Details

sample63.0ms

Algorithm

intervals

Results

17.0ms	194×	body	80	valid
9.0ms	30×	body	2560	valid
8.0ms	100×	body	80	nan
7.0ms	28×	body	1280	valid
3.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	6×	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: 34.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 3.0 a) c)
1.2b	(- (* b b) (* (* 3.0 a) c))
1.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`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-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
2.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
45.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune205.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.2b

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.8b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.8b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite102.0ms

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:

11.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
42.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
36.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
140.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
169.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (89.0ms)

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

prune462.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.9b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
1.4b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0b	(/ (* 3.0 a) (* 3.0 (* a c)))
23.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

2.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	417	636
1	2439	522
2	5001	492

prune223.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 3.0 a) c)
1.2b	(- (* b b) (* (* 3.0 a) c))
1.4b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `associate-r` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `associate-l` `neg-log` `*-commutative`

Counts

4 → 63

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
2.0ms	(- (* b b) (* (* 3.0 a) c))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* 3.0 a) c)
43.0ms	(- (* b b) (* (* 3.0 a) c))
76.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	298	517
1	1262	478
2	5001	471

prune183.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.9b

regimes341.0ms

Accuracy

78.6% (4.8b remaining)

Error of 12.5b against oracle of 7.8b and baseline of 30.0b

bsearch125.0ms

Steps

Iters	Range		Point
5	3.0336165705843857e+124	7.533619617198572e+124	5.486208249157789e+124
10	-2.4076762225838956e-89	-7.528955394503449e-103	-3.581294904804354e-96

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	28
1	46	28
2	46	28

end0.0ms

sample1.5s

Algorithm

intervals

Results

398.0ms	5935×	body	80	valid
268.0ms	1018×	body	2560	valid
191.0ms	2907×	body	80	nan
190.0ms	882×	body	1280	valid
78.0ms	435×	body	640	valid
38.0ms	252×	body	320	valid
36.0ms	116×	body	5120	valid
11.0ms	106×	body	160	valid