Details

sample87.0ms

Algorithm

intervals

Results

19.0ms	43×	body	2560	valid
14.0ms	185×	body	80	valid
9.0ms	119×	body	80	nan
9.0ms	25×	body	1280	valid
2.0ms	5×	body	5120	valid
2.0ms	10×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	4×	body	160	valid

simplify82.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.1b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

112.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
18.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series475.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
72.0ms	(- (* b b) (* 4.0 (* a c)))
101.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
107.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify792.0ms

Counts: 82 → 82

prune381.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.0b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
26.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite310.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

28.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
149.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
114.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series643.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
187.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
250.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
84.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts: 166 → 166

prune639.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
11.0b	(/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
26.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
30×	`add-cbrt-cube`
18×	`times-frac`
17×	`div-exp`
16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`cbrt-undiv` `associate-/l*`
11×	`add-cube-cbrt`
10×	`prod-exp`
8×	`add-log-exp`
6×	`associate-*r/` `associate-/r/` `cbrt-unprod`
5×	`pow1` `flip3--` `flip--`
4×	`sqrt-prod` `div-inv`
3×	`1-exp` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 103

Calls

4 calls:

38.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
59.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
76.0ms	(/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series731.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
243.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
273.0ms	(/ (+ 0 (* 4.0 (* a c))) (* 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
105.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts: 115 → 115

prune429.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.6b	(/ (* 2.0 a) (* 4.0 (* a c)))
26.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `add-log-exp`
9×	`*-un-lft-identity` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
5×	`pow1` `add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `neg-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
41.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
31.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* b b) (* 4.0 (* a c)))
114.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
85.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify798.0ms

Counts: 82 → 82

prune273.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.1b

regimes200.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.9b

bsearch269.0ms

Steps

Iters	Range	Point
8	1.890514070312107e+96	2.5656331724562416e+99	9.684322567234166e+98
10	-1.9820519825293395e-291	3.2969789195161873e-308	-1.519893370196746e-307
9	-1.3204298692890892e+123	-1.196267803426671e+118	-1.8440038131758226e+119

Iters

Range

Point

1.890514070312107e+96

2.5656331724562416e+99

9.684322567234166e+98

-1.9820519825293395e-291

3.2969789195161873e-308

-1.519893370196746e-307

-1.3204298692890892e+123

-1.196267803426671e+118

-1.8440038131758226e+119

simplify688.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

890.0ms	5799×	body	80	valid
486.0ms	1144×	body	2560	valid
387.0ms	859×	body	1280	valid
317.0ms	3016×	body	80	nan
140.0ms	438×	body	640	valid
106.0ms	243×	body	320	valid
100.0ms	126×	body	5120	valid
15.0ms	111×	body	160	valid