Details

sample91.0ms

Algorithm

intervals

Results

52.0ms	279×	body	80	valid
14.0ms	96×	body	80	nan

simplify208.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	168
7	168
6	166
5	160
4	151
3	125
2	75
1	38
0	20

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize160.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4 a) c))
1.4b	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
19.8b	(sqrt (- (* b b) (* (* 4 a) c)))
19.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip--`
3×	`diff-log`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 60

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4 a) c))
18.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (* b b) (* (* 4 a) c))
86.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
106.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
122.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
3	2568
2	738
1	234
0	96

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize180.0ms

Local error

Found 4 expressions with local error:

11.5b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
19.8b	(sqrt (- (* b b) (* (* 4 a) c)))
19.8b	(sqrt (- (* b b) (* (* 4 a) c)))
19.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

14.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
18.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
82.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
95.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
113.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify706.0ms

Counts

72 → 72

Iterations

Iter	Nodes
3	2116
2	661
1	222
0	89

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize192.0ms

Local error

Found 4 expressions with local error:

19.8b	(sqrt (- (* b b) (* (* 4 a) c)))
19.8b	(sqrt (- (* b b) (* (* 4 a) c)))
20.6b	(cbrt (- (* b b) (* (* 4 a) c)))
20.6b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`cbrt-div` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

12.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
108.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
157.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
145.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify4.0s

Counts

68 → 68

Iterations

Iter	Nodes
4	6480
3	1892
2	579
1	198
0	87

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.1b

localize210.0ms

Local error

Found 4 expressions with local error:

19.8b	(sqrt (- (* b b) (* (* 4 a) c)))
20.6b	(cbrt (- (* b b) (* (* 4 a) c)))
20.6b	(cbrt (- (* b b) (* (* 4 a) c)))
20.6b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `flip--` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
15.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
112.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
136.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
135.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify4.3s

Counts

66 → 66

Iterations

Iter	Nodes
4	6480
3	1892
2	579
1	198
0	87

prune1.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.1b

regimes486.0ms

Accuracy

94.2% (0.8b remaining)

Error of 7.2b against oracle of 6.5b and baseline of 19.4b

bsearch686.0ms

Steps

Iters	Range		Point
7	5.414027326126016e+143	6.558935220062663e+145	6.7864129831087e+143
9	-2.1186688695348193e+154	-5.841327702345065e+146	-1.3622257246714918e+154

simplify20.0ms

Iterations

Iter	Nodes
2	52
1	52
0	43

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.8s	8738×	body	80	valid
498.0ms	2886×	body	80	nan