Details

sample91.0ms

Algorithm

intervals

Results

19.0ms	38×	body	2560	valid
17.0ms	192×	body	80	valid
10.0ms	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

simplify69.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize46.0ms

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)))

rewrite234.0ms

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:

145.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(- (* b b) (* (* 4.0 a) c))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
120.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(- (* b b) (* (* 4.0 a) c))
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify803.0ms

Counts: 82 → 82

prune371.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.7b

localize19.0ms

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)))

rewrite164.0ms

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:

81.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
47.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
134.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms	(- (* b b) (* (* 4.0 a) c))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify915.0ms

Counts: 126 → 126

prune417.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize15.0ms

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)))

rewrite181.0ms

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-l`
5×	`associate-r`
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-*r/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `distribute-rgt-in` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

127.0ms	(* (/ 1 (* 2.0 a)) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
31.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(* (/ 1 (* 2.0 a)) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
107.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
62.0ms	(- (* b b) (* (* 4.0 a) c))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify979.0ms

Counts: 93 → 93

prune342.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.6b

localize25.0ms

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)))

rewrite79.0ms

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:

29.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
29.0ms	(exp (log (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms	(- (* b b) (* (* 4.0 a) c))
111.0ms	(exp (log (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
83.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts: 73 → 73

prune271.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

regimes403.0ms

Accuracy

83.3% (4.7b remaining)

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

bsearch110.0ms

Steps

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

simplify201.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	5956×	body	80	valid
525.0ms	1036×	body	2560	valid
262.0ms	857×	body	1280	valid
214.0ms	2895×	body	80	nan
99.0ms	458×	body	640	valid
69.0ms	247×	body	320	valid
45.0ms	117×	body	160	valid
38.0ms	101×	body	5120	valid