Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	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	5×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	4×	body	160	valid

simplify12.0ms

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

prune3.0ms

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)))

rewrite60.0ms

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:

39.0ms	(/ (+ (- 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)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

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

prune304.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize12.0ms

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)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`prod-diff`
15×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `fma-neg` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 103

Calls

4 calls:

31.0ms	(/ (- b (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 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)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (- b (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
79.0ms	(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	484	1547
1	1813	1147
2	5001	1128

prune478.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize13.0ms

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)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
11×	`add-cube-cbrt`
10×	`fma-def` `prod-exp` `add-log-exp`
7×	`pow1` `associate-r`
5×	`distribute-rgt-neg-in` `associate-l`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
3×	`distribute-lft-neg-in` `flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

52.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	514	1011
1	2322	856
2	5001	843

prune303.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.8b

localize14.0ms

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)))

rewrite18.0ms

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))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
47.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify91.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	170	542
1	665	506
2	2968	498
3	5001	488

prune270.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.8b

regimes194.0ms

Accuracy

85% (4.4b remaining)

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

bsearch122.0ms

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	34	15
1	36	15
2	36	15

end0.0ms

sample1.2s

Algorithm

intervals

Results

255.0ms	1117×	body	2560	valid
218.0ms	5730×	body	80	valid
177.0ms	928×	body	1280	valid
113.0ms	2856×	body	80	nan
67.0ms	473×	body	640	valid
27.0ms	100×	body	5120	valid
26.0ms	244×	body	320	valid
8.0ms	108×	body	160	valid