Details

sample75.0ms

Algorithm

intervals

Results

18.0ms	32×	body	1280	valid
12.0ms	36×	body	2560	valid
11.0ms	184×	body	80	valid
5.0ms	90×	body	80	nan
3.0ms	12×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify150.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite588.0ms

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:

491.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
59.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series410.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
116.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
65.0ms	(- (* b b) (* 4.0 (* a c)))
105.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify794.0ms

Counts: 89 → 89

prune428.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

10.0ms	(- (* b b) (* 4.0 (* a c)))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (* b b) (* 4.0 (* a c)))
130.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
103.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
103.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.3s

Counts: 69 → 69

prune402.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.0b

localize44.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.5b	(cbrt (- (* b b) (* 4.0 (* a c))))
23.5b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
6.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
7.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series508.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
96.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
145.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
171.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts: 68 → 68

prune634.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.0b

localize78.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.5b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 58

Calls

4 calls:

18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
21.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
6.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
90.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
85.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
177.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify1.3s

Counts: 70 → 70

prune646.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.0b

regimes446.0ms

Accuracy

86% (3.9b remaining)

Error of 9.7b against oracle of 5.8b and baseline of 33.9b

bsearch413.0ms

Steps

Iters	Range		Point
8	1.8560558009645164e+92	4.334214702125778e+95	1.2077138742766504e+93
7	-1.111767792999381e-98	-3.477188559758563e-100	-2.8303449773363815e-99
9	-2.957490079694442e-65	-3.9605318961576293e-72	-4.1118069715081213e-72
8	-3.014080757910363e-12	-3.956563252082953e-16	-2.9683391048089956e-12

simplify2.3s

end0.0ms

sample2.9s

Algorithm

intervals

Results

996.0ms	1105×	body	2560	valid
455.0ms	5897×	body	80	valid
420.0ms	843×	body	1280	valid
245.0ms	2965×	body	80	nan
109.0ms	467×	body	640	valid
90.0ms	106×	body	5120	valid
52.0ms	102×	body	160	valid
42.0ms	226×	body	320	valid