Details

sample41.0ms

Algorithm

intervals

Results

6.0ms	184×	body	80	valid
5.0ms	34×	body	1280	valid
5.0ms	25×	body	2560	valid
4.0ms	115×	body	80	nan
2.0ms	9×	body	5120	valid
2.0ms	15×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	5×	body	160	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: 36.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 3.0 a) c))
0.4b	(* (* 3.0 a) c)
1.7b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

10.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(* (* 3.0 a) c)
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series183.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(* (* 3.0 a) c)
68.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
58.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune253.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))
12.2b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
53×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1/2`
15×	`swap-sqr`
10×	`fma-def`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3--` `flip--` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`rem-sqrt-square` `associate-r/` `associate-l/` `sum-log`
1×	`+-commutative` `pow2` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `pow-plus` `sqrt-unprod` `neg-log` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 144

Calls

4 calls:

59.0ms	(* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))
11.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
10.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))
69.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
61.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
59.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	356	1458
1	1500	1280
2	5001	1245

prune353.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ b (sqrt (- (* b b) (* (* 3.0 a) c))))
3.5b	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
10.2b	(/ (+ 0 (* (* 3.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
117×	`*-un-lft-identity`
76×	`add-sqr-sqrt`
75×	`add-cube-cbrt`
45×	`associate-/l*`
40×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
21×	`distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r*`
10×	`neg-mul-1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `distribute-neg-frac` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-def` `sqrt-prod` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `sum-log` `flip--`

Counts

4 → 209

Calls

4 calls:

15.0ms	(+ b (sqrt (- (* b b) (* (* 3.0 a) c))))
108.0ms	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
73.0ms	(/ (+ 0 (* (* 3.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ b (sqrt (- (* b b) (* (* 3.0 a) c))))
127.0ms	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
151.0ms	(/ (+ 0 (* (* 3.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))))
62.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify117.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	822	3590
1	3789	3333
2	5001	3330

prune635.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.6b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ b (sqrt (- (* b b) (* (* 3.0 a) c))))
2.9b	(/ (* 3.0 a) (/ (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
3.5b	(/ (* (/ 1 (- 1)) (/ (* 3.0 a) (/ (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))) c))) (* 3.0 a))
24.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

235×	`add-exp-log`
133×	`add-cbrt-cube`
116×	`div-exp`
79×	`prod-exp`
62×	`cbrt-undiv`
41×	`times-frac` `cbrt-unprod`
36×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
17×	`associate-/r*`
10×	`rec-exp` `1-exp`
7×	`distribute-lft-out`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`fma-def` `sqrt-prod` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l*`
1×	`+-commutative` `frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `associate-l/` `sum-log` `associate-/r/` `flip--` `flip-+`

Counts

4 → 170

Calls

4 calls:

14.0ms	(+ b (sqrt (- (* b b) (* (* 3.0 a) c))))
37.0ms	(/ (* 3.0 a) (/ (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
46.0ms	(/ (* (/ 1 (- 1)) (/ (* 3.0 a) (/ (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))) c))) (* 3.0 a))
10.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ b (sqrt (- (* b b) (* (* 3.0 a) c))))
171.0ms	(/ (* 3.0 a) (/ (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
140.0ms	(/ (* (/ 1 (- 1)) (/ (* 3.0 a) (/ (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))) c))) (* 3.0 a))
62.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1118	2861
1	5001	2126

prune318.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.1b

regimes331.0ms

Accuracy

91.8% (1.7b remaining)

Error of 10.3b against oracle of 8.6b and baseline of 29.5b

bsearch153.0ms

Steps

Iters	Range	Point
9	2.5943009456277367e+151	2.863179527023367e+158	1.4992330086717143e+153
6	-3.405927582379186e-150	-4.860750269204613e-151	-4.9276367402926466e-151
7	-3.260864156300871e+111	-2.161458270686658e+109	-2.3929031452945402e+111

Iters

Range

Point

2.5943009456277367e+151

2.863179527023367e+158

1.4992330086717143e+153

-3.405927582379186e-150

-4.860750269204613e-151

-4.9276367402926466e-151

-3.260864156300871e+111

-2.161458270686658e+109

-2.3929031452945402e+111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	54
1	61	54
2	61	54

end0.0ms

sample1.1s

Algorithm

intervals

Results

210.0ms	1059×	body	2560	valid
203.0ms	5786×	body	80	valid
148.0ms	897×	body	1280	valid
99.0ms	2934×	body	80	nan
63.0ms	489×	body	640	valid
28.0ms	114×	body	5120	valid
22.0ms	230×	body	320	valid
8.0ms	119×	body	160	valid