Details

sample224.0ms

Algorithm

intervals

Results

19.0ms	36×	body	2560	valid
17.0ms	188×	body	80	valid
8.0ms	21×	body	1280	valid
7.0ms	90×	body	80	nan
5.0ms	15×	body	640	valid
3.0ms	13×	body	320	valid
2.0ms	4×	body	5120	valid
0.0ms	2×	body	160	valid

simplify59.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.1b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

103.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
21.0ms	(- (* b_2 b_2) (* a c))
45.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
42.0ms	(- (* b_2 b_2) (* a c))
115.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.2s

Counts: 92 → 92

prune364.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
1.0b	(- (* b_2 b_2) (* a c))
1.1b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

118.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
14.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
48.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify860.0ms

Counts: 96 → 96

prune330.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
15.4b	(* (/ 1 a) (* a c))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cbrt-cube`
13×	`associate-l`
12×	`add-cube-cbrt` `prod-exp`
10×	`pow1` `add-log-exp`
9×	`times-frac`
6×	`cbrt-unprod`
4×	`div-exp` `sqrt-prod`
3×	`flip3--` `diff-log` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `associate-r` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 82

Calls

4 calls:

48.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(- (* b_2 b_2) (* a c))
64.0ms	(* (/ 1 a) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
40.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(* (/ 1 a) (* a c))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts: 94 → 94

prune330.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (* (/ 1 a) 0) (* (/ 1 1) c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite202.0ms

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-/r*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/l/` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-*l/` `associate-/r/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `neg-log` `frac-add` `clear-num` `flip-+` `div-inv`

Counts

4 → 93

Calls

4 calls:

134.0ms	(/ (+ (* (/ 1 a) 0) (* (/ 1 1) c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
41.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ (+ (* (/ 1 a) 0) (* (/ 1 1) c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
109.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify891.0ms

Counts: 105 → 105

prune380.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.9b

regimes204.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 29.4b

bsearch238.0ms

Steps

Iters	Range	Point
8	1.8560558009645164e+92	2.630949047752582e+95	3.310436447834858e+94
9	-1.6996100869427896e-292	-1.150605175955605e-297	-2.9814431073825827e-294
9	-2.3363356027674214e+137	-1.485581033519284e+131	-3.766148915908884e+131

Iters

Range

Point

1.8560558009645164e+92

2.630949047752582e+95

3.310436447834858e+94

-1.6996100869427896e-292

-1.150605175955605e-297

-2.9814431073825827e-294

-2.3363356027674214e+137

-1.485581033519284e+131

-3.766148915908884e+131

simplify447.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

761.0ms	2966×	body	80	nan
621.0ms	5845×	body	80	valid
481.0ms	1073×	body	2560	valid
462.0ms	909×	body	1280	valid
173.0ms	480×	body	640	valid
55.0ms	109×	body	5120	valid
45.0ms	226×	body	320	valid
16.0ms	114×	body	160	valid