Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	195×	body	80	valid
8.0ms	37×	body	1280	valid
7.0ms	26×	body	2560	valid
3.0ms	73×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	6×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune2.0ms

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: 32.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.4b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.6b	(- (* b b) (* (* 3.0 a) c))
19.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

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:

11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
82.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
48.0ms	(- (* b b) (* (* 3.0 a) c))
75.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	391	774
1	1518	684
2	5001	674

prune209.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Merged error: 4.6b

Counts

83 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* 3.0 a) c))
3.0b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.6b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
19.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite46.0ms

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:

3.0ms	(- (* b b) (* (* 3.0 a) c))
20.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series636.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 3.0 a) c))
228.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
287.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	634	2580
1	3161	2341
2	5001	2328

prune368.0ms

Filtered

160 candidates to 106 candidates (66.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	159	13	172

Merged error: 4.5b

Counts

172 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

9.7b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))))
10.2b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
19.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))
19.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube`
5×	`difference-of-squares`
4×	`flip3--` `sqrt-div` `associate-/r*` `flip--`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

4 → 80

Calls

4 calls:

8.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))))
4.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

294.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))))
80.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
75.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify78.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	404	1604
1	1921	1363
2	5001	1321

prune308.0ms

Filtered

92 candidates to 79 candidates (85.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	92	13	105

Merged error: 4.5b

Counts

105 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
1.4b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.6b	(- (* b b) (* (* 3.0 a) c))
19.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
113×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
61×	`add-cube-cbrt`
26×	`distribute-lft-out`
19×	`associate-/l*`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `div-exp` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `sqrt-div` `div-sub` `sum-log` `flip--`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `neg-log` `clear-num` `flip-+` `associate-/l/`

Counts

4 → 137

Calls

4 calls:

17.0ms	(/ (/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) a)
83.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms	(- (* b b) (* (* 3.0 a) c))
77.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	601	1956
1	2340	1862
2	5001	1841

prune296.0ms

Filtered

149 candidates to 102 candidates (68.5%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	2	8	10
Picked	0	1	1
Done	0	2	2
Total	149	13	162

Merged error: 4.5b

Counts

162 → 13

regimes680.0ms

Accuracy

84.1% (4.3b remaining)

Error of 10.1b against oracle of 5.8b and baseline of 32.8b

bsearch118.0ms

Steps

Iters	Range		Point
10	9.076168226220815e-77	1.5530881076411509e-65	6.779092232466221e-73
7	-2.699945253400381e+124	-1.5580135688955996e+123	-1.0469728991192871e+124

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms

sample1.3s

Algorithm

intervals

Results

276.0ms	5912×	body	80	valid
275.0ms	1064×	body	2560	valid
185.0ms	861×	body	1280	valid
133.0ms	2882×	body	80	nan
77.0ms	454×	body	640	valid
35.0ms	110×	body	5120	valid
33.0ms	227×	body	320	valid
10.0ms	116×	body	160	valid

Details

sample43.0ms

simplify11.0ms

prune2.0ms

localize10.0ms

rewrite28.0ms

series369.0ms

simplify67.0ms

prune209.0ms

localize14.0ms

rewrite46.0ms

series636.0ms

simplify114.0ms

prune368.0ms

localize18.0ms

rewrite22.0ms

series525.0ms

simplify78.0ms

prune308.0ms

localize11.0ms

rewrite39.0ms

series356.0ms

simplify70.0ms

prune296.0ms

regimes680.0ms

bsearch118.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling