Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	36×	body	2560	valid
7.0ms	187×	body	80	valid
4.0ms	22×	body	1280	valid
3.0ms	76×	body	80	nan
1.0ms	5×	body	5120	valid
1.0ms	9×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	4×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

12.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
49.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	404	891
1	1481	801
2	5001	796

prune253.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

14.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	533	1804
1	2544	1605
2	5002	1531

prune275.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac`
250×	`add-sqr-sqrt`
249×	`*-un-lft-identity`
149×	`add-cube-cbrt`
87×	`add-exp-log`
58×	`div-exp`
50×	`distribute-lft-out--` `difference-of-squares`
37×	`div-inv`
28×	`sqrt-prod`
27×	`associate-/r*`
25×	`distribute-rgt-neg-in` `add-cbrt-cube`
17×	`associate-/r/`
15×	`rec-exp` `1-exp`
13×	`cbrt-undiv`
12×	`prod-exp`
11×	`flip3--` `flip--`
10×	`add-log-exp`
7×	`associate-/l*`
5×	`pow1`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 314

Calls

4 calls:

21.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
7.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series307.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
44.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify73.0ms

Algorithm

egg-herbie

Counts

326 → 326

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1231	6003
1	5001	5343

prune531.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a)
0.6b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
27×	`associate-l`
23×	`times-frac`
17×	`add-cube-cbrt`
13×	`add-exp-log`
10×	`add-log-exp`
9×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`pow1` `sqrt-prod`
4×	`flip3--` `distribute-rgt-neg-in` `prod-exp` `flip--`
3×	`diff-log` `associate-r` `unswap-sqr`
2×	`sub-neg` `sqrt-div` `div-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

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

series310.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a)
44.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	427	1041
1	1733	934
2	5002	913

prune286.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.9b

regimes267.0ms

Accuracy

84.2% (4.6b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 34.7b

bsearch94.0ms

Steps

Iters	Range		Point
6	1.7071993853452014e+98	1.0593861995340862e+99	1.0479007947857462e+99
8	-2.0898868129100636e-78	-1.06178241226232e-82	-4.653701756906352e-82

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	15
1	32	15

end0.0ms

sample1.1s

Algorithm

intervals

Results

246.0ms	1068×	body	2560	valid
225.0ms	5772×	body	80	valid
178.0ms	919×	body	1280	valid
102.0ms	2858×	body	80	nan
68.0ms	466×	body	640	valid
36.0ms	127×	body	5120	valid
25.0ms	228×	body	320	valid
10.0ms	128×	body	160	valid