Details

sample64.0ms

Algorithm

intervals

Results

17.0ms	186×	body	80	valid
15.0ms	42×	body	2560	valid
7.0ms	23×	body	1280	valid
5.0ms	79×	body	80	nan
3.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	8×	body	160	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: 34.9b

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)))
2.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite78.0ms

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:

46.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify74.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	590	3306
1	2101	2212
2	5002	2128

prune337.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

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)))
2.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite88.0ms

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:

57.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (- 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:

94.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
43.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify88.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (60.0ms)

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

prune325.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize13.0ms

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)))
2.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite78.0ms

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:

43.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify74.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (51.0ms)

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

prune326.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) (* 2.0 a))
0.5b	(fma b b (- (* 4.0 (* a c))))
2.3b	(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
20.4b	(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 149

Calls

4 calls:

30.0ms	(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) (* 2.0 a))
0.0ms	(fma b b (- (* 4.0 (* a c))))
12.0ms	(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
1.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) (* 2.0 a))
56.0ms	(fma b b (- (* 4.0 (* a c))))
87.0ms	(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
79.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	514	3218
1	1659	2128
2	5001	2044

prune298.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.5b

regimes153.0ms

Accuracy

83.9% (4.6b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 34.4b

bsearch143.0ms

Steps

Iters	Range		Point
9	1.0966316111626227e+109	8.247031634266059e+117	4.250491858915138e+117
9	-4.966762827316324e-118	-1.3701001010226256e-126	-4.1515494582665793e-119

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	18
1	59	18
2	59	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

459.0ms	5878×	body	80	valid
391.0ms	1066×	body	2560	valid
271.0ms	892×	body	1280	valid
206.0ms	2992×	body	80	nan
108.0ms	445×	body	640	valid
52.0ms	115×	body	5120	valid
43.0ms	222×	body	320	valid
15.0ms	117×	body	160	valid