Details

sample97.0ms

Algorithm

intervals

Results

22.0ms	26×	body	2560	valid
20.0ms	182×	body	80	valid
19.0ms	35×	body	1280	valid
9.0ms	91×	body	80	nan
6.0ms	15×	body	640	valid
3.0ms	4×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify145.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	134
7	134
6	132
5	129
4	126
3	103
2	62
1	28
0	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
1.0b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.6b	(- (* b b) (* 4 (* a c)))
24.0b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 81

Calls

4 calls:

88.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
31.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
16.0ms	(- (* b b) (* 4 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
100.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
62.0ms	(- (* b b) (* 4 (* a c)))
111.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.9s

Counts

93 → 93

Iterations

Iter	Nodes
3	4241
2	1197
1	400
0	154

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
1.0b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.6b	(- (* b b) (* 4 (* a c)))
24.0b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
4×	`insert-posit16`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 129

Calls

4 calls:

64.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
30.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
17.0ms	(- (* b b) (* 4 (* a c)))
21.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series457.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
132.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
56.0ms	(- (* b b) (* 4 (* a c)))
94.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify4.0s

Counts

141 → 141

Iterations

Iter	Nodes
3	6394
2	1609
1	554
0	229

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.7b

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.6b	(- (* b b) (* 4 (* a c)))
15.3b	(* (- 0 (* -4 (* a c))) (/ 1/2 a))
24.0b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`associate-r` `add-cube-cbrt`
10×	`times-frac` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-l` `sqrt-prod`
2×	`frac-times` `sum-log` `sqrt-div` `associate-*l/` `prod-exp` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`
1×	`distribute-lft-neg-out` `neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `sub-neg` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `associate-+l-` `flip-+` `div-inv` `sub0-neg`

Counts

4 → 83

Calls

4 calls:

25.0ms	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
8.0ms	(- (* b b) (* 4 (* a c)))
29.0ms	(* (- 0 (* -4 (* a c))) (/ 1/2 a))
14.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
60.0ms	(- (* b b) (* 4 (* a c)))
20.0ms	(* (- 0 (* -4 (* a c))) (/ 1/2 a))
93.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify4.3s

Counts

95 → 95

Iterations

Iter	Nodes
3	6135
2	1480
1	474
0	181

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2 c) (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))))
1.0b	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.6b	(- (* b b) (* 4 (* a c)))
24.0b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite98.0ms

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` `associate-/r*` `times-frac`
4×	`insert-posit16`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-/r/` `flip-+` `flip--`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `prod-exp` `associate-+l-` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 73

Calls

4 calls:

63.0ms	(/ (* 2 c) (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))))
14.0ms	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
8.0ms	(- (* b b) (* 4 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series624.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(/ (* 2 c) (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))))
143.0ms	(+ (- b) (sqrt (- (* b b) (* 4 (* a c)))))
77.0ms	(- (* b b) (* 4 (* a c)))
113.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify2.4s

Counts

85 → 85

Iterations

Iter	Nodes
3	4579
2	1216
1	383
0	145

prune930.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.6b

regimes479.0ms

Accuracy

94.3% (1.4b remaining)

Error of 7.2b against oracle of 5.8b and baseline of 29.8b

bsearch295.0ms

Steps

Iters	Range		Point
6	2.332248586404817e+54	2.734436825826664e+55	2.6656023684116586e+55
9	3.982835295656457e-262	3.0659571773327548e-257	4.0232110844075136e-262
7	-4.611849920572465e+95	-3.3021145473587595e+93	-3.575938583654324e+94

simplify12.0ms

Iterations

Iter	Nodes
2	44
1	44
0	37

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.3s	5890×	body	80	valid
1.3s	1042×	body	2560	valid
717.0ms	935×	body	1280	valid
399.0ms	2913×	body	80	nan
300.0ms	476×	body	640	valid
126.0ms	109×	body	5120	valid
107.0ms	203×	body	320	valid
59.0ms	107×	body	160	valid