Details

sample39.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
6.0ms	181×	body	80	valid
6.0ms	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	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: 37.0b

localize9.0ms

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)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

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

series283.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
44.0ms	(- (* b b) (* (* 3.0 a) c))
74.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
63.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune279.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize17.0ms

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)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 232

Calls

4 calls:

10.0ms	(- (- 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))
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
138.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
166.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify139.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	825	5119
1	3738	3863
2	5001	3860

prune526.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize18.0ms

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)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

190×	`add-sqr-sqrt`
188×	`times-frac`
163×	`*-un-lft-identity`
121×	`add-cube-cbrt`
94×	`add-exp-log`
85×	`associate-r`
61×	`prod-diff`
58×	`add-cbrt-cube`
49×	`div-exp`
43×	`sqrt-prod`
31×	`distribute-rgt-neg-in`
27×	`cbrt-undiv`
26×	`associate-l`
25×	`prod-exp`
21×	`distribute-lft-neg-in`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`cbrt-unprod`
11×	`fma-neg`
10×	`add-log-exp`
8×	`div-inv` `unswap-sqr`
7×	`pow1` `neg-mul-1` `associate-/r/`
6×	`flip3--` `flip--`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u`
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 → 288

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
10.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
59.0ms	(* (/ 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)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* (* 3.0 a) c))
72.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
153.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify75.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1510	5648
1	5002	4129

prune606.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`fma-def` `*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`pow1` `distribute-lft-neg-in` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 88

Calls

4 calls:

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

series287.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	234	668
1	888	610
2	3709	588
3	5001	584

prune342.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.9b

regimes279.0ms

Accuracy

85.5% (4.4b remaining)

Error of 10.1b against oracle of 5.7b and baseline of 36.1b

bsearch205.0ms

Steps

Iters	Range		Point
9	1.4411111155905935e-45	3.477369949839467e-39	8.172328003229442e-43
7	4.5889784209003685e-58	1.26880125744389e-56	8.284843074981433e-57
9	1.6136504421647031e-96	5.650527849255048e-90	2.0821834876358133e-90
7	-4.5555429976450076e+126	-1.4509995558059801e+125	-1.2448541423515275e+126

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	39
1	46	39
2	49	39
3	49	39

end0.0ms

sample1.1s

Algorithm

intervals

Results

232.0ms	1057×	body	2560	valid
219.0ms	5836×	body	80	valid
153.0ms	878×	body	1280	valid
97.0ms	2892×	body	80	nan
67.0ms	459×	body	640	valid
35.0ms	135×	body	5120	valid
25.0ms	245×	body	320	valid
7.0ms	96×	body	160	valid