Details

sample45.0ms

Algorithm

intervals

Results

10.0ms	40×	body	2560	valid
8.0ms	171×	body	80	valid
7.0ms	35×	body	1280	valid
4.0ms	89×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	1×	body	5120	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite108.0ms

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:

22.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
63.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
12.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
88.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
40.0ms	(- (* b b) (* 4.0 (* a c)))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune416.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
54×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
30×	`add-exp-log`
29×	`add-cube-cbrt`
20×	`associate-/r*`
18×	`add-cbrt-cube`
14×	`div-exp`
12×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-/r/`
9×	`sqrt-prod`
7×	`cbrt-undiv` `flip3--` `flip--`
6×	`pow1` `distribute-rgt-neg-in` `div-inv` `add-log-exp`
4×	`prod-exp` `associate-/l*`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `sqrt-div` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `diff-log` `inv-pow`

Counts

4 → 138

Calls

4 calls:

42.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
49.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series381.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
104.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
63.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	557	2001
1	2735	1754
2	5001	1683

prune543.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.2b	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

23.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
105.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
105.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
64.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify60.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	475	1025
1	2257	896
2	5001	893

prune425.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
0.6b	(- (* b b) (* 4.0 (* a c)))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

23.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
62.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
8.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
89.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
45.0ms	(- (* b b) (* 4.0 (* a c)))
63.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	381	1101
1	1343	1035
2	5001	1026

prune506.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

regimes309.0ms

Accuracy

85.2% (4.2b remaining)

Error of 9.7b against oracle of 5.4b and baseline of 33.9b

bsearch98.0ms

Steps

Iters	Range		Point
8	2.068553019413577e+125	1.5793235108451263e+128	8.824801410527501e+125
4	-9.285856612195885e-64	-5.291128096587059e-64	-5.365827530591872e-64

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	22
1	39	22

end0.0ms

sample1.4s

Algorithm

intervals

Results

405.0ms	5861×	body	80	valid
286.0ms	1087×	body	2560	valid
194.0ms	890×	body	1280	valid
127.0ms	3052×	body	80	nan
82.0ms	476×	body	640	valid
34.0ms	107×	body	5120	valid
24.0ms	195×	body	320	valid
9.0ms	114×	body	160	valid