Details

sample41.0ms

Algorithm

intervals

Results

7.0ms	191×	body	80	valid
6.0ms	33×	body	2560	valid
6.0ms	37×	body	1280	valid
3.0ms	96×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
27.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

63.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
38.0ms	(- (* b b) (* (* 3.0 a) c))
69.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
62.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	400	780
1	1529	686
2	5002	675

prune207.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.9b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.7b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
27.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`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 → 154

Calls

4 calls:

22.0ms	(- (- 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)))))
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
129.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
160.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	647	2692
1	3114	2439
2	5001	2426

prune387.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.6b

localize22.0ms

Local error

Found 4 expressions with local error:

5.7b	(exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))
11.3b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))))
15.8b	(- (- b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))
27.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

13.0ms	(exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))
77.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))))
27.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))
162.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))))
68.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))
59.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify79.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	448	1711
1	1916	1544
2	5001	1503

prune335.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0)
0.8b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
27.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

62.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0)
8.0ms	(- (* b b) (* (* 3.0 a) c))
20.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0)
39.0ms	(- (* b b) (* (* 3.0 a) c))
71.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
63.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	350	901
1	1306	833
2	5001	813

prune229.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 8.6b

regimes361.0ms

Accuracy

83.7% (4.4b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 32.5b

bsearch120.0ms

Steps

Iters	Range		Point
11	2.3891583283226283e-88	7.742207968491296e-67	1.6400361122264901e-83
9	-4.3398659734944224e+136	-6.188138656270848e+129	-7.88076297831028e+133

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

222.0ms	1089×	body	2560	valid
210.0ms	5832×	body	80	valid
154.0ms	908×	body	1280	valid
92.0ms	2813×	body	80	nan
71.0ms	473×	body	640	valid
27.0ms	109×	body	5120	valid
25.0ms	232×	body	320	valid
8.0ms	126×	body	160	valid