Details

sample75.0ms

Algorithm

intervals

Results

13.0ms	177×	body	80	valid
13.0ms	38×	body	1280	valid
12.0ms	32×	body	2560	valid
6.0ms	90×	body	80	nan
4.0ms	7×	body	5120	valid
2.0ms	9×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify8.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

102.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms	(- (* b b) (* 4.0 (* a c)))
40.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
87.0ms	(- (* b b) (* 4.0 (* a c)))
113.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
120.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify39.0ms

Counts: 89 → 89

prune378.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.8b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
0.4b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

91.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
16.0ms	(- (* b b) (* 4.0 (* a c)))
37.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series454.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
88.0ms	(- (* b b) (* 4.0 (* a c)))
111.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
108.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify63.0ms

Counts: 103 → 103

prune465.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

localize50.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.7b	(/ (/ (+ (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
8.2b	(/ (+ (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite400.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

65.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
167.0ms	(/ (/ (+ (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
137.0ms	(/ (+ (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series776.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
255.0ms	(/ (/ (+ (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
283.0ms	(/ (+ (* 4.0 (* a c)) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
107.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify118.0ms

Counts: 199 → 199

prune839.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (/ a (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
13.3b	(/ a (* 4.0 (* a c)))
22.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite361.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
33×	`add-cbrt-cube`
24×	`prod-exp`
22×	`div-exp`
14×	`add-sqr-sqrt`
11×	`cbrt-undiv` `*-un-lft-identity`
10×	`cbrt-unprod`
9×	`add-cube-cbrt`
8×	`pow1`
6×	`times-frac` `associate-/l*` `add-log-exp`
5×	`rec-exp` `1-exp` `associate-/r/`
4×	`flip3--` `sqrt-prod` `flip--`
2×	`frac-times` `pow-flip` `frac-2neg` `sqrt-div` `associate-r/` `clear-num` `associate-/r` `div-inv` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-*l/` `distribute-lft-out--` `inv-pow`

Counts

4 → 98

Calls

4 calls:

251.0ms	(/ 1 (* (/ a (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
59.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
31.0ms	(/ a (* 4.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series471.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ 1 (* (/ a (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
118.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
19.0ms	(/ a (* 4.0 (* a c)))
115.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify70.0ms

Counts: 110 → 110

prune460.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.7b

regimes262.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 30.2b

bsearch245.0ms

Steps

Iters	Range		Point
9	1.126266178272183e+86	9.307219265615864e+90	7.493206037388171e+90
10	9.421053113373393e-302	2.626961042225499e-286	8.803712622257929e-290
7	-1.307088067977472e+71	-1.0608558557274316e+69	-1.2770913942233635e+71

simplify39.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

934.0ms	1102×	body	2560	valid
728.0ms	5838×	body	80	valid
485.0ms	240×	body	320	valid
476.0ms	910×	body	1280	valid
272.0ms	2932×	body	80	nan
135.0ms	465×	body	640	valid
74.0ms	100×	body	5120	valid
17.0ms	125×	body	160	valid