Details

sample47.0ms

Algorithm

intervals

Results

10.0ms	205×	body	80	valid
8.0ms	29×	body	2560	valid
6.0ms	28×	body	1280	valid
4.0ms	94×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify11.0ms

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

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: 34.0b

Counts

2 → 1

localize12.0ms

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)))
0.8b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

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:

16.0ms	(/ (+ (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))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674

prune221.0ms

Filtered

82 candidates to 63 candidates (76.8%)

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: 6.0b

Counts

83 → 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)))
0.8b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
45×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`div-exp`
11×	`associate-/r*`
10×	`distribute-lft-out` `add-log-exp`
9×	`associate-/r/`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `flip3-+` `flip-+` `div-inv`
3×	`rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 114

Calls

4 calls:

13.0ms	(/ 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))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
43.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify67.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	521	1586
1	2522	1373
2	5002	1306

prune232.0ms

Filtered

126 candidates to 71 candidates (56.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	126	9	135

Merged error: 5.9b

Counts

135 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.8b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

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:

8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series624.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
292.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
185.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify100.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	640	2692
1	2911	2439
2	5001	2426

prune358.0ms

Filtered

166 candidates to 110 candidates (66.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	166	9	175

Merged error: 5.9b

Counts

175 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.1b	(/ 2.0 (* a c))
16.5b	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
22.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

191×	`times-frac`
151×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
99×	`add-exp-log`
85×	`associate-r`
82×	`add-cube-cbrt`
63×	`add-cbrt-cube`
51×	`div-exp`
29×	`cbrt-undiv`
26×	`associate-l` `prod-exp`
20×	`distribute-lft-out--` `difference-of-squares`
16×	`cbrt-unprod`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
9×	`div-inv`
8×	`add-log-exp` `unswap-sqr`
7×	`pow1` `associate-/r/`
5×	`flip3--` `flip--`
4×	`rec-exp` `1-exp`
3×	`associate-/l*`
2×	`sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `associate-/r` `-commutative`

Counts

4 → 217

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(/ 2.0 (* a c))
60.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series315.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.0ms	(/ 2.0 (* a c))
146.0ms	(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1331	3208
1	5002	2733

prune468.0ms

Filtered

229 candidates to 141 candidates (61.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	229	9	238

Merged error: 5.9b

Counts

238 → 9

Details

sample47.0ms

simplify11.0ms

prune3.0ms

localize12.0ms

rewrite33.0ms

series303.0ms

simplify45.0ms

prune221.0ms

localize13.0ms

rewrite32.0ms

series340.0ms

simplify67.0ms

prune232.0ms

localize15.0ms

rewrite48.0ms

series624.0ms

simplify100.0ms

prune358.0ms

localize15.0ms

rewrite89.0ms

series315.0ms

simplify56.0ms

prune468.0ms

regimes190.0ms

bsearch3.0ms

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