Details

sample52.0ms

Algorithm

intervals

Results

9.0ms	32×	body	2560	valid
9.0ms	38×	body	1280	valid
9.0ms	168×	body	80	valid
4.0ms	89×	body	80	nan
4.0ms	20×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	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: 36.1b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune237.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	9	90

Merged error: 5.9b

Counts

90 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

14.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series319.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
51.0ms	(- (* b b) (* 4.0 (* a c)))
82.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify73.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	533	1802
1	2544	1603
2	5002	1529

prune244.0ms

Filtered

137 candidates to 72 candidates (52.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	137	9	146

Merged error: 5.8b

Counts

146 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (* 2.0 a)) (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac`
250×	`add-sqr-sqrt`
249×	`*-un-lft-identity`
149×	`add-cube-cbrt`
87×	`add-exp-log`
58×	`div-exp`
50×	`distribute-lft-out--` `difference-of-squares`
37×	`div-inv`
28×	`sqrt-prod`
27×	`associate-/r*`
25×	`distribute-rgt-neg-in` `add-cbrt-cube`
17×	`associate-/r/`
15×	`rec-exp` `1-exp`
13×	`cbrt-undiv`
12×	`prod-exp`
11×	`flip3--` `flip--`
10×	`add-log-exp`
7×	`associate-/l*`
5×	`pow1`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 314

Calls

4 calls:

22.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
50.0ms	(- (* b b) (* 4.0 (* a c)))
75.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify87.0ms

Algorithm

egg-herbie

Counts

326 → 326

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1231	6001
1	5001	5341

prune474.0ms

Filtered

326 candidates to 130 candidates (39.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	324	2	326
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	325	10	335

Merged error: 5.8b

Counts

335 → 10

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	3	3
Total	10	10

Merged error: 5.8b

Counts

10 → 10

Details

sample52.0ms

simplify15.0ms

prune3.0ms

localize18.0ms

rewrite31.0ms

series305.0ms

simplify47.0ms

prune237.0ms

localize13.0ms

rewrite39.0ms

series319.0ms

simplify73.0ms

prune244.0ms

localize15.0ms

rewrite61.0ms

series318.0ms

simplify87.0ms

prune474.0ms

localize4.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune0.0ms

regimes352.0ms

bsearch3.0ms

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