Details

sample125.0ms

Algorithm

intervals

Results

30.0ms	36×	body	2560	valid
27.0ms	184×	body	80	valid
20.0ms	29×	body	1280	valid
11.0ms	77×	body	80	nan
6.0ms	10×	body	640	valid
4.0ms	10×	body	320	valid
4.0ms	4×	body	5120	valid
1.0ms	4×	body	160	valid

simplify129.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.2b	(- (* b b) (* (* 4 a) c))
23.1b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`insert-posit16`
3×	`distribute-rgt-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*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 74

Calls

4 calls:

85.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
25.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
8.0ms	(- (* b b) (* (* 4 a) c))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
119.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
69.0ms	(- (* b b) (* (* 4 a) c))
94.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.8s

Counts

86 → 86

Iterations

Iter	Nodes
3	4960
2	1314
1	402
0	153

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2 (/ (- (sqrt (+ (* b b) (* -4 (* a c)))) b) a))
1.1b	(- (sqrt (+ (* b b) (* -4 (* a c)))) b)
1.2b	(+ (* b b) (* -4 (* a c)))
23.1b	(sqrt (+ (* b b) (* -4 (* a c))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-/r/` `flip--`

Counts

4 → 151

Calls

4 calls:

31.0ms	(/ 2 (/ (- (sqrt (+ (* b b) (* -4 (* a c)))) b) a))
31.0ms	(- (sqrt (+ (* b b) (* -4 (* a c)))) b)
9.0ms	(+ (* b b) (* -4 (* a c)))
8.0ms	(sqrt (+ (* b b) (* -4 (* a c))))

series374.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ 2 (/ (- (sqrt (+ (* b b) (* -4 (* a c)))) b) a))
98.0ms	(- (sqrt (+ (* b b) (* -4 (* a c)))) b)
54.0ms	(+ (* b b) (* -4 (* a c)))
79.0ms	(sqrt (+ (* b b) (* -4 (* a c))))

simplify1.2s

Counts

163 → 163

Iterations

Iter	Nodes
2	2261
1	703
0	273

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ 2 (- (sqrt (+ (* b b) (* -4 (* a c)))) b)) a))
1.1b	(- (sqrt (+ (* b b) (* -4 (* a c)))) b)
1.2b	(+ (* b b) (* -4 (* a c)))
23.1b	(sqrt (+ (* b b) (* -4 (* a c))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `div-exp`
8×	`pow1` `add-log-exp`
7×	`add-cube-cbrt`
6×	`prod-exp`
4×	`cbrt-undiv` `sqrt-prod` `insert-posit16`
3×	`rec-exp` `times-frac` `1-exp` `associate-/l*`
2×	`flip3-+` `sqrt-div` `cbrt-unprod` `flip-+` `pow-flip` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-/r/` `div-inv` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 78

Calls

4 calls:

57.0ms	(/ 1 (* (/ 2 (- (sqrt (+ (* b b) (* -4 (* a c)))) b)) a))
37.0ms	(- (sqrt (+ (* b b) (* -4 (* a c)))) b)
8.0ms	(+ (* b b) (* -4 (* a c)))
6.0ms	(sqrt (+ (* b b) (* -4 (* a c))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ 1 (* (/ 2 (- (sqrt (+ (* b b) (* -4 (* a c)))) b)) a))
87.0ms	(- (sqrt (+ (* b b) (* -4 (* a c)))) b)
53.0ms	(+ (* b b) (* -4 (* a c)))
77.0ms	(sqrt (+ (* b b) (* -4 (* a c))))

simplify2.3s

Counts

90 → 90

Iterations

Iter	Nodes
3	5745
2	1380
1	431
0	168

prune866.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1/2 a) (- (sqrt (+ (* b b) (* -4 (* a c)))) b))
1.1b	(- (sqrt (+ (* b b) (* -4 (* a c)))) b)
1.2b	(+ (* b b) (* -4 (* a c)))
23.1b	(sqrt (+ (* b b) (* -4 (* a c))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`associate-l` `add-cube-cbrt`
10×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-r`
5×	`sqrt-prod`
4×	`insert-posit16` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `flip3-+` `sqrt-div` `prod-exp` `associate-*r/` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 88

Calls

4 calls:

97.0ms	(* (/ 1/2 a) (- (sqrt (+ (* b b) (* -4 (* a c)))) b))
37.0ms	(- (sqrt (+ (* b b) (* -4 (* a c)))) b)
8.0ms	(+ (* b b) (* -4 (* a c)))
6.0ms	(sqrt (+ (* b b) (* -4 (* a c))))

series432.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (/ 1/2 a) (- (sqrt (+ (* b b) (* -4 (* a c)))) b))
106.0ms	(- (sqrt (+ (* b b) (* -4 (* a c)))) b)
59.0ms	(+ (* b b) (* -4 (* a c)))
92.0ms	(sqrt (+ (* b b) (* -4 (* a c))))

simplify2.2s

Counts

100 → 100

Iterations

Iter	Nodes
3	6122
2	1534
1	450
0	168

prune728.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.4b

regimes340.0ms

Accuracy

88.7% (3.1b remaining)

Error of 8.6b against oracle of 5.5b and baseline of 33.3b

bsearch235.0ms

Steps

Iters	Range		Point
9	6607563971730746.0	6.913138166624131e+23	1.3233344071163898e+19
5	1.2424503213670916e-242	3.1631049633436394e-242	3.1232170674377175e-242
8	-5.520406447692031e+155	-8.116303404487084e+152	-4.82289647433212e+153

simplify9.0ms

Iterations

Iter	Nodes
2	39
1	39
0	33

end0.0ms

sample3.4s

Algorithm

intervals

Results

995.0ms	1114×	body	2560	valid
909.0ms	5824×	body	80	valid
534.0ms	912×	body	1280	valid
326.0ms	2907×	body	80	nan
149.0ms	414×	body	640	valid
95.0ms	110×	body	5120	valid
83.0ms	232×	body	320	valid
17.0ms	100×	body	160	valid