Details

analyze1.0s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 25.512052%

Guaranteed chance to sample good point: 74.783178%

sample45.0ms

Algorithm

intervals

Results

12.0ms	32×	body	2560	valid
8.0ms	169×	body	80	valid
7.0ms	28×	body	1280	valid
3.0ms	15×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	18×	body	80	nan
1.0ms	5×	body	320	valid
1.0ms	14×	body	80	invalid
0.0ms	4×	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

prune4.0ms

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: 34.5b

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))
1.2b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.6b	(- (* b b) (* (* 3.0 a) c))
22.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite26.0ms

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))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

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

prune180.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

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: 6.5b

Counts

83 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* 3.0 a) c))
3.3b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.3b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite40.0ms

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)))))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series128.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
45.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
56.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
18.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (91.0ms)

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

prune292.0ms

Filtered

106 candidates to 160 candidates (-50.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	156	4	160
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	160	12	172

Merged error: 6.4b

Counts

172 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* 3.0 a) c))
3.3b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
11.3b	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
22.0b	(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)))

series128.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (* b b) (* (* 3.0 a) c))
44.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
59.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify123.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (107.0ms)

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

prune190.0ms

Filtered

81 candidates to 122 candidates (-50.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	124	10	134

Merged error: 6.4b

Counts

134 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* 3.0 a) c))
3.3b	(/ (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
11.0b	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
13.0ms	(/ (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
10.0ms	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
42.0ms	(/ (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
56.0ms	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify79.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	591	1957
1	2896	1749
2	5001	1733

prune214.0ms

Filtered

98 candidates to 142 candidates (-44.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	143	9	152

Merged error: 6.4b

Counts

152 → 9

Details

analyze1.0s

sample45.0ms

simplify9.0ms

prune4.0ms

localize10.0ms

rewrite26.0ms

series67.0ms

simplify44.0ms

prune180.0ms

localize14.0ms

rewrite40.0ms

series128.0ms

simplify113.0ms

prune292.0ms

localize17.0ms

rewrite39.0ms

series128.0ms

simplify123.0ms

prune190.0ms

localize15.0ms

rewrite35.0ms

series123.0ms

simplify79.0ms

prune214.0ms

regimes442.0ms

bsearch2.0ms

Profiling