Details

sample37.0ms

Algorithm

intervals

Results

6.0ms	183×	body	80	valid
5.0ms	28×	body	2560	valid
4.0ms	29×	body	1280	valid
3.0ms	89×	body	80	nan
3.0ms	22×	body	640	valid
1.0ms	5×	body	5120	valid
0.0ms	7×	body	160	valid
0.0ms	1×	body	320	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: 36.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
25.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite108.0ms

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:

63.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
13.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
43.0ms	(- (* b b) (* (* 3.0 a) c))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune266.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.1b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.0b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite189.0ms

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:

29.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
82.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
57.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
143.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
175.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify139.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	825	5119
1	3738	3863
2	5001	3860

prune495.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.1b	(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
10.8b	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
25.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-exp-log`
61×	`add-sqr-sqrt`
60×	`*-un-lft-identity` `prod-diff`
54×	`add-cbrt-cube`
48×	`add-cube-cbrt`
40×	`div-exp`
36×	`sqrt-prod`
30×	`prod-exp`
24×	`distribute-rgt-neg-in`
22×	`cbrt-undiv`
21×	`distribute-lft-neg-in`
16×	`cbrt-unprod`
10×	`fma-neg`
8×	`times-frac` `1-exp` `associate-/l*` `add-log-exp`
7×	`neg-mul-1`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num` `associate-/r*` `div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-sub` `associate-*r/` `neg-log`

Counts

4 → 185

Calls

4 calls:

28.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
42.0ms	(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
74.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
13.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
123.0ms	(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
98.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	946	4085
1	4560	2694
2	5001	2692

prune314.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
25.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

89.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
45.0ms	(- (* b b) (* (* 3.0 a) c))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	645	1311
1	3129	1145
2	5001	1130

prune296.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.5b

regimes299.0ms

Accuracy

82.8% (4.7b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 33.0b

bsearch101.0ms

Steps

Iters	Range		Point
7	2.7637149443965607e-30	2.267024976733402e-28	8.955698051059873e-30
10	-5.024868303916657e+156	-7.485719939656648e+141	-2.675733832275466e+144

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	17
1	39	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

214.0ms	1058×	body	2560	valid
207.0ms	5791×	body	80	valid
144.0ms	934×	body	1280	valid
92.0ms	2915×	body	80	nan
58.0ms	456×	body	640	valid
24.0ms	101×	body	5120	valid
21.0ms	224×	body	320	valid
7.0ms	112×	body	160	valid