Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	39×	body	2560	valid
7.0ms	171×	body	80	valid
5.0ms	26×	body	1280	valid
3.0ms	74×	body	80	nan
3.0ms	9×	body	5120	valid
2.0ms	12×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	2×	body	160	valid

simplify15.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
25.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite74.0ms

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:

44.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
67.0ms	(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

prune341.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
25.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite83.0ms

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:

54.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
15.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
42.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify90.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (60.0ms)

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

prune326.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

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) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
25.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite74.0ms

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:

41.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
6.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify79.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (55.0ms)

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

prune366.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.4b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
12.5b	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
25.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
25.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`fma-neg` `prod-diff`
10×	`add-log-exp`
6×	`pow1` `distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	313	1367
1	1139	1090
2	5001	1064

prune359.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.4b

regimes299.0ms

Accuracy

84.5% (4.4b remaining)

Error of 9.9b against oracle of 5.4b and baseline of 34.1b

bsearch135.0ms

Steps

Iters	Range		Point
8	1.9559514031553493e+101	2.0413668072230428e+104	1.6764314440115407e+104
11	-1.4160683835321931e-14	-4.058620405728376e-48	-8.260729798395838e-43

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms

sample1.2s

Algorithm

intervals

Results

272.0ms	1068×	body	2560	valid
244.0ms	5808×	body	80	valid
174.0ms	853×	body	1280	valid
111.0ms	2843×	body	80	nan
75.0ms	468×	body	640	valid
32.0ms	110×	body	5120	valid
29.0ms	246×	body	320	valid
12.0ms	143×	body	160	valid