Details

sample97.0ms

Algorithm

intervals

Results

22.0ms	90×	body	80	nan
16.0ms	35×	body	2560	valid
15.0ms	188×	body	80	valid
8.0ms	22×	body	1280	valid
5.0ms	15×	body	640	valid
3.0ms	13×	body	320	valid
2.0ms	4×	body	5120	valid
0.0ms	2×	body	160	valid

simplify104.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite181.0ms

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:

109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
28.0ms	(- (* b b) (* (* 4.0 a) c))
27.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
52.0ms	(- (* b b) (* (* 4.0 a) c))
105.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
103.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify873.0ms

Counts: 82 → 82

prune329.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite230.0ms

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:

166.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
16.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
85.0ms	(- (* b b) (* (* 4.0 a) c))
122.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify980.0ms

Counts: 92 → 92

prune398.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 1) 2.0) (/ (sqrt 1) a))
1.0b	(- (* b b) (* (* 4.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
31×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `add-cbrt-cube`
24×	`times-frac`
22×	`associate-r`
20×	`add-cube-cbrt`
14×	`sqrt-prod`
12×	`prod-exp`
10×	`div-exp` `add-log-exp`
8×	`cbrt-unprod`
7×	`pow1` `cbrt-undiv` `associate-l`
4×	`unswap-sqr`
2×	`flip3--` `sqrt-div` `1-exp` `sum-log` `flip--` `div-inv` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `frac-times` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 101

Calls

4 calls:

142.0ms	(* (/ (* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 1) 2.0) (/ (sqrt 1) a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (/ (* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 1) 2.0) (/ (sqrt 1) a))
71.0ms	(- (* b b) (* (* 4.0 a) c))
114.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts: 113 → 113

prune495.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.9b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
3.0b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
128.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
76.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series628.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* b b) (* (* 4.0 a) c))
205.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
262.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts: 160 → 160

prune638.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.9b

regimes432.0ms

Accuracy

88.8% (3.2b remaining)

Error of 8.9b against oracle of 5.7b and baseline of 34.3b

bsearch325.0ms

Steps

Iters	Range		Point
5	2.873313012992052e+35	7.83918174516471e+35	4.004824807396492e+35
8	6.908187905727454e-147	1.3490170765451891e-142	1.0583319055304793e-144
9	-3.494733358578083e+156	-1.1278306941613648e+148	-4.829903230896134e+148

simplify845.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

668.0ms	5843×	body	80	valid
616.0ms	1069×	body	2560	valid
448.0ms	109×	body	5120	valid
314.0ms	910×	body	1280	valid
295.0ms	2968×	body	80	nan
201.0ms	479×	body	640	valid
45.0ms	229×	body	320	valid
15.0ms	115×	body	160	valid