Details

sample41.0ms

Algorithm

intervals

Results

8.0ms	38×	body	2560	valid
6.0ms	177×	body	80	valid
4.0ms	26×	body	1280	valid
4.0ms	112×	body	80	nan
3.0ms	20×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	4×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

10.0ms	(* (* 3.0 a) c)
51.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* 3.0 a) c)
107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	457	805
1	2021	703
2	5001	695

prune290.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.2b	(* (* 3.0 a) c)
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(* (* 3.0 a) c)
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 3.0 a) c))
19.0ms	(* (* 3.0 a) c)
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
66.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune242.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.2b	(* (* 3.0 a) c)
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(* (* 3.0 a) c)
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 3.0 a) c))
20.0ms	(* (* 3.0 a) c)
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune252.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.3b	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
21×	`add-cbrt-cube`
14×	`associate-l`
12×	`pow1`
11×	`prod-exp`
10×	`fma-def`
8×	`div-exp` `distribute-lft-out` `add-log-exp`
7×	`distribute-rgt-neg-in` `cbrt-unprod`
6×	`unswap-sqr`
4×	`cbrt-undiv` `expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`rec-exp` `sqrt-div` `1-exp` `sum-log` `*-commutative` `div-inv`
1×	`+-commutative` `neg-sub0` `frac-times` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `neg-log` `associate-l/` `flip--` `flip-+`

Counts

4 → 128

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
56.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
109.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	686	1261
1	3404	1097
2	5002	1084

prune334.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

regimes380.0ms

Accuracy

84.2% (4.6b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 34.5b

bsearch112.0ms

Steps

Iters	Range		Point
8	1.1520002419246582e-113	3.708199175444509e-110	2.6814156115033013e-110
9	-3.6963232668708646e+158	-3.0922224130316533e+150	-3.2206966109851016e+150

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

228.0ms	1084×	body	2560	valid
213.0ms	5820×	body	80	valid
151.0ms	889×	body	1280	valid
98.0ms	2903×	body	80	nan
67.0ms	455×	body	640	valid
26.0ms	99×	body	5120	valid
24.0ms	240×	body	320	valid
9.0ms	127×	body	160	valid