Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
6.0ms	181×	body	80	valid
5.0ms	33×	body	1280	valid
3.0ms	92×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	6×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	2×	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: 37.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite31.0ms

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:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
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)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

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

prune216.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize15.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.2b	(/ (/ (+ 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)))))
23.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite49.0ms

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:

8.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
14.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
143.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
195.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (90.0ms)

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

prune402.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 3.0 a) c))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.1b	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
23.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

188×	`times-frac`
149×	`add-sqr-sqrt`
122×	`*-un-lft-identity`
94×	`add-exp-log`
85×	`associate-r`
80×	`add-cube-cbrt`
58×	`add-cbrt-cube`
49×	`div-exp`
27×	`cbrt-undiv`
26×	`associate-l`
25×	`prod-exp`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`cbrt-unprod`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in` `add-log-exp`
8×	`div-inv` `unswap-sqr`
7×	`pow1` `associate-/r/`
6×	`flip3--` `flip--`
4×	`rec-exp` `1-exp`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `*-commutative`

Counts

4 → 208

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
57.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* (* 3.0 a) c))
73.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
140.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1327	3225
1	5002	2663

prune534.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

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:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
42.0ms	(- (* b b) (* (* 3.0 a) c))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

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

prune188.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.9b

regimes313.0ms

Accuracy

86.1% (4.2b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 36.1b

bsearch98.0ms

Steps

Iters	Range		Point
9	1.4411111155905935e-45	3.477369949839467e-39	5.998855237299608e-44
7	-4.333566438159085e+154	-4.450998173879583e+152	-4.987323159316817e+152

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	18
1	44	18
2	44	18

end0.0ms

sample1.1s

Algorithm

intervals

Results

231.0ms	1057×	body	2560	valid
223.0ms	5836×	body	80	valid
158.0ms	878×	body	1280	valid
104.0ms	2892×	body	80	nan
63.0ms	459×	body	640	valid
39.0ms	135×	body	5120	valid
25.0ms	245×	body	320	valid
7.0ms	96×	body	160	valid