Details

sample84.0ms

Algorithm

intervals

Results

22.0ms	188×	body	80	valid
15.0ms	30×	body	2560	valid
12.0ms	31×	body	1280	valid
9.0ms	91×	body	80	nan
5.0ms	15×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
1.0ms	6×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 33.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite61.0ms

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:

38.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms	(- (* b b) (* (* 4.0 a) c))
88.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735

prune350.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.9b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
30.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
168.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
204.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify163.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	829	5121
1	3763	3863
2	5001	3860

prune667.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

localize32.0ms

Local error

Found 4 expressions with local error:

14.1b	(cbrt (+ 0 (* 4.0 (* a c))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 66

Calls

4 calls:

2.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
83.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	274	583
1	1163	556
2	5001	550

prune499.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
9.9b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
71×	`add-cube-cbrt`
60×	`prod-diff`
51×	`add-exp-log`
46×	`times-frac`
41×	`sqrt-prod`
29×	`distribute-rgt-neg-in`
27×	`associate-l` `add-cbrt-cube`
21×	`distribute-lft-neg-in`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
10×	`fma-neg`
8×	`cbrt-undiv` `cbrt-unprod` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-/r*`
4×	`expm1-log1p-u` `rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `diff-log` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 227

Calls

4 calls:

17.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
28.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series557.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
172.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
211.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
84.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify183.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	921	4844
1	4551	3468
2	5001	3468

prune608.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

regimes188.0ms

Accuracy

83.4% (4.4b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 32.4b

bsearch156.0ms

Steps

Iters	Range		Point
8	2.3682374127768157e-71	9.144612143045527e-68	1.1752867948836086e-69
7	-1.2511146020293208e+129	-2.5570389401985865e+127	-4.032376794487168e+127

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample2.3s

Algorithm

intervals

Results

613.0ms	5912×	body	80	valid
522.0ms	1057×	body	2560	valid
343.0ms	843×	body	1280	valid
270.0ms	2844×	body	80	nan
151.0ms	460×	body	640	valid
59.0ms	228×	body	320	valid
57.0ms	93×	body	5120	valid
24.0ms	128×	body	160	valid