Details

sample54.0ms

Algorithm

intervals

Results

9.0ms	40×	body	1280	valid
9.0ms	183×	body	80	valid
8.0ms	32×	body	2560	valid
4.0ms	98×	body	80	nan
3.0ms	13×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify4.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.5b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod`
3×	`distribute-rgt-neg-in` `associate-r` `pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `associate-l` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv`

Counts

4 → 76

Calls

4 calls:

18.0ms	(* (* 3.0 a) c)
122.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
31.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* 3.0 a) c)
151.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
95.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
99.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify62.0ms

Counts: 88 → 88

prune368.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.9b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
7.3b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

30.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
104.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
90.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
10.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series701.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
213.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
266.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
104.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify93.0ms

Counts: 166 → 166

prune693.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (/ (* 3.0 a) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
0.6b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.6b	(/ (* 3.0 a) (* 3.0 (* a c)))
22.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-exp-log`
63×	`add-cbrt-cube`
57×	`prod-exp`
40×	`div-exp`
25×	`cbrt-unprod`
20×	`cbrt-undiv`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
8×	`pow1` `rec-exp` `1-exp` `add-log-exp`
7×	`add-cube-cbrt`
5×	`associate-/r/`
4×	`flip3--` `times-frac` `sqrt-prod` `flip--` `associate-/l*`
2×	`frac-times` `pow-flip` `frac-2neg` `sqrt-div` `diff-log` `associate-r/` `clear-num` `associate-/r` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-*l/` `inv-pow`

Counts

4 → 115

Calls

4 calls:

152.0ms	(/ 1 (* (/ (* 3.0 a) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
30.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
10.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ 1 (* (/ (* 3.0 a) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
86.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
80.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify104.0ms

Counts: 127 → 127

prune396.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ 1 c))
0.2b	(* (* 3.0 a) c)
0.6b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
28×	`add-exp-log`
14×	`div-exp` `add-cbrt-cube`
13×	`associate-/r*`
12×	`pow1`
8×	`add-log-exp`
7×	`rec-exp` `1-exp`
5×	`div-inv`
4×	`pow-flip` `sqrt-prod`
3×	`cbrt-undiv` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3--` `sqrt-div` `diff-log` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l` `neg-log` `clear-num` `associate-/r/` `*-commutative` `remove-double-div`

Counts

4 → 136

Calls

4 calls:

16.0ms	(/ 1 (/ 1 c))
30.0ms	(* (* 3.0 a) c)
46.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ 1 (/ 1 c))
21.0ms	(* (* 3.0 a) c)
91.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
85.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify63.0ms

Counts: 148 → 148

prune482.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

regimes456.0ms

Accuracy

89.6% (2.5b remaining)

Error of 8.2b against oracle of 5.7b and baseline of 29.9b

bsearch253.0ms

Steps

Iters	Range		Point
8	6.830756908302209e+71	2.772849885831336e+75	2.730494439370032e+75
9	-9.135136184186538e-305	3.248654678508165e-307	-1.0148143787745408e-305
8	-2.039468834635472e-27	-5.081197715878726e-31	-2.001685131789919e-27

simplify68.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1084×	body	2560	valid
427.0ms	5888×	body	80	valid
415.0ms	898×	body	1280	valid
264.0ms	2886×	body	80	nan
135.0ms	430×	body	640	valid
83.0ms	100×	body	5120	valid
40.0ms	225×	body	320	valid
12.0ms	102×	body	160	valid