Details

sample57.0ms

Algorithm

intervals

Results

9.0ms	32×	body	2560	valid
9.0ms	182×	body	80	valid
8.0ms	33×	body	1280	valid
4.0ms	81×	body	80	nan
3.0ms	14×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	5120	valid

simplify9.0ms

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

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: 31.8b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
1.6b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

10.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5002	673

prune147.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 4.1b

Counts

83 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
7.2b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
18.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

7.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
55.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	646	2693
1	3163	2447
2	5003	2434

prune303.0ms

Filtered

111 candidates to 166 candidates (-49.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	162	4	166
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	165	10	175

Merged error: 4.1b

Counts

175 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b	(/ (* 1 (/ 4.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
7.3b	(/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
18.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-exp-log`
54×	`add-cbrt-cube`
40×	`div-exp`
30×	`prod-exp`
22×	`cbrt-undiv`
20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
16×	`cbrt-unprod`
8×	`times-frac` `1-exp` `associate-/l*` `add-log-exp`
7×	`add-cube-cbrt`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
3×	`flip3--` `distribute-rgt-neg-in` `flip--` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num` `associate-/r*` `div-inv`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-sub` `associate-*r/` `neg-log`

Counts

4 → 107

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
28.0ms	(/ (* 1 (/ 4.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
19.0ms	(/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
31.0ms	(/ (* 1 (/ 4.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c)))) (* 2.0 a))
20.0ms	(/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* a c))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify91.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	785	1659
1	4100	1315
2	5001	1303

prune144.0ms

Filtered

68 candidates to 119 candidates (-75.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	121	8	129

Merged error: 4.1b

Counts

129 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.1b	(* (/ 1 a) (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
3.6b	(/ (* 1 (/ 4.0 (* (/ 1 a) (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c)))) (* 2.0 a))
18.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

243×	`add-exp-log`
118×	`div-exp`
101×	`prod-exp`
89×	`add-cbrt-cube`
57×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
38×	`times-frac`
36×	`cbrt-undiv`
31×	`cbrt-unprod`
30×	`1-exp`
25×	`associate-r`
23×	`add-cube-cbrt`
13×	`associate-l`
10×	`rec-exp`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`unswap-sqr`
4×	`distribute-rgt-neg-in`
3×	`div-inv`
2×	`flip3--` `sqrt-div` `diff-log` `associate-*r/` `flip--`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `associate-/r` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 171

Calls

4 calls:

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

series110.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
37.0ms	(* (/ 1 a) (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
44.0ms	(/ (* 1 (/ 4.0 (* (/ 1 a) (/ (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c)))) (* 2.0 a))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1185	2689
1	5001	2126

prune175.0ms

Filtered

91 candidates to 183 candidates (-101.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	183	8	191

Merged error: 4.1b

Counts

191 → 8

regimes428.0ms

Accuracy

89% (2.9b remaining)

Error of 8.9b against oracle of 6.0b and baseline of 32.1b

bsearch111.0ms

Steps

Iters	Range	Point
9	1.318498360392027e-43	5.6448683288908945e-37	5.402086626703997e-37
9	-2.9946619164961094e-294	-1.1315401293481145e-301	-3.3230439988347835e-301
11	-3.2417942991699406e+183	-6.054191780274212e+145	-7.123874050873163e+145

Iters

Range

Point

1.318498360392027e-43

5.6448683288908945e-37

5.402086626703997e-37

-2.9946619164961094e-294

-1.1315401293481145e-301

-3.3230439988347835e-301

-3.2417942991699406e+183

-6.054191780274212e+145

-7.123874050873163e+145

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	29
1	50	29
2	50	29

end0.0ms

sample1.6s

Algorithm

intervals

Results

336.0ms	1099×	body	2560	valid
314.0ms	5825×	body	80	valid
217.0ms	846×	body	1280	valid
138.0ms	2639×	body	80	nan
89.0ms	444×	body	640	valid
44.0ms	116×	body	5120	valid
35.0ms	234×	body	320	valid
10.0ms	103×	body	160	valid

Details

sample57.0ms

simplify9.0ms

prune3.0ms

localize14.0ms

rewrite25.0ms

series63.0ms

simplify42.0ms

prune147.0ms

localize15.0ms

rewrite45.0ms

series127.0ms

simplify109.0ms

prune303.0ms

localize28.0ms

rewrite65.0ms

series82.0ms

simplify91.0ms

prune144.0ms

localize19.0ms

rewrite64.0ms

series110.0ms

simplify46.0ms

prune175.0ms

regimes428.0ms

bsearch111.0ms

simplify2.0ms

end0.0ms

sample1.6s

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