Details

sample94.0ms

Algorithm

intervals

Results

31.0ms	33×	body	2560	valid
11.0ms	35×	body	1280	valid
11.0ms	168×	body	80	valid
6.0ms	92×	body	80	nan
4.0ms	15×	body	640	valid
3.0ms	6×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	8×	body	160	valid

simplify6.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.2b	(- (* b b) (* (* 3.0 a) c))
2.0b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

110.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
12.0ms	(- (* b b) (* (* 3.0 a) c))
33.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
59.0ms	(- (* b b) (* (* 3.0 a) c))
109.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
103.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify55.0ms

Counts: 82 → 82

prune296.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.3b

localize34.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
3.9b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.6b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

13.0ms	(- (* b b) (* (* 3.0 a) c))
146.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
76.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b b) (* (* 3.0 a) c))
163.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
251.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
107.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify101.0ms

Counts: 160 → 160

prune481.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b	(- (* b b) (* (* 3.0 a) c))
16.5b	(/ (* 3.0 a) (* 3.0 (* a c)))
24.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

39.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(- (* b b) (* (* 3.0 a) c))
30.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
63.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
101.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify71.0ms

Counts: 82 → 82

prune290.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ 1 1) (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
0.7b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b	(- (* b b) (* (* 3.0 a) c))
24.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
40×	`div-exp`
31×	`times-frac`
25×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`1-exp`
14×	`prod-exp`
13×	`associate-/l*`
11×	`cbrt-undiv`
10×	`add-log-exp`
6×	`rec-exp`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`sqrt-prod` `cbrt-unprod`
3×	`diff-log` `div-inv`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-l/` `clear-num` `associate-/r` `associate-/l/`

Counts

4 → 115

Calls

4 calls:

54.0ms	(/ (/ 1 1) (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
41.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(- (* b b) (* (* 3.0 a) c))
13.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(/ (/ 1 1) (* (/ 1.0 c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
99.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
57.0ms	(- (* b b) (* (* 3.0 a) c))
101.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify76.0ms

Counts: 127 → 127

prune339.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.2b

regimes421.0ms

Accuracy

93.8% (1.5b remaining)

Error of 7.1b against oracle of 5.6b and baseline of 29.6b

bsearch226.0ms

Steps

Iters	Range	Point
5	1.2073698495971617e+61	2.9312978430050554e+61	2.4217285567441938e+61
8	-7.621802709561935e-152	-2.1001871704112802e-155	-2.1434134071196154e-155
10	-3.742210988141449e+103	-1.1204690717208776e+87	-8.594947000714855e+98

Iters

Range

Point

1.2073698495971617e+61

2.9312978430050554e+61

2.4217285567441938e+61

-7.621802709561935e-152

-2.1001871704112802e-155

-2.1434134071196154e-155

-3.742210988141449e+103

-1.1204690717208776e+87

-8.594947000714855e+98

simplify30.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

909.0ms	5868×	body	80	valid
539.0ms	1051×	body	2560	valid
303.0ms	891×	body	1280	valid
258.0ms	2845×	body	80	nan
142.0ms	480×	body	640	valid
50.0ms	100×	body	5120	valid
40.0ms	217×	body	320	valid
14.0ms	111×	body	160	valid