Details

sample59.0ms

Algorithm

intervals

Results

12.0ms	206×	body	80	valid
10.0ms	29×	body	2560	valid
8.0ms	28×	body	1280	valid
5.0ms	96×	body	80	nan
3.0ms	12×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	5120	valid

simplify6.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite554.0ms

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:

503.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
28.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series460.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
123.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
95.0ms	(- (* b b) (* 4.0 (* a c)))
97.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Counts: 89 → 89

prune340.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite125.0ms

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:

54.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
27.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
110.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
82.0ms	(- (* b b) (* 4.0 (* a c)))
102.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify68.0ms

Counts: 137 → 137

prune648.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.2b	(- (* b b) (* 4.0 (* a c)))
5.1b	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite170.0ms

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:

43.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
18.0ms	(- (* b b) (* 4.0 (* a c)))
92.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series528.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
64.0ms	(- (* b b) (* 4.0 (* a c)))
188.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
92.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Counts: 88 → 88

prune373.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.6b

localize51.0ms

Local error

Found 4 expressions with local error:

2.0b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.1b	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
18.3b	(- (pow b 2) (pow b 2))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`unpow-prod-down`
19×	`add-exp-log`
16×	`difference-of-squares`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--` `add-log-exp`
8×	`distribute-lft-out--`
7×	`div-exp`
5×	`pow1` `associate-/l/`
4×	`cbrt-undiv` `prod-exp`
3×	`flip3-+` `times-frac` `associate-/r*` `sqrt-prod` `flip-+`
2×	`frac-times` `flip3--` `sqrt-div` `associate-*r/` `sum-log` `flip--` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `rec-exp` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `+-inverses` `diff-log` `1-exp` `neg-log` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 107

Calls

4 calls:

31.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
191.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
19.0ms	(- (pow b 2) (pow b 2))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
34.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
3.0ms	(- (pow b 2) (pow b 2))
114.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify81.0ms

Counts: 119 → 119

prune589.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.6b

regimes357.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.4b

bsearch354.0ms

Steps

Iters	Range		Point
9	1.2073698495971617e+61	8.75865749938149e+67	5.099089738165329e+67
10	1.610059141238142e-239	1.618698210595833e-224	2.094358742794728e-239
10	-3.742210988141449e+103	-1.0235731023437291e+92	-3.359953003549157e+103

simplify18.0ms

end0.0ms

sample2.9s

Algorithm

intervals

Results

753.0ms	5837×	body	80	valid
588.0ms	1047×	body	2560	valid
349.0ms	2844×	body	80	nan
313.0ms	897×	body	1280	valid
191.0ms	466×	body	640	valid
58.0ms	106×	body	160	valid
56.0ms	112×	body	5120	valid
43.0ms	241×	body	320	valid