Details

sample111.0ms

Algorithm

intervals

Results

31.0ms	18×	body	2560	valid
17.0ms	195×	body	80	valid
16.0ms	34×	body	1280	valid
9.0ms	107×	body	80	nan
4.0ms	13×	body	640	valid
2.0ms	9×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	5×	body	160	valid

simplify186.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	94
7	94
6	93
5	91
4	83
3	68
2	39
1	21
0	12

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
21.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite229.0ms

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:

139.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
42.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
25.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series636.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
138.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
115.0ms	(- (* b b) (* (* 3.0 a) c))
175.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.5s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1328
1	404
0	154

prune760.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c (* 3.0 a))
0.9b	(- (sqrt (- (* b b) (* c (* 3.0 a)))) b)
1.0b	(- (* b b) (* c (* 3.0 a)))
21.8b	(sqrt (- (* b b) (* c (* 3.0 a))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

31.0ms	(* c (* 3.0 a))
83.0ms	(- (sqrt (- (* b b) (* c (* 3.0 a)))) b)
17.0ms	(- (* b b) (* c (* 3.0 a)))
17.0ms	(sqrt (- (* b b) (* c (* 3.0 a))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* c (* 3.0 a))
153.0ms	(- (sqrt (- (* b b) (* c (* 3.0 a)))) b)
80.0ms	(- (* b b) (* c (* 3.0 a)))
131.0ms	(sqrt (- (* b b) (* c (* 3.0 a))))

simplify4.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	3078
2	844
1	282
0	119

prune732.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c (* 3.0 a))
0.9b	(- (sqrt (- (* b b) (* c (* 3.0 a)))) b)
1.0b	(- (* b b) (* c (* 3.0 a)))
21.8b	(sqrt (- (* b b) (* c (* 3.0 a))))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

31.0ms	(* c (* 3.0 a))
83.0ms	(- (sqrt (- (* b b) (* c (* 3.0 a)))) b)
18.0ms	(- (* b b) (* c (* 3.0 a)))
19.0ms	(sqrt (- (* b b) (* c (* 3.0 a))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* c (* 3.0 a))
144.0ms	(- (sqrt (- (* b b) (* c (* 3.0 a)))) b)
93.0ms	(- (* b b) (* c (* 3.0 a)))
139.0ms	(sqrt (- (* b b) (* c (* 3.0 a))))

simplify4.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	3078
2	844
1	282
0	119

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
0.9b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
1.0b	(- (* b b) (* 3.0 (* a c)))
21.8b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

40.0ms	(* 3.0 (* a c))
85.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
18.0ms	(- (* b b) (* 3.0 (* a c)))
19.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series459.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* 3.0 (* a c))
170.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
75.0ms	(- (* b b) (* 3.0 (* a c)))
176.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify4.0s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	2961
2	802
1	276
0	117

prune537.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.9b

regimes897.0ms

Accuracy

82.2% (5.2b remaining)

Error of 10.7b against oracle of 5.5b and baseline of 34.7b

bsearch207.0ms

Steps

Iters	Range		Point
9	1.177766511972955e-157	7.998381519079639e-153	7.923524897992037e-153
6	-4.525167845450207e+100	-9.36795079059543e+99	-2.7668189408748547e+100

simplify12.0ms

Iterations

Iter	Nodes
done	32
1	32
0	27

end0.0ms

sample3.9s

Algorithm

intervals

Results

900.0ms	5752×	body	80	valid
790.0ms	480×	body	640	valid
766.0ms	1081×	body	2560	valid
446.0ms	924×	body	1280	valid
376.0ms	2817×	body	80	nan
68.0ms	97×	body	5120	valid
61.0ms	238×	body	320	valid
21.0ms	120×	body	160	valid