Details

sample57.0ms

Algorithm

intervals

Results

12.0ms	32×	body	2560	valid
10.0ms	184×	body	80	valid
8.0ms	31×	body	1280	valid
4.0ms	84×	body	80	nan
4.0ms	17×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify97.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	75
2	40
1	22
0	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.4b	(- (* b b) (* (* 3.0 a) c))
24.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite125.0ms

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:

25.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
80.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms	(- (* b b) (* (* 3.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
177.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
80.0ms	(- (* b b) (* (* 3.0 a) c))
91.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.8s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1410
1	437
0	167

prune713.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.2b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.4b	(- (* b b) (* (* 3.0 a) c))
24.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

27.0ms	(* (* 3.0 a) c)
64.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms	(- (* b b) (* (* 3.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* 3.0 a) c)
114.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
78.0ms	(- (* b b) (* (* 3.0 a) c))
113.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.6s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
3	3944
2	1090
1	411
0	161

prune605.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.2b	(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
1.4b	(- (* b b) (* (* 3.0 a) c))
24.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`fma-neg`
6×	`associate-/r*` `times-frac` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/r/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 105

Calls

4 calls:

80.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
54.0ms	(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
13.0ms	(- (* b b) (* (* 3.0 a) c))
10.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
269.0ms	(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
66.0ms	(- (* b b) (* (* 3.0 a) c))
106.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	5009
2	1587
1	495
0	188

prune739.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 4.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 1 (* 3.0 a)))
0.3b	(/ 1 (* 3.0 a))
1.4b	(- (* b b) (* (* 3.0 a) c))
24.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
18×	`add-cbrt-cube`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `prod-exp`
10×	`pow1` `add-cube-cbrt`
8×	`div-exp`
7×	`associate-r`
6×	`times-frac` `add-log-exp`
5×	`associate-l` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `rec-exp` `1-exp` `log1p-expm1-u`
3×	`sqrt-prod` `associate-/l*`
2×	`frac-times` `flip3-+` `flip3--` `sqrt-div` `pow-prod-down` `associate-*l/` `flip-+` `div-inv` `pow-flip` `flip--` `distribute-lft-out`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-r/` `un-div-inv` `*-commutative` `inv-pow` `unswap-sqr`

Counts

4 → 103

Calls

4 calls:

110.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 1 (* 3.0 a)))
13.0ms	(/ 1 (* 3.0 a))
7.0ms	(- (* b b) (* (* 3.0 a) c))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (/ 1 (* 3.0 a)))
32.0ms	(/ 1 (* 3.0 a))
77.0ms	(- (* b b) (* (* 3.0 a) c))
118.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.7s

Counts

115 → 115

Iterations

Iter	Nodes
done	5006
2	2020
1	505
0	190

prune571.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.8b

regimes1.0s

Accuracy

83.8% (4.6b remaining)

Error of 10.7b against oracle of 6.1b and baseline of 34.5b

bsearch128.0ms

Steps

Iters	Range		Point
8	2.8373581988670566e-35	2.2677514638291856e-31	2.8983489306952693e-35
8	-2.748004767191833e+152	-7.260401024913698e+147	-2.221067196710922e+149

simplify5.0ms

Iterations

Iter	Nodes
done	35
1	35
0	29

end0.0ms

sample2.7s

Algorithm

intervals

Results

706.0ms	910×	body	1280	valid
662.0ms	1040×	body	2560	valid
443.0ms	5834×	body	80	valid
249.0ms	2881×	body	80	nan
113.0ms	453×	body	640	valid
51.0ms	101×	body	5120	valid
50.0ms	232×	body	320	valid
14.0ms	116×	body	160	valid