Details

sample134.0ms

Algorithm

intervals

Results

35.0ms	40×	body	2560	valid
31.0ms	187×	body	80	valid
23.0ms	32×	body	1280	valid
13.0ms	96×	body	80	nan
5.0ms	8×	body	640	valid
2.0ms	2×	body	5120	valid
2.0ms	5×	body	320	valid
1.0ms	2×	body	160	valid

simplify98.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
1.2b	(- (* b b) (* (* 3 a) c))
20.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

46.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
7.0ms	(- (* b b) (* (* 3 a) c))
8.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
115.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
60.0ms	(- (* b b) (* (* 3 a) c))
93.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.8s

Counts

102 → 102

Iterations

Iter	Nodes
3	5116
2	1384
1	436
0	166

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(* c (* a -3))
1.1b	(- (sqrt (fma b b (* c (* a -3)))) b)
1.5b	(fma b b (* c (* a -3)))
20.1b	(sqrt (fma b b (* c (* a -3))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-r` `*-commutative` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 86

Calls

4 calls:

12.0ms	(* c (* a -3))
18.0ms	(- (sqrt (fma b b (* c (* a -3)))) b)
0.0ms	(fma b b (* c (* a -3)))
2.0ms	(sqrt (fma b b (* c (* a -3))))

series358.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* c (* a -3))
151.0ms	(- (sqrt (fma b b (* c (* a -3)))) b)
58.0ms	(fma b b (* c (* a -3)))
129.0ms	(sqrt (fma b b (* c (* a -3))))

simplify1.1s

Counts

98 → 98

Iterations

Iter	Nodes
3	2327
2	742
1	299
0	140

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* -3 (* a c))
1.1b	(- (sqrt (fma b b (* -3 (* a c)))) b)
1.5b	(fma b b (* -3 (* a c)))
20.1b	(sqrt (fma b b (* -3 (* a c))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-r` `*-commutative` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 86

Calls

4 calls:

13.0ms	(* -3 (* a c))
6.0ms	(- (sqrt (fma b b (* -3 (* a c)))) b)
0.0ms	(fma b b (* -3 (* a c)))
1.0ms	(sqrt (fma b b (* -3 (* a c))))

series347.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* -3 (* a c))
141.0ms	(- (sqrt (fma b b (* -3 (* a c)))) b)
72.0ms	(fma b b (* -3 (* a c)))
107.0ms	(sqrt (fma b b (* -3 (* a c))))

simplify964.0ms

Counts

98 → 98

Iterations

Iter	Nodes
3	2389
2	752
1	297
0	138

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* 3 a))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
1.2b	(- (* b b) (* (* 3 a) c))
20.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
14×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube`
8×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `div-exp` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `times-frac` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sum-log` `flip3--` `sqrt-div` `1-exp` `pow-flip` `flip--` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `neg-log` `associate-+l-` `cbrt-unprod` `flip-+` `div-inv` `inv-pow`

Counts

4 → 90

Calls

4 calls:

8.0ms	(/ 1 (* 3 a))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
7.0ms	(- (* b b) (* (* 3 a) c))
20.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 1 (* 3 a))
105.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
62.0ms	(- (* b b) (* (* 3 a) c))
116.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.8s

Counts

102 → 102

Iterations

Iter	Nodes
3	3516
2	1089
1	374
0	151

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.5b

regimes583.0ms

Accuracy

84.7% (4.2b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 33.3b

bsearch194.0ms

Steps

Iters	Range		Point
8	1.248337945535211e-66	3.048951962881303e-62	3.0168583404714427e-66
8	-5.208994295225817e+99	-1.4013492266633723e+97	-4.170773079316174e+99

simplify5.0ms

Iterations

Iter	Nodes
2	37
1	37
0	30

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.2s	5910×	body	80	valid
1.2s	1086×	body	2560	valid
622.0ms	919×	body	1280	valid
335.0ms	2909×	body	80	nan
277.0ms	435×	body	640	valid
187.0ms	119×	body	5120	valid
69.0ms	214×	body	320	valid
28.0ms	108×	body	160	valid