Details

sample79.0ms

Algorithm

intervals

Results

16.0ms	204×	body	80	valid
13.0ms	28×	body	2560	valid
10.0ms	91×	body	80	nan
9.0ms	25×	body	1280	valid
4.0ms	13×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify18.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite73.0ms

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:

36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
21.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune346.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

52.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
12.0ms	(+ (- 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))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
75.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
42.0ms	(- (* b b) (* 4.0 (* a c)))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify59.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	515	1011
1	2277	856
2	5001	843

prune298.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

28.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
12.0ms	(+ (- 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))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
75.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms	(- (* b b) (* 4.0 (* a c)))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify70.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	556	1665
1	2664	1442
2	5002	1371

prune316.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
0.8b	(- (* b b) (* 4.0 (* a c)))
20.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series226.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* 4.0 (* a c)))
45.0ms	(- (* b b) (* 4.0 (* a c)))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify87.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	170	540
1	622	506
2	2864	498
3	5001	488

prune279.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.2b

regimes316.0ms

Accuracy

83.1% (4.9b remaining)

Error of 10.6b against oracle of 5.7b and baseline of 34.9b

bsearch119.0ms

Steps

Iters	Range		Point
8	1.0581952271802821e-68	3.094434386839899e-66	2.8340580980410285e-68
8	-6.6886088143369254e+38	-2.2615366197350152e+35	-6.6114837319571935e+38

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample1.3s

Algorithm

intervals

Results

296.0ms	1099×	body	2560	valid
272.0ms	5785×	body	80	valid
201.0ms	897×	body	1280	valid
121.0ms	2794×	body	80	nan
83.0ms	483×	body	640	valid
35.0ms	108×	body	5120	valid
30.0ms	232×	body	320	valid
10.0ms	118×	body	160	valid