Details

sample157.0ms

Algorithm

intervals

Results

51.0ms	498×	pre	80	true
29.0ms	157×	body	160	valid
22.0ms	242×	body	80	nan
13.0ms	47×	body	320	valid
5.0ms	52×	body	80	valid

simplify58.0ms

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: 45.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite170.0ms

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:

17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(- (* b b) (* (* 4.0 a) c))
114.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series468.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
79.0ms	(- (* b b) (* (* 4.0 a) c))
156.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
126.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2113
1	452
0	167

prune631.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite184.0ms

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:

29.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
1.0ms	(fma c (* 4.0 (- a)) (pow b 2))
100.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
46.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

series717.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
87.0ms	(fma c (* 4.0 (- a)) (pow b 2))
214.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
285.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

simplify2.1s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
2	4271
1	785
0	322

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- c) (* a 4.0) (* b b))
0.1b	(/ (* (* a 4.0) c) a)
0.3b	(/ 2.0 (/ (/ (* (* a 4.0) c) a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b)))))))
0.3b	(/ 1 (/ 2.0 (/ (/ (* (* a 4.0) c) a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b))))))))

rewrite548.0ms

Algorithm

rewrite-expression-head

Rules

4098×	`times-frac`
1921×	`*-un-lft-identity`
1473×	`add-sqr-sqrt` `add-cube-cbrt`
448×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
368×	`associate-/r*`
224×	`distribute-lft-out`
215×	`div-inv`
112×	`neg-mul-1`
102×	`add-exp-log`
63×	`div-exp`
60×	`add-cbrt-cube`
38×	`associate-/r/`
33×	`cbrt-undiv`
32×	`distribute-neg-frac`
16×	`flip3-+` `flip-+`
15×	`prod-exp`
9×	`cbrt-unprod`
7×	`associate-/l*`
6×	`rec-exp` `1-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`fma-udef` `pow-flip` `inv-pow`

Counts

4 → 1563

Calls

4 calls:

1.0ms	(fma (- c) (* a 4.0) (* b b))
22.0ms	(/ (* (* a 4.0) c) a)
85.0ms	(/ 2.0 (/ (/ (* (* a 4.0) c) a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b)))))))
205.0ms	(/ 1 (/ 2.0 (/ (/ (* (* a 4.0) c) a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b))))))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(fma (- c) (* a 4.0) (* b b))
12.0ms	(/ (* (* a 4.0) c) a)
128.0ms	(/ 2.0 (/ (/ (* (* a 4.0) c) a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b)))))))
214.0ms	(/ 1 (/ 2.0 (/ (/ (* (* a 4.0) c) a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b))))))))

simplify1.4s

Counts

1575 → 1575

Iterations

Iter	Nodes
done	5000
0	1972

prune11.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
91×	`*-un-lft-identity`
57×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
27×	`add-cbrt-cube` `add-exp-log`
17×	`distribute-lft-out`
15×	`associate-/r*` `div-inv`
10×	`cbrt-undiv` `div-exp`
8×	`neg-mul-1` `associate-/l*`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`fma-def`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-/r/` `flip-+` `distribute-neg-frac`
1×	`+-commutative` `sum-log` `fma-udef` `associate-/l/`

Counts

4 → 178

Calls

4 calls:

9.0ms	(+ b (sqrt (fma (- c) (* a 4.0) (* b b))))
35.0ms	(/ (/ (* (* a 4.0) c) a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b))))))
0.0ms	(fma (- c) (* a 4.0) (* b b))
18.0ms	(/ (* (* a 4.0) c) a)

series492.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(+ b (sqrt (fma (- c) (* a 4.0) (* b b))))
279.0ms	(/ (/ (* (* a 4.0) c) a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b))))))
86.0ms	(fma (- c) (* a 4.0) (* b b))
12.0ms	(/ (* (* a 4.0) c) a)

simplify912.0ms

Counts

190 → 190

Iterations

Iter	Nodes
done	5000
1	793
0	293

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes283.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	28
2	28
1	27
0	18

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.3s	4828×	body	160	valid
904.0ms	8239×	body	80	nan
692.0ms	16239×	pre	80	true
316.0ms	1352×	body	320	valid
235.0ms	1820×	body	80	valid