Details

sample48.0ms

Algorithm

intervals

Results

10.0ms	194×	body	80	valid
9.0ms	33×	body	2560	valid
5.0ms	23×	body	1280	valid
5.0ms	96×	body	80	nan
3.0ms	18×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	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: 35.1b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
25.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

5.0ms	(* (* 4.0 a) c)
8.0ms	(+ (- 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)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 4.0 a) c)
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune178.0ms

Filtered

72 candidates to 52 candidates (72.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	6	73

Merged error: 12.9b

Counts

73 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
2.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.6b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

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×	`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` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
150.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
180.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify118.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	640	2579
1	3155	2333
2	5001	2320

prune407.0ms

Filtered

160 candidates to 106 candidates (66.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	153	7	160
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	154	12	166

Merged error: 12.4b

Counts

166 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* b b) (- 0 (* 4.0 (* a c))))
2.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
9.6b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))))
25.3b	(sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))

rewrite54.0ms

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`
9×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1`
4×	`div-inv`
3×	`flip3--` `flip3-+` `flip--` `flip-+` `associate-/l/`
2×	`associate-+r+` `frac-2neg` `sub0-neg` `sqrt-div` `prod-exp` `clear-num` `sum-log` `cbrt-unprod`
1×	`+-commutative` `associate-+r-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `unsub-neg`

Counts

4 → 153

Calls

4 calls:

5.0ms	(+ (* b b) (- 0 (* 4.0 (* a c))))
22.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
14.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))))
5.0ms	(sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* b b) (- 0 (* 4.0 (* a c))))
143.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
180.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))))
73.0ms	(sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))

simplify108.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	646	2793
1	3132	2522
2	5001	2507

prune392.0ms

Filtered

165 candidates to 108 candidates (65.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	165	12	177

Merged error: 12.4b

Counts

177 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
13.0b	(/ (* 2.0 a) (* 4.0 (* a c)))
25.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

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

series203.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	429	637
1	2471	542
2	5003	534

prune183.0ms

Filtered

82 candidates to 55 candidates (67.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	83	11	94

Merged error: 8.9b

Counts

94 → 11

regimes200.0ms

Accuracy

96.2% (0.8b remaining)

Error of 8.7b against oracle of 7.9b and baseline of 29.3b

bsearch172.0ms

Steps

Iters	Range	Point
8	9.372835355027594e+147	1.4145176839448307e+152	1.1588673707323962e+152
6	1.8738695677263956e-213	2.1098662063919667e-212	1.9146441501386442e-213
7	-1.573165836586651e+155	-6.856469880078083e+152	-1.35463732932136e+154

Iters

Range

Point

9.372835355027594e+147

1.4145176839448307e+152

1.1588673707323962e+152

1.8738695677263956e-213

2.1098662063919667e-212

1.9146441501386442e-213

-1.573165836586651e+155

-6.856469880078083e+152

-1.35463732932136e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	37
1	54	37

end0.0ms

sample1.4s

Algorithm

intervals

Results

324.0ms	1092×	body	2560	valid
305.0ms	5847×	body	80	valid
219.0ms	875×	body	1280	valid
150.0ms	2883×	body	80	nan
91.0ms	451×	body	640	valid
39.0ms	111×	body	5120	valid
35.0ms	233×	body	320	valid
11.0ms	118×	body	160	valid