Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
7.0ms	181×	body	80	valid
6.0ms	36×	body	1280	valid
3.0ms	99×	body	80	nan
3.0ms	20×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	1×	body	160	valid

simplify11.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.6b	(- (* b b) (* (* 4.0 a) c))
23.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

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:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
73.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
41.0ms	(- (* b b) (* (* 4.0 a) c))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (44.0ms)

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

prune289.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.4b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.5b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite64.0ms

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:

10.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series504.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
167.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
175.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
92.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify141.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	829	5119
1	3763	3863
2	5001	3860

prune549.0ms

Filtered

244 candidates to 141 candidates (57.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize27.0ms

Local error

Found 4 expressions with local error:

10.5b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
21×	`times-frac`
19×	`add-cube-cbrt`
13×	`sqrt-prod`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1` `associate-/r*`
6×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3--` `distribute-rgt-neg-in` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 100

Calls

4 calls:

13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify78.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	363	1311
1	1840	1237
2	5001	1228

prune475.0ms

Filtered

112 candidates to 87 candidates (77.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.6b	(- (* b b) (* (* 4.0 a) c))
23.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

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:

15.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	514	1011
1	2322	856
2	5001	843

prune287.0ms

Filtered

112 candidates to 85 candidates (75.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.0b

regimes215.0ms

Accuracy

80.3% (5.3b remaining)

Error of 11.0b against oracle of 5.8b and baseline of 32.6b

bsearch126.0ms

Steps

Iters	Range		Point
8	3.7617494421382894e-70	2.7052557960737888e-67	7.743214049057519e-69
10	-2693.2368339428763	-1.4570494276460042e-08	-2655.8773955326765

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	16
1	38	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

263.0ms	1141×	body	2560	valid
229.0ms	5762×	body	80	valid
177.0ms	938×	body	1280	valid
110.0ms	2987×	body	80	nan
69.0ms	465×	body	640	valid
25.0ms	91×	body	5120	valid
25.0ms	232×	body	320	valid
8.0ms	110×	body	160	valid