Details

sample154.0ms

Algorithm

intervals

Results

56.0ms	177×	body	80	valid
29.0ms	36×	body	2560	valid
18.0ms	25×	body	1280	valid
11.0ms	81×	body	80	nan
10.0ms	19×	body	640	valid
4.0ms	9×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify169.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	134
7	134
6	132
5	129
4	126
3	103
2	62
1	28
0	14

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.2b	(- (* b b) (* 4 (* a c)))
23.5b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `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` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 81

Calls

4 calls:

58.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
19.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
17.0ms	(- (* b b) (* 4 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
116.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
65.0ms	(- (* b b) (* 4 (* a c)))
106.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify2.0s

Counts

93 → 93

Iterations

Iter	Nodes
3	4241
2	1197
1	400
0	154

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.2b	(- (* b b) (* 4 (* a c)))
23.5b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite99.0ms

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`
4×	`insert-posit16`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 129

Calls

4 calls:

43.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
10.0ms	(- (* b b) (* 4 (* a c)))
7.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ 1 (/ (* 2 a) (- (- b) (sqrt (- (* b b) (* 4 (* a c)))))))
117.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
52.0ms	(- (* b b) (* 4 (* a c)))
94.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify3.7s

Counts

141 → 141

Iterations

Iter	Nodes
3	6394
2	1609
1	554
0	229

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize38.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* a c) 4))
2.7b	(- (sqrt (- (* b b) (* (* a c) 4))) b)
15.2b	(* (- 0 (* -4 (* a c))) (/ 1/2 a))
23.5b	(sqrt (- (* b b) (* (* a c) 4)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`associate-r` `add-cube-cbrt`
10×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`pow1`
5×	`flip3--` `flip--`
4×	`sqrt-prod` `insert-posit16`
3×	`associate-l`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `associate-*l/` `prod-exp` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`distribute-lft-neg-out` `cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `distribute-lft-out--` `sub0-neg`

Counts

4 → 83

Calls

4 calls:

7.0ms	(- (* b b) (* (* a c) 4))
32.0ms	(- (sqrt (- (* b b) (* (* a c) 4))) b)
15.0ms	(* (- 0 (* -4 (* a c))) (/ 1/2 a))
7.0ms	(sqrt (- (* b b) (* (* a c) 4)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* b b) (* (* a c) 4))
104.0ms	(- (sqrt (- (* b b) (* (* a c) 4))) b)
11.0ms	(* (- 0 (* -4 (* a c))) (/ 1/2 a))
75.0ms	(sqrt (- (* b b) (* (* a c) 4)))

simplify4.7s

Counts

95 → 95

Iterations

Iter	Nodes
3	6417
2	1422
1	453
0	180

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2 c) (/ 1 (- (sqrt (- (* b b) (* (* a c) 4))) b)))
1.2b	(- (* b b) (* (* a c) 4))
2.7b	(- (sqrt (- (* b b) (* (* a c) 4))) b)
23.5b	(sqrt (- (* b b) (* (* a c) 4)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
26×	`add-exp-log`
24×	`associate-r`
23×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cbrt-cube`
15×	`add-cube-cbrt`
12×	`prod-exp`
10×	`pow1`
8×	`add-log-exp` `difference-of-squares`
7×	`sqrt-prod`
6×	`cbrt-unprod`
4×	`flip3--` `div-exp` `insert-posit16` `flip--` `distribute-lft-out--`
3×	`pow-prod-down`
2×	`cbrt-undiv` `rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp` `associate-/r/`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

83.0ms	(* (* 2 c) (/ 1 (- (sqrt (- (* b b) (* (* a c) 4))) b)))
13.0ms	(- (* b b) (* (* a c) 4))
31.0ms	(- (sqrt (- (* b b) (* (* a c) 4))) b)
7.0ms	(sqrt (- (* b b) (* (* a c) 4)))

series573.0ms

Counts

4 → 12

Calls

4 calls:

310.0ms	(* (* 2 c) (/ 1 (- (sqrt (- (* b b) (* (* a c) 4))) b)))
55.0ms	(- (* b b) (* (* a c) 4))
108.0ms	(- (sqrt (- (* b b) (* (* a c) 4))) b)
100.0ms	(sqrt (- (* b b) (* (* a c) 4)))

simplify2.8s

Counts

107 → 107

Iterations

Iter	Nodes
3	4764
2	1501
1	509
0	185

prune1.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.1b

regimes531.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 29.7b

bsearch286.0ms

Steps

Iters	Range	Point
6	1.890398075878753e+149	8.723340275486535e+149	4.0392005370549217e+149
7	-5.199438090477325e-294	-2.7067083760276696e-295	-2.7394104193355045e-295
5	-4.5624341740005415e+97	-1.2645606246842859e+97	-4.463381827278506e+97

Iters

Range

Point

1.890398075878753e+149

8.723340275486535e+149

4.0392005370549217e+149

-5.199438090477325e-294

-2.7067083760276696e-295

-2.7394104193355045e-295

-4.5624341740005415e+97

-1.2645606246842859e+97

-4.463381827278506e+97

simplify14.0ms

Iterations

Iter	Nodes
2	44
1	44
0	36

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.5s	1119×	body	2560	valid
871.0ms	5783×	body	80	valid
763.0ms	901×	body	1280	valid
584.0ms	128×	body	5120	valid
361.0ms	2863×	body	80	nan
262.0ms	471×	body	640	valid
129.0ms	230×	body	320	valid
51.0ms	108×	body	160	valid