Details

sample71.0ms

Algorithm

intervals

Results

16.0ms	209×	body	80	valid
11.0ms	31×	body	1280	valid
11.0ms	25×	body	2560	valid
8.0ms	103×	body	80	nan
4.0ms	15×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	1×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.1b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(- (* b b) (* (* 4.0 a) c))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

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:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune274.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	8	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	8	103

Merged error: 3.6b

Counts

103 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.4b	(- (* b b) (* (* 4.0 a) c))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
48×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`associate-/r*`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
9×	`associate-/r/`
8×	`distribute-rgt-neg-in`
6×	`pow1`
5×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 134

Calls

4 calls:

14.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify75.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	556	1665
1	2707	1442
2	5001	1371

prune285.0ms

Filtered

146 candidates to 90 candidates (61.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	145	9	154

Merged error: 3.5b

Counts

154 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.4b	(- (* b b) (* (* 4.0 a) c))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

333×	`times-frac`
224×	`*-un-lft-identity`
125×	`add-sqr-sqrt`
124×	`add-cube-cbrt`
87×	`add-exp-log`
58×	`div-exp`
50×	`distribute-lft-out`
31×	`div-inv`
28×	`distribute-rgt-neg-in`
25×	`add-cbrt-cube`
21×	`associate-/r*`
17×	`associate-/r/`
15×	`rec-exp` `1-exp`
13×	`cbrt-undiv`
12×	`prod-exp`
10×	`fma-def` `add-log-exp`
9×	`flip3-+` `flip-+`
7×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `cbrt-unprod`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 283

Calls

4 calls:

19.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

295 → 295

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1142	4786
1	5001	4210

prune443.0ms

Filtered

295 candidates to 134 candidates (45.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	294	1	295
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	295	9	304

Merged error: 3.5b

Counts

304 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1 (* 2.0 a)))
0.5b	(cbrt (/ 1 (* 2.0 a)))
0.5b	(* (cbrt (/ 1 (* 2.0 a))) (cbrt (/ 1 (* 2.0 a))))
17.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

50×	`cbrt-prod`
30×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`times-frac`
12×	`pow1` `swap-sqr`
10×	`associate-r` `associate-l`
8×	`pow1/3` `div-inv`
6×	`add-exp-log` `cbrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`sqrt-div` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 112

Calls

4 calls:

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

series678.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt (/ 1 (* 2.0 a)))
192.0ms	(cbrt (/ 1 (* 2.0 a)))
229.0ms	(* (cbrt (/ 1 (* 2.0 a))) (cbrt (/ 1 (* 2.0 a))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	289	885
1	1078	816
2	5001	722

prune330.0ms

Filtered

124 candidates to 85 candidates (68.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	124	9	133

Merged error: 3.5b

Counts

133 → 9

regimes177.0ms

Accuracy

88.7% (3.2b remaining)

Error of 8.9b against oracle of 5.7b and baseline of 33.9b

bsearch199.0ms

Steps

Iters	Range	Point
9	1.7536266209730185e+54	9.156208036690931e+61	2.5096626454411205e+56
10	8.752895080382474e-191	7.198562597133285e-172	4.980465732074938e-179
4	-2.2709498629311444e+153	-1.3123487377944479e+153	-1.5396067403637575e+153

Iters

Range

Point

1.7536266209730185e+54

9.156208036690931e+61

2.5096626454411205e+56

8.752895080382474e-191

7.198562597133285e-172

4.980465732074938e-179

-2.2709498629311444e+153

-1.3123487377944479e+153

-1.5396067403637575e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	29
1	51	29
2	51	29

end0.0ms

sample1.4s

Algorithm

intervals

Results

300.0ms	1051×	body	2560	valid
289.0ms	5872×	body	80	valid
205.0ms	896×	body	1280	valid
148.0ms	2929×	body	80	nan
83.0ms	461×	body	640	valid
36.0ms	105×	body	5120	valid
30.0ms	216×	body	320	valid
11.0ms	107×	body	160	valid