Details

sample127.0ms

Algorithm

intervals

Results

43.0ms	562×	pre	80	true
19.0ms	306×	body	80	nan
19.0ms	138×	body	160	valid
8.0ms	118×	body	80	valid

simplify112.0ms

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite116.0ms

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:

9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms	(- (* b b) (* (* 4.0 a) c))
178.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
99.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2113
1	452
0	167

prune587.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
0.2b	(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))
0.4b	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

rewrite178.0ms

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:

18.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
0.0ms	(fma c (* 4.0 (- a)) (pow b 2))
75.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
67.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

series752.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
79.0ms	(fma c (* 4.0 (- a)) (pow b 2))
270.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
288.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

simplify2.0s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
2	4271
1	785
0	322

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite118.0ms

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:

22.0ms	(/ (* (* a 4.0) c) a)
6.0ms	(+ b (sqrt (fma (- c) (* a 4.0) (* b b))))
75.0ms	(/ (/ (* (* a 4.0) c) a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b))))))
1.0ms	(fma (- c) (* a 4.0) (* b b))

series449.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (* (* a 4.0) c) a)
116.0ms	(+ b (sqrt (fma (- c) (* a 4.0) (* b b))))
229.0ms	(/ (/ (* (* a 4.0) c) a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b))))))
87.0ms	(fma (- c) (* a 4.0) (* b b))

simplify488.0ms

Counts

190 → 190

Iterations

Iter	Nodes
done	5000
1	793
0	293

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac`
52×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`add-cbrt-cube` `add-exp-log`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
13×	`associate-/r*` `div-inv`
10×	`cbrt-undiv` `div-exp`
8×	`neg-mul-1` `associate-/l*`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `fma-udef`
1×	`associate-/l/`

Counts

4 → 153

Calls

4 calls:

24.0ms	(/ (* (* a 4.0) c) a)
23.0ms	(/ (/ (* (* a 4.0) c) a) (- (fma (sqrt b) (sqrt b) (sqrt (fma (- c) (* a 4.0) (* b b))))))
0.0ms	(fma (- c) (* a 4.0) (* b b))
0.0ms	(fma (sqrt b) (sqrt b) (sqrt (fma (- c) (* a 4.0) (* b b))))

series666.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (* (* a 4.0) c) a)
314.0ms	(/ (/ (* (* a 4.0) c) a) (- (fma (sqrt b) (sqrt b) (sqrt (fma (- c) (* a 4.0) (* b b))))))
85.0ms	(fma (- c) (* a 4.0) (* b b))
246.0ms	(fma (sqrt b) (sqrt b) (sqrt (fma (- c) (* a 4.0) (* b b))))

simplify524.0ms

Counts

165 → 165

Iterations

Iter	Nodes
done	5000
1	760
0	288

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes321.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	24
1	24
0	19

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.2s	8508×	body	80	nan
837.0ms	4419×	body	160	valid
653.0ms	16508×	pre	80	true
302.0ms	3581×	body	80	valid