Details

sample319.0ms

Algorithm

intervals

Results

11.0ms	205×	body	80	valid
7.0ms	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	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	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune4.0ms

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

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

10.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune239.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	8	93

Merged error: 6.0b

Counts

93 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

13.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
34.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	569	2098
1	2561	1898
2	5002	1761

prune256.0ms

Filtered

174 candidates to 85 candidates (48.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	171	3	174
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	173	9	182

Merged error: 5.9b

Counts

182 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-l`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-r`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `prod-exp` `difference-of-squares`
3×	`unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `sqrt-div` `diff-log` `associate-*r/` `div-exp` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

14.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
36.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	402	793
1	1580	706
2	5002	698

prune207.0ms

Filtered

100 candidates to 71 candidates (71.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	100	9	109

Merged error: 5.9b

Counts

109 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.3b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.8b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
158×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
89×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 206

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
140.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
170.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	741	3477
1	3292	3295
2	5001	3269

prune455.0ms

Filtered

218 candidates to 146 candidates (67.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	215	3	218
Fresh	2	4	6
Picked	1	0	1
Done	1	1	2
Total	219	8	227

Merged error: 5.9b

Counts

227 → 8

Details

sample319.0ms

simplify15.0ms

prune4.0ms

localize33.0ms

rewrite31.0ms

series283.0ms

simplify43.0ms

prune239.0ms

localize10.0ms

rewrite37.0ms

series296.0ms

simplify73.0ms

prune256.0ms

localize10.0ms

rewrite32.0ms

series293.0ms

simplify47.0ms

prune207.0ms

localize11.0ms

rewrite55.0ms

series443.0ms

simplify113.0ms

prune455.0ms

regimes189.0ms

bsearch4.0ms

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