Details

sample46.0ms

Algorithm

intervals

Results

10.0ms	186×	body	80	valid
8.0ms	40×	body	2560	valid
5.0ms	31×	body	1280	valid
3.0ms	96×	body	80	nan
2.0ms	8×	body	5120	valid
1.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	9
1	65	9
2	121	9
3	151	9
4	160	9
5	164	9
6	164	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
28.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

75.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
31.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
40.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify77.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	590	3305
1	2101	2212
2	5002	2128

prune352.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.5b

localize7.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune19.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt b)
0.8b	(- (* b b) (* 4.0 (* a c)))
23.1b	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
28.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `sqrt-prod`
2×	`flip3--` `sqrt-div` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `pow1/3` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt b)
9.0ms	(- (* b b) (* 4.0 (* a c)))
0.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt b)
40.0ms	(- (* b b) (* 4.0 (* a c)))
138.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify102.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	246	491
1	810	444
2	3581	426
3	5001	423

prune263.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 8.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
5.6b	(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
22.9b	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))))
28.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`log-prod` `exp-prod` `exp-sum` `sqrt-prod` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `log-pow` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff`
1×	`sub-neg` `rem-sqrt-square` `fma-neg` `diff-log` `prod-diff` `fma-udef` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
0.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* 4.0 (* a c)))
67.0ms	(exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))
127.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify95.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	262	681
1	782	630
2	3362	603
3	5001	584

prune272.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 8.5b

regimes561.0ms

Accuracy

87.1% (4.4b remaining)

Error of 10.2b against oracle of 5.7b and baseline of 40.0b

bsearch97.0ms

Steps

Iters	Range		Point
6	4.231934083523606e+52	2.717919616353272e+53	2.678238127073729e+53
9	-1.1345718484749e-82	-1.1127264026331332e-88	-1.3696943711263392e-83

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	20
1	38	20

end0.0ms

sample1.2s

Algorithm

intervals

Results

237.0ms	1050×	body	2560	valid
222.0ms	5880×	body	80	valid
164.0ms	921×	body	1280	valid
94.0ms	2795×	body	80	nan
58.0ms	426×	body	640	valid
32.0ms	111×	body	5120	valid
24.0ms	231×	body	320	valid
7.0ms	103×	body	160	valid