Details

sample62.0ms

Algorithm

intervals

Results

16.0ms	42×	body	2560	valid
12.0ms	181×	body	80	valid
11.0ms	41×	body	1280	valid
5.0ms	79×	body	80	nan
3.0ms	12×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	320	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
21.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite53.0ms

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:

37.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
21.0ms	(* (* 3.0 a) c)
47.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	433	741
1	1995	651
2	5001	645

prune245.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
21.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

38.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
20.0ms	(* (* 3.0 a) c)
51.0ms	(- (* b b) (* (* 3.0 a) c))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	637	1923
1	2590	1829
2	5001	1813

prune375.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
21.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite52.0ms

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:

36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
21.0ms	(* (* 3.0 a) c)
50.0ms	(- (* b b) (* (* 3.0 a) c))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	433	741
1	1995	651
2	5001	645

prune214.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 1) (* (/ 3.0 (- (sqrt (- (* b b) (* (* 3.0 a) c))) b)) a))
0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
21.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-exp-log`
40×	`div-exp`
31×	`times-frac`
30×	`add-cbrt-cube`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
17×	`prod-exp`
15×	`1-exp`
13×	`associate-/l*`
11×	`cbrt-undiv`
10×	`pow1`
7×	`cbrt-unprod`
6×	`rec-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down` `sqrt-prod` `div-inv`
2×	`flip3--` `sqrt-div` `flip--`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `*-commutative` `associate-/l/`

Counts

4 → 121

Calls

4 calls:

18.0ms	(/ (/ 1 1) (* (/ 3.0 (- (sqrt (- (* b b) (* (* 3.0 a) c))) b)) a))
6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (/ 1 1) (* (/ 3.0 (- (sqrt (- (* b b) (* (* 3.0 a) c))) b)) a))
23.0ms	(* (* 3.0 a) c)
45.0ms	(- (* b b) (* (* 3.0 a) c))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify79.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	681	1180
1	3335	1002
2	5002	963

prune232.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.4b

regimes512.0ms

Accuracy

85% (4.3b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 34.2b

bsearch145.0ms

Steps

Iters	Range		Point
10	1.6961005291296945e-95	4.32588531784649e-85	1.2529910715609764e-90
10	-5.769371586257069e+162	-1.6124847451767553e+146	-1.4052299045085703e+151

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample1.6s

Algorithm

intervals

Results

390.0ms	5819×	body	80	valid
371.0ms	1081×	body	2560	valid
249.0ms	903×	body	1280	valid
181.0ms	2983×	body	80	nan
99.0ms	455×	body	640	valid
45.0ms	113×	body	5120	valid
36.0ms	215×	body	320	valid
13.0ms	109×	body	160	valid