Details

sample59.0ms

Algorithm

intervals

Results

11.0ms	2×	body	5120	valid
9.0ms	197×	body	80	valid
9.0ms	34×	body	2560	valid
7.0ms	32×	body	1280	valid
5.0ms	111×	body	80	nan
2.0ms	13×	body	320	valid
1.0ms	7×	body	640	valid
0.0ms	2×	body	160	valid

simplify87.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite106.0ms

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:

60.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify500.0ms

Counts: 89 → 89

prune227.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

100.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
8.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
44.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify617.0ms

Counts: 97 → 97

prune223.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite103.0ms

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:

64.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify500.0ms

Counts: 89 → 89

prune222.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
0.6b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.5b	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
23.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
57.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series361.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
164.0ms	(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts: 83 → 83

prune220.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

regimes281.0ms

Accuracy

82.5% (4.7b remaining)

Error of 9.9b against oracle of 5.2b and baseline of 31.9b

bsearch229.0ms

Steps

Iters	Range		Point
9	1.2233118428759713e-33	3.057073162550245e-28	3.0217206771227585e-28
11	-4.7850247156883905e-129	-4.8694142967264886e-152	-1.682322748689228e-130
4	-3.364555191417683e-120	-2.3619525948516786e-120	-2.3891201500640816e-120
6	-2.8106225860795078e+34	-5.813460508438586e+33	-1.6283081095555592e+34

simplify799.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

805.0ms	1101×	body	2560	valid
346.0ms	5838×	body	80	valid
231.0ms	934×	body	1280	valid
150.0ms	2873×	body	80	nan
105.0ms	455×	body	640	valid
35.0ms	99×	body	5120	valid
30.0ms	235×	body	320	valid
10.0ms	112×	body	160	valid