4.0 (* a (* (cbrt c) (cbrt c)))) (+ (- (cbrt c)) (cbrt c)))
19.8b	(sqrt (+ (fma b b (- (* (cbrt c) (* 4.0 (* a (* (cbrt c) (cbrt c))))))) (* (* 4.0 (* a (* (cbrt c) (cbrt c)))) (+ (- (cbrt c)) (cbrt c)))))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

249×	`add-sqr-sqrt`
158×	`*-un-lft-identity`
108×	`unswap-sqr`
107×	`associate-l`
102×	`associate-r`
90×	`prod-diff`
82×	`add-cube-cbrt`
67×	`sqrt-prod`
61×	`cbrt-prod`
42×	`distribute-lft-neg-in`
40×	`distribute-lft-out`
37×	`distribute-rgt-neg-in`
29×	`add-cbrt-cube`
22×	`cbrt-unprod`
19×	`pow1`
18×	`add-exp-log`
14×	`swap-sqr`
13×	`neg-mul-1`
12×	`distribute-rgt-out` `hypot-def`
10×	`fma-neg` `pow-prod-down` `prod-exp`
8×	`*-commutative` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft1-in`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sqrt-div` `diff-log` `associate-*r/` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `pow1/3` `neg-log` `flip--`

Counts

4 → 294

Calls

4 calls:

1.0ms	(cbrt c)
86.0ms	(- (- b) (sqrt (+ (fma b b (- (* (cbrt c) (* 4.0 (* a (* (cbrt c) (cbrt c))))))) (* (* 4.0 (* a (* (cbrt c) (cbrt c)))) (+ (- (cbrt c)) (cbrt c))))))
69.0ms	(* (* 4.0 (* a (* (cbrt c) (cbrt c)))) (+ (- (cbrt c)) (cbrt c)))
81.0ms	(sqrt (+ (fma b b (- (* (cbrt c) (* 4.0 (* a (* (cbrt c) (cbrt c))))))) (* (* 4.0 (* a (* (cbrt c) (cbrt c)))) (+ (- (cbrt c)) (cbrt c)))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt c)
108.0ms	(- (- b) (sqrt (+ (fma b b (- (* (cbrt c) (* 4.0 (* a (* (cbrt c) (cbrt c))))))) (* (* 4.0 (* a (* (cbrt c) (cbrt c)))) (+ (- (cbrt c)) (cbrt c))))))
2.0ms	(* (* 4.0 (* a (* (cbrt c) (cbrt c)))) (+ (- (cbrt c)) (cbrt c)))
113.0ms	(sqrt (+ (fma b b (- (* (cbrt c) (* 4.0 (* a (* (cbrt c) (cbrt c))))))) (* (* 4.0 (* a (* (cbrt c) (cbrt c)))) (+ (- (cbrt c)) (cbrt c)))))

simplify120.0ms

Algorithm

egg-herbie

Counts

306 → 306

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1169	12309
1	5001	8023

prune759.0ms

Filtered

306 candidates to 171 candidates (55.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	306	0	306
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	306	9	315

Merged error: 4.3b

Counts

315 → 9

regimes210.0ms

Accuracy

82% (5.0b remaining)

Error of 10.9b against oracle of 5.9b and baseline of 33.5b

bsearch106.0ms

Steps

Iters	Range		Point
9	2.8787744468916765e+83	8.390568855339406e+90	7.775131276953344e+90
7	-4.6417297347823423e-91	-2.5527576166225183e-92	-1.7445837442398665e-91

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

258.0ms	1068×	body	2560	valid
227.0ms	5863×	body	80	valid
168.0ms	907×	body	1280	valid
114.0ms	2983×	body	80	nan
60.0ms	415×	body	640	valid
29.0ms	93×	body	5120	valid
26.0ms	236×	body	320	valid
9.0ms	121×	body	160	valid