Details

sample53.0ms

Algorithm

intervals

Results

12.0ms	40×	body	2560	valid
11.0ms	35×	body	1280	valid
9.0ms	171×	body	80	valid
4.0ms	89×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	1×	body	5120	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite143.0ms

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:

31.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
83.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series255.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
83.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
39.0ms	(- (* b b) (* 4.0 (* a c)))
64.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify80.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	590	3305
1	2101	2212
2	5001	2128

prune596.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
54×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
30×	`add-exp-log`
29×	`add-cube-cbrt`
20×	`associate-/r*`
18×	`add-cbrt-cube`
14×	`div-exp`
12×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-/r/`
9×	`sqrt-prod`
7×	`cbrt-undiv` `flip3--` `flip--`
6×	`pow1` `distribute-rgt-neg-in` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `associate-/l*`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `sqrt-div` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `inv-pow`

Counts

4 → 148

Calls

4 calls:

48.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
51.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
12.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series362.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
101.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
39.0ms	(- (* b b) (* 4.0 (* a c)))
65.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify83.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	590	2075
1	2867	1822
2	5002	1745

prune579.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2.0 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a))
0.2b	(/ 1 (/ 2.0 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)))
0.6b	(- (* b b) (* 4.0 (* a c)))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
585×	`add-sqr-sqrt`
584×	`*-un-lft-identity`
392×	`add-cube-cbrt`
105×	`associate-/r*`
96×	`distribute-lft-out--` `difference-of-squares`
51×	`sqrt-prod`
48×	`distribute-rgt-neg-in`
30×	`add-exp-log`
22×	`div-inv`
18×	`div-exp` `add-cbrt-cube`
9×	`cbrt-undiv`
6×	`pow1` `associate-/r/` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `inv-pow`

Counts

4 → 503

Calls

4 calls:

48.0ms	(/ 2.0 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a))
67.0ms	(/ 1 (/ 2.0 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)))
10.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ 2.0 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a))
87.0ms	(/ 1 (/ 2.0 (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)))
44.0ms	(- (* b b) (* 4.0 (* a c)))
61.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify115.0ms

Algorithm

egg-herbie

Counts

515 → 515

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1447	9430
1	5001	8880

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.1b	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
0.6b	(- (* b b) (* 4.0 (* a c)))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 244

Calls

4 calls:

31.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
13.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
82.0ms	(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
44.0ms	(- (* b b) (* 4.0 (* a c)))
65.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify109.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	864	4951
1	3179	3814
2	5002	3773

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

regimes264.0ms

Accuracy

85.3% (4.2b remaining)

Error of 9.6b against oracle of 5.4b and baseline of 33.9b

bsearch93.0ms

Steps

Iters	Range		Point
8	2.068553019413577e+125	1.5793235108451263e+128	8.824801410527501e+125
4	-9.285856612195885e-64	-5.291128096587059e-64	-5.365827530591872e-64

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	31	15

end0.0ms

sample1.5s

Algorithm

intervals

Results

350.0ms	1087×	body	2560	valid
320.0ms	5861×	body	80	valid
236.0ms	890×	body	1280	valid
152.0ms	3052×	body	80	nan
101.0ms	476×	body	640	valid
44.0ms	107×	body	5120	valid
30.0ms	195×	body	320	valid
14.0ms	114×	body	160	valid