Details

sample127.0ms

Algorithm

intervals

Results

36.0ms	178×	body	80	valid
24.0ms	38×	body	2560	valid
12.0ms	24×	body	1280	valid
10.0ms	104×	body	80	nan
8.0ms	16×	body	640	valid
4.0ms	5×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify104.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	105
7	105
6	104
5	102
4	94
3	79
2	43
1	25
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite152.0ms

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:

89.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
21.0ms	(- (* b b) (* (* 4.0 a) c))
20.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
61.0ms	(- (* b b) (* (* 4.0 a) c))
124.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1411
1	440
0	167

prune758.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

107.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
13.0ms	(- (* b b) (* (* 4.0 a) c))
29.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
63.0ms	(- (* b b) (* (* 4.0 a) c))
125.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
103.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

112 → 112

Iterations

Iter	Nodes
done	5007
2	1926
1	519
0	194

prune755.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* a 2.0) (- (sqrt (- (* b b) (* (* a c) 4.0))) b)))
0.4b	(- (* b b) (* (* a c) 4.0))
1.4b	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
21.3b	(sqrt (- (* b b) (* (* a c) 4.0)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`associate-/r*` `div-exp`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 152

Calls

4 calls:

71.0ms	(/ 1 (/ (* a 2.0) (- (sqrt (- (* b b) (* (* a c) 4.0))) b)))
7.0ms	(- (* b b) (* (* a c) 4.0))
66.0ms	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
18.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(/ 1 (/ (* a 2.0) (- (sqrt (- (* b b) (* (* a c) 4.0))) b)))
60.0ms	(- (* b b) (* (* a c) 4.0))
122.0ms	(- (sqrt (- (* b b) (* (* a c) 4.0))) b)
130.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

simplify1.8s

Counts

164 → 164

Iterations

Iter	Nodes
done	5002
2	2130
1	650
0	259

prune832.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) (* a 2.0))
0.4b	(- (* b b) (* (* c a) 4.0))
1.4b	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
21.3b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite171.0ms

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×	`times-frac` `associate-/l*` `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-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

77.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) (* a 2.0))
7.0ms	(- (* b b) (* (* c a) 4.0))
66.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
17.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) (* a 2.0))
60.0ms	(- (* b b) (* (* c a) 4.0))
100.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
113.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.8s

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	1635
1	522
0	195

prune615.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.1b

regimes608.0ms

Accuracy

83.6% (4.7b remaining)

Error of 10.2b against oracle of 5.6b and baseline of 34.1b

bsearch227.0ms

Steps

Iters	Range		Point
10	2.044647849876085e-45	1.359053137570048e-33	5.668416736491797e-35
10	-8.897020078895062e+156	-1.101416214509623e+146	-1.0061247252330729e+153

simplify10.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample3.1s

Algorithm

intervals

Results

639.0ms	1027×	body	2560	valid
550.0ms	5812×	body	80	valid
463.0ms	118×	body	5120	valid
455.0ms	885×	body	1280	valid
345.0ms	2885×	body	80	nan
153.0ms	505×	body	640	valid
45.0ms	217×	body	320	valid
17.0ms	120×	body	160	valid