Details

sample89.0ms

Algorithm

intervals

Results

17.0ms	187×	body	80	valid
16.0ms	32×	body	2560	valid
13.0ms	32×	body	1280	valid
7.0ms	94×	body	80	nan
5.0ms	14×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify125.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite216.0ms

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:

124.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
18.0ms	(- (* b b) (* 4.0 (* a c)))
59.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series440.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
71.0ms	(- (* b b) (* 4.0 (* a c)))
131.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
89.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify864.0ms

Counts: 89 → 89

prune391.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

74.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
19.0ms	(- (* b b) (* 4.0 (* a c)))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series450.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
65.0ms	(- (* b b) (* 4.0 (* a c)))
100.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
93.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts: 137 → 137

prune459.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 1) (* (/ a 1) (/ 2.0 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

69.0ms	(/ (sqrt 1) (* (/ a 1) (/ 2.0 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
31.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series479.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ (sqrt 1) (* (/ a 1) (/ 2.0 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
116.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
134.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.0s

Counts: 95 → 95

prune376.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
7.1b	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

37.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
66.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series477.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
66.0ms	(- (* b b) (* 4.0 (* a c)))
149.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
94.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify711.0ms

Counts: 88 → 88

prune281.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.3b

regimes246.0ms

Accuracy

89.5% (3.0b remaining)

Error of 8.5b against oracle of 5.5b and baseline of 34.1b

bsearch224.0ms

Steps

Iters	Range		Point
10	1.1938117014962488e+94	7.783906932586822e+104	4.2945314309789726e+104
6	-6.811146580735316e-291	-1.4054369994792086e-291	-2.2776246100069977e-291
5	-986703.3404809777	-447673.70935774763	-977083.9042033921

simplify798.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1073×	body	2560	valid
636.0ms	5868×	body	80	valid
424.0ms	895×	body	1280	valid
228.0ms	2858×	body	80	nan
123.0ms	443×	body	640	valid
51.0ms	107×	body	5120	valid
48.0ms	233×	body	320	valid
16.0ms	117×	body	160	valid