Details

sample40.0ms

Algorithm

intervals

Results

7.0ms	189×	body	80	valid
6.0ms	37×	body	1280	valid
5.0ms	27×	body	2560	valid
3.0ms	98×	body	80	nan
2.0ms	16×	body	640	valid
0.0ms	2×	body	5120	valid
0.0ms	5×	body	320	valid
0.0ms	4×	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: 32.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b	(- (* b b) (* (* 3.0 a) c))
20.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite107.0ms

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:

65.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms	(- (* b b) (* (* 3.0 a) c))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
68.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
43.0ms	(- (* b b) (* (* 3.0 a) c))
64.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

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

prune288.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
2.5b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.2b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
84.0ms	(/ (/ (+ 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)))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b b) (* (* 3.0 a) c))
132.0ms	(/ (/ (+ 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)))))
63.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify126.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	669	2663
1	3431	2412
2	5001	2406

prune435.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
2.5b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
9.1b	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
20.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac`
19×	`cbrt-undiv` `div-exp`
18×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
17×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*r/` `associate-/r/`
8×	`associate-/l*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 120

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
44.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
39.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 3.0 a) c))
133.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
163.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
64.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify125.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	714	2019
1	4679	1554
2	5001	1549

prune357.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
2.5b	(/ (/ (- (* c (* 3.0 a))) (- (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))) a)
9.1b	(/ (- (* c (* 3.0 a))) (- (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
20.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
115×	`add-sqr-sqrt`
114×	`add-cube-cbrt` `*-un-lft-identity`
62×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
48×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-*r/` `associate-/r/` `distribute-neg-frac`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`div-sub` `distribute-frac-neg` `sqrt-prod`
2×	`neg-sub0` `frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 289

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
27.0ms	(/ (/ (- (* c (* 3.0 a))) (- (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))) a)
14.0ms	(/ (- (* c (* 3.0 a))) (- (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 3.0 a) c))
210.0ms	(/ (/ (- (* c (* 3.0 a))) (- (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))) a)
211.0ms	(/ (- (* c (* 3.0 a))) (- (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1305	5662
1	5002	5457

prune996.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

regimes321.0ms

Accuracy

93.8% (1.5b remaining)

Error of 7.1b against oracle of 5.6b and baseline of 29.8b

bsearch170.0ms

Steps

Iters	Range	Point
9	2.9889477240664976e+32	2.7299937233713154e+37	2.6958459483246036e+37
10	-2.8640974595711112e-244	-2.9259838810542055e-263	-1.4498491900648225e-249
8	-1.725175994935517e+137	-3.3947692407777386e+132	-2.3290627742868755e+134

Iters

Range

Point

2.9889477240664976e+32

2.7299937233713154e+37

2.6958459483246036e+37

-2.8640974595711112e-244

-2.9259838810542055e-263

-1.4498491900648225e-249

-1.725175994935517e+137

-3.3947692407777386e+132

-2.3290627742868755e+134

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	30
1	55	30
2	55	30

end0.0ms

sample1.2s

Algorithm

intervals

Results

220.0ms	5864×	body	80	valid
220.0ms	1096×	body	2560	valid
147.0ms	911×	body	1280	valid
100.0ms	3004×	body	80	nan
61.0ms	464×	body	640	valid
26.0ms	101×	body	5120	valid
20.0ms	209×	body	320	valid
8.0ms	125×	body	160	valid