Details

sample111.0ms

Algorithm

intervals

Results

33.0ms	38×	body	2560	valid
18.0ms	192×	body	80	valid
12.0ms	25×	body	1280	valid
8.0ms	98×	body	80	nan
5.0ms	15×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify88.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
21.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite207.0ms

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:

126.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
58.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
132.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
60.0ms	(- (* b b) (* (* 4.0 a) c))
126.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify804.0ms

Counts: 82 → 82

prune412.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
21.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

100.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
114.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(- (* b b) (* (* 4.0 a) c))
113.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts: 126 → 126

prune499.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
21.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

156.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
30.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
109.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms	(- (* b b) (* (* 4.0 a) c))
108.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts: 92 → 92

prune412.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
3.4b	(exp (log (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`pow1`
5×	`log-prod` `exp-sum`
4×	`add-exp-log` `exp-prod` `add-cbrt-cube` `distribute-lft-out`
3×	`sqrt-prod`
2×	`log-div` `flip3--` `distribute-rgt-neg-in` `flip3-+` `exp-diff` `sqrt-div` `sum-log` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `log-pow` `rem-exp-log`

Counts

4 → 61

Calls

4 calls:

33.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(- (* b b) (* (* 4.0 a) c))
43.0ms	(exp (log (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
30.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
90.0ms	(- (* b b) (* (* 4.0 a) c))
120.0ms	(exp (log (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
108.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts: 73 → 73

prune395.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

regimes471.0ms

Accuracy

83.3% (4.7b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 33.6b

bsearch145.0ms

Steps

Iters	Range		Point
6	3.2999883719107076e-115	1.481810096151352e-114	5.81843322574321e-115
8	-1.3549447721302977e+118	-2.218977696437643e+113	-1.2609617020890706e+118

simplify241.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.1s	5956×	body	80	valid
686.0ms	1036×	body	2560	valid
413.0ms	857×	body	1280	valid
228.0ms	2895×	body	80	nan
194.0ms	458×	body	640	valid
186.0ms	101×	body	5120	valid
91.0ms	247×	body	320	valid
17.0ms	117×	body	160	valid