Details

sample73.0ms

Algorithm

intervals

Results

19.0ms	4×	body	5120	valid
11.0ms	188×	body	80	valid
10.0ms	35×	body	2560	valid
5.0ms	22×	body	1280	valid
5.0ms	90×	body	80	nan
3.0ms	15×	body	640	valid
2.0ms	13×	body	320	valid
0.0ms	2×	body	160	valid

simplify70.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize33.0ms

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)))

rewrite149.0ms

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:

83.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
22.0ms	(- (* b b) (* (* 4.0 a) c))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
95.0ms	(- (* b b) (* (* 4.0 a) c))
150.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
119.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify865.0ms

Counts: 82 → 82

prune420.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.0b

localize30.0ms

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)))

rewrite224.0ms

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:

158.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
8.0ms	(- (* b b) (* (* 4.0 a) c))
26.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.0ms	(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)))
56.0ms	(- (* b b) (* (* 4.0 a) c))
132.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify899.0ms

Counts: 92 → 92

prune335.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) (/ (cbrt 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)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

127.0ms	(* (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) (/ (cbrt 1) a))
13.0ms	(- (* 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)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) (/ (cbrt 1) a))
61.0ms	(- (* b b) (* (* 4.0 a) c))
119.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
107.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts: 123 → 123

prune538.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.0b

localize21.0ms

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)))

rewrite239.0ms

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:

14.0ms	(- (* b b) (* (* 4.0 a) c))
126.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
81.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series671.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (* b b) (* (* 4.0 a) c))
209.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
288.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
99.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts: 160 → 160

prune583.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.9b

regimes346.0ms

Accuracy

88.8% (3.2b remaining)

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

bsearch261.0ms

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

simplify656.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

680.0ms	2968×	body	80	nan
651.0ms	1069×	body	2560	valid
626.0ms	5843×	body	80	valid
365.0ms	910×	body	1280	valid
168.0ms	479×	body	640	valid
58.0ms	109×	body	5120	valid
40.0ms	229×	body	320	valid
14.0ms	115×	body	160	valid