Details

sample45.0ms

Algorithm

intervals

Results

11.0ms	189×	body	80	valid
6.0ms	34×	body	1280	valid
6.0ms	28×	body	2560	valid
3.0ms	92×	body	80	nan
2.0ms	16×	body	640	valid
2.0ms	7×	body	5120	valid
0.0ms	4×	body	160	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.1b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite62.0ms

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:

39.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
13.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
97.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
52.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune311.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
1.1b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite61.0ms

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:

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

series318.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
87.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
51.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify51.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (40.0ms)

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

prune322.0ms

Filtered

112 candidates to 88 candidates (78.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.1b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite53.0ms

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:

29.0ms	(/ 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))))

series526.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
266.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify73.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (56.0ms)

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

prune313.0ms

Filtered

146 candidates to 90 candidates (61.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (* 2.0 a)) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
1.1b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(- (* b b) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite79.0ms

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-l`
5×	`distribute-rgt-neg-in` `associate-r`
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-*r/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `distribute-rgt-in` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

54.0ms	(* (/ 1 (* 2.0 a)) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
15.0ms	(+ (- 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))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (/ 1 (* 2.0 a)) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
79.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify68.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	540	1014
1	2814	861
2	5001	850

prune274.0ms

Filtered

113 candidates to 83 candidates (73.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.8b

regimes218.0ms

Accuracy

85.4% (4.1b remaining)

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

bsearch99.0ms

Steps

Iters	Range		Point
7	1.9426594712364374e-87	2.1051237392284573e-85	1.667046824505827e-85
8	-3.734333779790662e+128	-2.2987999557012895e+125	-5.238946631357967e+127

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

240.0ms	1050×	body	2560	valid
230.0ms	5875×	body	80	valid
162.0ms	905×	body	1280	valid
106.0ms	2863×	body	80	nan
67.0ms	457×	body	640	valid
27.0ms	99×	body	5120	valid
26.0ms	212×	body	320	valid
9.0ms	128×	body	160	valid