Details

sample105.0ms

Algorithm

intervals

Results

64.0ms	276×	body	80	valid
19.0ms	96×	body	80	nan

simplify147.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	152
7	152
6	151
5	144
4	132
3	101
2	62
1	35
0	20

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize176.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4 a) c))
1.4b	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.1b	(sqrt (- (* b b) (* (* 4 a) c)))
20.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite57.0ms

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:

13.0ms	(- (* b b) (* (* 4 a) c))
16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
19.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b b) (* (* 4 a) c))
90.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
93.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
125.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify939.0ms

Counts

72 → 72

Iterations

Iter	Nodes
3	2568
2	738
1	234
0	96

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize196.0ms

Local error

Found 4 expressions with local error:

8.3b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
20.1b	(sqrt (- (* b b) (* (* 4 a) c)))
20.1b	(sqrt (- (* b b) (* (* 4 a) c)))
20.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite56.0ms

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:

15.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
13.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
108.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
109.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
99.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify961.0ms

Counts

72 → 72

Iterations

Iter	Nodes
3	2116
2	661
1	222
0	89

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.1b

localize214.0ms

Local error

Found 4 expressions with local error:

20.1b	(sqrt (- (* b b) (* (* 4 a) c)))
20.1b	(sqrt (- (* b b) (* (* 4 a) c)))
20.8b	(cbrt (- (* b b) (* (* 4 a) c)))
20.8b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite44.0ms

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:

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

series442.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
85.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
144.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
112.0ms	(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

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.1b

localize175.0ms

Local error

Found 4 expressions with local error:

20.1b	(sqrt (- (* b b) (* (* 4 a) c)))
20.8b	(cbrt (- (* b b) (* (* 4 a) c)))
20.8b	(cbrt (- (* b b) (* (* 4 a) c)))
20.8b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite34.0ms

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:

12.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
7.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
126.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
123.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
135.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify4.2s

Counts

66 → 66

Iterations

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

prune1.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.1b

regimes567.0ms

Accuracy

93.8% (0.8b remaining)

Error of 7.3b against oracle of 6.6b and baseline of 19.1b

bsearch399.0ms

Steps

Iters	Range		Point
9	1.5347927881719531e+137	5.414027326126016e+143	4.3408267342133627e+139
10	-1.4822773699476263e+142	-1.1905227125653903e+132	-1.4623077909156017e+142

simplify17.0ms

Iterations

Iter	Nodes
2	52
1	52
0	43

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.3s	8792×	body	80	valid
583.0ms	2909×	body	80	nan