Details

sample44.0ms

Algorithm

intervals

Results

9.0ms	42×	body	2560	valid
7.0ms	183×	body	80	valid
5.0ms	30×	body	1280	valid
3.0ms	90×	body	80	nan
3.0ms	18×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	2×	body	320	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.6b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
26.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
3×	`associate-r` `pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `flip--` `associate-/l/`
1×	`neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `div-sub` `associate-l` `prod-diff` `clear-num` `associate-/r` `-commutative` `flip-+` `div-inv`

Counts

4 → 83

Calls

4 calls:

16.0ms	(* (* 4.0 a) c)
66.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (* 4.0 a) c)
97.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.0ms	(- (* b b) (* (* 4.0 a) c))
65.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	460	740
1	1973	650
2	5002	641

prune258.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
26.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

21.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
63.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
99.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
42.0ms	(- (* b b) (* 4.0 (* a c)))
64.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify53.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	438	854
1	1658	750
2	5001	735

prune272.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
0.6b	(- (* b b) (* 4.0 (* a c)))
26.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

21.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
60.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
9.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
89.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
40.0ms	(- (* b b) (* 4.0 (* a c)))
65.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	402	977
1	1485	896
2	5001	874

prune312.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.3b	(/ a (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
26.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
137×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
32×	`distribute-lft-out`
26×	`associate-/r*`
17×	`add-exp-log`
16×	`distribute-rgt-neg-in`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp`
6×	`pow1` `div-inv` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`rec-exp` `flip3--` `frac-2neg` `sqrt-div` `1-exp` `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 → 182

Calls

4 calls:

44.0ms	(/ 1 (/ a (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
39.0ms	(/ a (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ 1 (/ a (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
176.0ms	(/ a (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
40.0ms	(- (* b b) (* 4.0 (* a c)))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify78.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	590	2523
1	2754	2251
2	5001	2124

prune352.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.1b

regimes321.0ms

Accuracy

84.5% (4.5b remaining)

Error of 10.0b against oracle of 5.6b and baseline of 34.4b

bsearch112.0ms

Steps

Iters	Range		Point
10	2.2777662256792016e-86	1.8614563384609176e-67	1.2091207453430995e-70
6	-1.3854637168610187e+102	-1.5284190780878897e+101	-9.912439588753869e+101

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	21
1	43	21

end0.0ms

sample1.2s

Algorithm

intervals

Results

247.0ms	1127×	body	2560	valid
218.0ms	5786×	body	80	valid
166.0ms	916×	body	1280	valid
106.0ms	2998×	body	80	nan
60.0ms	438×	body	640	valid
28.0ms	105×	body	5120	valid
23.0ms	222×	body	320	valid
10.0ms	117×	body	160	valid