Details

sample80.0ms

Algorithm

intervals

Results

17.0ms	25×	body	2560	valid
13.0ms	196×	body	80	valid
9.0ms	23×	body	1280	valid
6.0ms	95×	body	80	nan
5.0ms	21×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	5×	body	160	valid

simplify8.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize28.0ms

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))))

rewrite187.0ms

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:

121.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
36.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series433.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
73.0ms	(- (* b b) (* 4.0 (* a c)))
110.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
95.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Counts: 82 → 82

prune427.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize32.0ms

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))))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

120.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
18.0ms	(- (* b b) (* 4.0 (* a c)))
23.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
75.0ms	(- (* b b) (* 4.0 (* a c)))
110.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
97.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify93.0ms

Counts: 149 → 149

prune462.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite339.0ms

Algorithm

rewrite-expression-head

Rules

2801×	`times-frac`
1612×	`*-un-lft-identity`
1105×	`add-sqr-sqrt`
1104×	`add-cube-cbrt`
254×	`distribute-lft-out`
127×	`distribute-rgt-neg-in`
120×	`div-inv`
64×	`add-exp-log`
62×	`associate-/r*`
54×	`div-exp`
25×	`add-cbrt-cube`
15×	`cbrt-undiv` `1-exp` `associate-/r/`
13×	`associate-/l*`
10×	`add-log-exp`
6×	`rec-exp`
5×	`pow1`
3×	`sqrt-prod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `neg-log` `clear-num` `flip-+` `associate-/l/`

Counts

4 → 962

Calls

4 calls:

119.0ms	(/ (/ 1 1) (/ a (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
19.0ms	(- (* b b) (* 4.0 (* a c)))
50.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series492.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(/ (/ 1 1) (/ a (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
56.0ms	(- (* b b) (* 4.0 (* a c)))
110.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
95.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify276.0ms

Counts: 974 → 974

prune2.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.0b

localize18.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.0b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite304.0ms

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:

31.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
127.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
123.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series714.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
229.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
242.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
125.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify77.0ms

Counts: 166 → 166

prune681.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.0b

regimes393.0ms

Accuracy

88.7% (3.3b remaining)

Error of 8.8b against oracle of 5.5b and baseline of 34.9b

bsearch254.0ms

Steps

Iters	Range		Point
8	28054940268784.336	1.4901160436865062e+18	19249548690054332.0
9	6.319227112886395e-143	7.998932146282991e-135	8.151170165531846e-143
6	-4.651160104454807e+99	-4.746630789373686e+98	-3.546317250153943e+99

simplify110.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.0s	1088×	body	2560	valid
546.0ms	5835×	body	80	valid
457.0ms	914×	body	1280	valid
275.0ms	2919×	body	80	nan
214.0ms	443×	body	640	valid
73.0ms	132×	body	5120	valid
48.0ms	220×	body	320	valid
14.0ms	100×	body	160	valid