Details

sample48.0ms

Algorithm

intervals

Results

11.0ms	183×	body	80	valid
8.0ms	33×	body	2560	valid
6.0ms	31×	body	1280	valid
3.0ms	85×	body	80	nan
3.0ms	17×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune4.0ms

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: 35.4b

Counts

2 → 1

localize13.0ms

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))
23.1b	(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:

13.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
91.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
55.0ms	(- (* b b) (* (* 4.0 a) c))
84.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (47.0ms)

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

prune343.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	92	10	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	10	103

Merged error: 7.9b

Counts

103 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
3.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.2b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite47.0ms

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:

4.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
14.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series537.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b b) (* (* 4.0 a) c))
179.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
219.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify135.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	674	2663
1	3462	2412
2	5001	2406

prune505.0ms

Filtered

170 candidates to 117 candidates (68.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	166	4	170
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	170	10	180

Merged error: 7.8b

Counts

180 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
15.3b	(/ (* 2.0 a) (* 4.0 (* a c)))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

11.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
85.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	610	3042
1	3078	1945
2	5002	1857

prune352.0ms

Filtered

162 candidates to 79 candidates (48.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	163	9	172

Merged error: 7.8b

Counts

172 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
144×	`add-sqr-sqrt`
138×	`*-un-lft-identity`
130×	`add-cube-cbrt`
95×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
19×	`neg-mul-1`
13×	`associate-l`
11×	`fma-neg`
10×	`times-frac` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`frac-times` `sqrt-div` `associate-*r/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 289

Calls

4 calls:

26.0ms	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
91.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
86.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify145.0ms

Algorithm

egg-herbie

Counts

301 → 301

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	927	8466
1	3570	5475
2	5002	5159

prune405.0ms

Filtered

301 candidates to 106 candidates (35.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	299	2	301
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	301	9	310

Merged error: 7.8b

Counts

310 → 9

regimes215.0ms

Accuracy

94.4% (1.3b remaining)

Error of 7.2b against oracle of 5.8b and baseline of 30.0b

bsearch249.0ms

Steps

Iters	Range	Point
8	3.182319375801986e+130	1.3165557463351014e+133	1.4487681671356545e+131
10	-3.794709535053859e-185	-7.043002195311016e-204	-4.928841649337541e-202
9	-9.104669698408525e+86	-9.304287469108188e+80	-1.6507510594910507e+86

Iters

Range

Point

3.182319375801986e+130

1.3165557463351014e+133

1.4487681671356545e+131

-3.794709535053859e-185

-7.043002195311016e-204

-4.928841649337541e-202

-9.104669698408525e+86

-9.304287469108188e+80

-1.6507510594910507e+86

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	38
1	66	38
2	70	38
3	70	38

end0.0ms

sample1.4s

Algorithm

intervals

Results

483.0ms	5876×	body	80	valid
268.0ms	1068×	body	2560	valid
180.0ms	882×	body	1280	valid
113.0ms	2898×	body	80	nan
70.0ms	446×	body	640	valid
31.0ms	103×	body	5120	valid
26.0ms	220×	body	320	valid
9.0ms	115×	body	160	valid