Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
7.0ms	198×	body	80	valid
4.0ms	24×	body	1280	valid
3.0ms	92×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	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	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

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:

36.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735

prune401.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- b (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 2.0 a)))
0.9b	(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
36×	`times-frac`
32×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
16×	`difference-of-squares`
8×	`distribute-lft-out--` `add-log-exp`
7×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
6×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `fma-neg` `flip--` `log1p-expm1-u`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 136

Calls

4 calls:

34.0ms	(/ (- b (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 2.0 a)))
16.0ms	(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (- b (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 2.0 a)))
73.0ms	(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	571	2159
1	2269	1775
2	5001	1756

prune347.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- b (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (- (* 2.0 a))))
0.9b	(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
29×	`add-cube-cbrt`
22×	`associate-r`
20×	`times-frac`
19×	`prod-diff`
14×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `fma-neg` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 125

Calls

4 calls:

37.0ms	(* (- b (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (- (* 2.0 a))))
9.0ms	(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (- b (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (- (* 2.0 a))))
75.0ms	(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify76.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	600	1857
1	2730	1402
2	5001	1372

prune437.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.8b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

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

series229.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
43.0ms	(- (* b b) (* (* 4.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify90.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	170	540
1	665	506
2	2968	498
3	5001	488

prune276.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.8b

regimes187.0ms

Accuracy

85% (4.4b remaining)

Error of 9.8b against oracle of 5.4b and baseline of 34.6b

bsearch128.0ms

Steps

Iters	Range		Point
9	3.6106127752583374e-71	6.7695755698382385e-65	9.390367471089922e-69
9	-8.652530131639494e+154	-2.4576771469086066e+149	-2.9358923729233266e+149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	15
1	38	15
2	38	15

end0.0ms

sample1.2s

Algorithm

intervals

Results

257.0ms	1117×	body	2560	valid
236.0ms	5730×	body	80	valid
166.0ms	928×	body	1280	valid
103.0ms	2856×	body	80	nan
67.0ms	473×	body	640	valid
28.0ms	244×	body	320	valid
28.0ms	100×	body	5120	valid
8.0ms	108×	body	160	valid