Details

sample47.0ms

Algorithm

intervals

Results

8.0ms	29×	body	1280	valid
7.0ms	32×	body	2560	valid
7.0ms	184×	body	80	valid
4.0ms	94×	body	80	nan
3.0ms	21×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	8×	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: 35.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite57.0ms

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:

34.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
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))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(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

prune252.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite78.0ms

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×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

57.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
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))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms	(- (* b b) (* 4.0 (* a c)))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	469	991
1	2048	866
2	5002	857

prune246.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
19.9b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
10×	`add-log-exp`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`times-frac` `distribute-lft-out` `associate-/l*`
3×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+`
2×	`flip3--` `sqrt-div` `associate-*l/` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 71

Calls

4 calls:

14.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
23.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series365.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
168.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	502	969
1	3079	812
2	5002	794

prune246.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.8b

localize20.0ms

Local error

Found 4 expressions with local error:

6.0b	(+ (- b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
20.9b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a)))
24.1b	(cbrt (- (* b b) (* 4.0 (* a c))))
24.1b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `add-cbrt-cube`
10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
6×	`cbrt-prod`
4×	`pow1` `cbrt-div` `times-frac` `associate-/l*`
3×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+`
2×	`flip3--` `pow1/3` `associate-*l/` `sum-log` `associate-/r/` `flip--` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `frac-2neg` `neg-log` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 68

Calls

4 calls:

5.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
16.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a)))
2.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
2.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series745.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
468.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a)))
94.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
98.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify122.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	730	1666
1	4122	1406
2	5001	1382

prune375.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.8b

regimes244.0ms

Accuracy

85.4% (4.2b remaining)

Error of 9.5b against oracle of 5.4b and baseline of 34.0b

bsearch205.0ms

Steps

Iters	Range		Point
8	9.456042252142157e+48	5.633410846004884e+51	5.5792500737545097e+51
7	-8.729222821301493e-116	-3.4297016692569784e-117	-8.637249247672526e-116
8	-3.850575226512855e-63	-1.8205692925253357e-66	-1.89742085527562e-66
7	-2.7171447498643977e+47	-4.861855348193037e+45	-1.2864134951106807e+46

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	32
1	50	32

end0.0ms

sample1.2s

Algorithm

intervals

Results

237.0ms	1029×	body	2560	valid
234.0ms	5915×	body	80	valid
173.0ms	918×	body	1280	valid
108.0ms	2875×	body	80	nan
67.0ms	457×	body	640	valid
28.0ms	101×	body	5120	valid
22.0ms	196×	body	320	valid
11.0ms	131×	body	160	valid