Details

sample70.0ms

Algorithm

intervals

Results

10.0ms	194×	body	80	valid
9.0ms	92×	body	80	nan
8.0ms	34×	body	1280	valid
8.0ms	25×	body	2560	valid
3.0ms	13×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	5×	body	320	valid
1.0ms	5×	body	160	valid

simplify9.0ms

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

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: 31.7b

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))
1.0b	(- (* b b) (* (* 3.0 a) c))
1.1b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

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))
3.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

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

prune164.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 4.4b

Counts

83 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.5b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.6b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite42.0ms

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))
16.0ms	(/ (/ (+ 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)))))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series119.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
42.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
55.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (90.0ms)

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

prune327.0ms

Filtered

106 candidates to 160 candidates (-50.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	160	11	171

Merged error: 4.4b

Counts

171 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

8.2b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
10.5b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))))
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite21.0ms

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:

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

series102.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
54.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (66.0ms)

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

prune255.0ms

Filtered

79 candidates to 92 candidates (-16.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	92	11	103

Merged error: 4.4b

Counts

103 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.5b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
10.6b	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
20.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac`
19×	`cbrt-undiv` `div-exp`
18×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
17×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*r/` `associate-/r/`
8×	`associate-/l*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/r*`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 110

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
13.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
43.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
55.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify118.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	679	1938
1	4478	1484
2	5001	1443

prune155.0ms

Filtered

81 candidates to 122 candidates (-50.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	124	9	133

Merged error: 4.3b

Counts

133 → 9

regimes459.0ms

Accuracy

82.6% (4.7b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 32.6b

bsearch70.0ms

Steps

Iters	Range		Point
8	4.6842429409994347e-64	1.8297242317365662e-59	6.377775949629369e-64
11	-1.425910122141892e+88	-5.686279252022679e+68	-1.4133850058944391e+88

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms

sample1.5s

Algorithm

intervals

Results

310.0ms	1042×	body	2560	valid
303.0ms	5838×	body	80	valid
229.0ms	915×	body	1280	valid
137.0ms	2765×	body	80	nan
92.0ms	470×	body	640	valid
38.0ms	105×	body	5120	valid
35.0ms	227×	body	320	valid
12.0ms	120×	body	160	valid

Details

sample70.0ms

simplify9.0ms

prune3.0ms

localize10.0ms

rewrite27.0ms

series63.0ms

simplify44.0ms

prune164.0ms

localize15.0ms

rewrite42.0ms

series119.0ms

simplify114.0ms

prune327.0ms

localize18.0ms

rewrite21.0ms

series102.0ms

simplify80.0ms

prune255.0ms

localize14.0ms

rewrite39.0ms

series120.0ms

simplify118.0ms

prune155.0ms

regimes459.0ms

bsearch70.0ms

simplify1.0ms

end0.0ms

sample1.5s

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