Details

sample235.0ms

Algorithm

intervals

Results

54.0ms	256×	body	80	nan
29.0ms	116×	body	320	valid
21.0ms	512×	pre	80	true
15.0ms	98×	body	160	valid
5.0ms	16×	body	640	valid
2.0ms	26×	body	80	valid

simplify99.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	128
5	128
4	119
3	86
2	46
1	25
0	14

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite147.0ms

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:

19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(- (* b b) (* (* 4.0 a) c))
85.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series518.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
60.0ms	(- (* b b) (* (* 4.0 a) c))
179.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
158.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2113
1	452
0	167

prune630.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma c (* 4.0 (- a)) (pow b 2))
0.1b	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
0.2b	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
0.3b	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
60×	`prod-diff`
41×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube` `add-exp-log`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `div-inv` `flip--`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `diff-log` `prod-exp` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3-+` `neg-log` `flip-+` `fma-udef`

Counts

4 → 225

Calls

4 calls:

0.0ms	(fma c (* 4.0 (- a)) (pow b 2))
29.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
60.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
45.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

series711.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(fma c (* 4.0 (- a)) (pow b 2))
123.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
248.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
262.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

simplify1.9s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
2	4041
1	784
0	322

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 4.0 (- (* a c)) (pow b 2))
0.1b	(+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2))))
0.1b	(/ (* a c) a)
0.2b	(* (/ (* a c) a) (/ 4.0 (- (+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2)))))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
43×	`times-frac`
42×	`associate-r`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
30×	`add-cbrt-cube` `add-exp-log`
12×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
7×	`associate-l` `distribute-lft-out`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*` `neg-mul-1` `fma-def` `div-inv`
2×	`flip3-+` `associate-/r/` `flip-+` `distribute-neg-frac` `unswap-sqr`
1×	`frac-times` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `-commutative` `fma-udef` `associate-/l`

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma 4.0 (- (* a c)) (pow b 2))
7.0ms	(+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2))))
7.0ms	(/ (* a c) a)
117.0ms	(* (/ (* a c) a) (/ 4.0 (- (+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2)))))))

series425.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma 4.0 (- (* a c)) (pow b 2))
104.0ms	(+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2))))
8.0ms	(/ (* a c) a)
229.0ms	(* (/ (* a c) a) (/ 4.0 (- (+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2)))))))

simplify350.0ms

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
1	740
0	235

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 4.0 (* (- c) a) (* b b))
0.1b	(+ (sqrt (fma 4.0 (* (- c) a) (* b b))) b)
0.2b	(* (/ a 1) (/ (* (/ c a) 4.0) (- (+ (sqrt (fma 4.0 (* (- c) a) (* b b))) b))))
0.3b	(/ (* (/ c a) 4.0) (- (+ (sqrt (fma 4.0 (* (- c) a) (* b b))) b)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log`
45×	`add-cbrt-cube`
38×	`*-un-lft-identity`
35×	`times-frac`
30×	`add-sqr-sqrt`
24×	`div-exp`
23×	`add-cube-cbrt`
20×	`prod-exp`
18×	`associate-r`
16×	`cbrt-undiv`
14×	`cbrt-unprod`
13×	`associate-l`
12×	`distribute-lft-neg-in` `associate-/r*` `distribute-rgt-neg-in`
7×	`distribute-lft-out`
6×	`pow1` `fma-def` `add-log-exp`
4×	`expm1-log1p-u` `1-exp` `associate-/r/` `log1p-expm1-u` `distribute-neg-frac`
3×	`neg-mul-1` `flip3-+` `sqrt-prod` `flip-+` `div-inv` `unswap-sqr`
2×	`associate-*l/`
1×	`frac-times` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `associate-/l*` `associate-/l/`

Counts

4 → 144

Calls

4 calls:

0.0ms	(fma 4.0 (* (- c) a) (* b b))
8.0ms	(+ (sqrt (fma 4.0 (* (- c) a) (* b b))) b)
104.0ms	(* (/ a 1) (/ (* (/ c a) 4.0) (- (+ (sqrt (fma 4.0 (* (- c) a) (* b b))) b))))
29.0ms	(/ (* (/ c a) 4.0) (- (+ (sqrt (fma 4.0 (* (- c) a) (* b b))) b)))

series691.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma 4.0 (* (- c) a) (* b b))
134.0ms	(+ (sqrt (fma 4.0 (* (- c) a) (* b b))) b)
193.0ms	(* (/ a 1) (/ (* (/ c a) 4.0) (- (+ (sqrt (fma 4.0 (* (- c) a) (* b b))) b))))
287.0ms	(/ (* (/ c a) 4.0) (- (+ (sqrt (fma 4.0 (* (- c) a) (* b b))) b)))

simplify398.0ms

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
1	799
0	251

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes236.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	35
2	35
1	32
0	19

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.1s	3042×	body	160	valid
810.0ms	3577×	body	320	valid
742.0ms	467×	body	640	valid
689.0ms	8098×	body	80	nan
645.0ms	16098×	pre	80	true
61.0ms	914×	body	80	valid