Details

sample153.0ms

Algorithm

intervals

Results

39.0ms	141×	body	160	valid
35.0ms	523×	pre	80	true
35.0ms	267×	body	80	nan
16.0ms	115×	body	80	valid

simplify136.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
5	134
4	125
3	90
2	47
1	25
0	14

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma (* c a) -4 (* b b)))
0.2b	(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
0.2b	(fma (* c a) -4 (* b b))
29.0b	(- (sqrt (fma (* c a) -4 (* b b))) b)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 114

Calls

4 calls:

2.0ms	(sqrt (fma (* c a) -4 (* b b)))
26.0ms	(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
0.0ms	(fma (* c a) -4 (* b b))
8.0ms	(- (sqrt (fma (* c a) -4 (* b b))) b)

series331.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (fma (* c a) -4 (* b b)))
90.0ms	(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
56.0ms	(fma (* c a) -4 (* b b))
105.0ms	(- (sqrt (fma (* c a) -4 (* b b))) b)

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	1071
1	337
0	157

prune721.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 26.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* b (* b b))
0.3b	(* (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))))
0.4b	(/ (- (* (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b)))) (* b (* b b))) (fma b (+ b (sqrt (fma (* -4 a) c (* b b)))) (fma (* -4 a) c (* b b))))
27.9b	(- (* (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b)))) (* b (* b b)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`pow1`
17×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
12×	`times-frac`
7×	`associate-r` `pow-prod-up`
6×	`cube-unmult` `associate-l` `pow3` `add-log-exp`
5×	`difference-cubes`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*` `unswap-sqr`
2×	`flip3--` `*-commutative` `flip--` `associate-/l/`
1×	`pow2` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `pow-sqr` `div-inv`

Counts

4 → 110

Calls

4 calls:

15.0ms	(* b (* b b))
13.0ms	(* (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))))
78.0ms	(/ (- (* (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b)))) (* b (* b b))) (fma b (+ b (sqrt (fma (* -4 a) c (* b b)))) (fma (* -4 a) c (* b b))))
22.0ms	(- (* (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b)))) (* b (* b b)))

series3.3s

Counts

4 → 12

Calls

4 calls:

59.0ms	(* b (* b b))
1.4s	(* (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))))
517.0ms	(/ (- (* (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b)))) (* b (* b b))) (fma b (+ b (sqrt (fma (* -4 a) c (* b b)))) (fma (* -4 a) c (* b b))))
1.3s	(- (* (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b)))) (* b (* b b)))

simplify1.7s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	2285
1	438
0	175

prune1.0s

Pruning

41 alts after pruning (41 fresh and 0 done)

Merged error: 25.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (* -4 a) c (* b b))
0.3b	(* b (* b b))
0.4b	(/ (fma (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))) (- (* b (* b b)))) (fma b (+ b (sqrt (fma (* -4 a) c (* b b)))) (fma (* -4 a) c (* b b))))
27.9b	(fma (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))) (- (* b (* b b))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
14×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l`
2×	`fma-udef`
1×	`pow2` `cbrt-undiv` `clear-num` `frac-2neg` `pow-plus` `cube-unmult` `div-exp` `associate-r` `pow-sqr` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

0.0ms	(fma (* -4 a) c (* b b))
30.0ms	(* b (* b b))
9.0ms	(/ (fma (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))) (- (* b (* b b)))) (fma b (+ b (sqrt (fma (* -4 a) c (* b b)))) (fma (* -4 a) c (* b b))))
1.0ms	(fma (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))) (- (* b (* b b))))

series751.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma (* -4 a) c (* b b))
62.0ms	(* b (* b b))
322.0ms	(/ (fma (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))) (- (* b (* b b)))) (fma b (+ b (sqrt (fma (* -4 a) c (* b b)))) (fma (* -4 a) c (* b b))))
295.0ms	(fma (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))) (- (* b (* b b))))

simplify1.2s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1217
1	274
0	128

prune935.0ms

Pruning

53 alts after pruning (53 fresh and 0 done)

Merged error: 25.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(* b (* b b))
0.4b	(/ (fma (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))) (- (* b (* b b)))) (fma b (+ b (sqrt (fma (* -4 a) c (* b b)))) (expm1 (log1p (fma (* -4 a) c (* b b))))))
1.8b	(expm1 (log1p (fma (* -4 a) c (* b b))))
27.9b	(fma (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))) (- (* b (* b b))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
14×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l`
1×	`pow2` `cbrt-undiv` `expm1-log1p` `clear-num` `frac-2neg` `pow-plus` `cube-unmult` `div-exp` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `div-inv` `expm1-udef` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

15.0ms	(* b (* b b))
4.0ms	(/ (fma (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))) (- (* b (* b b)))) (fma b (+ b (sqrt (fma (* -4 a) c (* b b)))) (expm1 (log1p (fma (* -4 a) c (* b b))))))
0.0ms	(expm1 (log1p (fma (* -4 a) c (* b b))))
0.0ms	(fma (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))) (- (* b (* b b))))

series22.9s

Counts

4 → 12

Calls

4 calls:

41.0ms	(* b (* b b))
22.4s	(/ (fma (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))) (- (* b (* b b)))) (fma b (+ b (sqrt (fma (* -4 a) c (* b b)))) (expm1 (log1p (fma (* -4 a) c (* b b))))))
255.0ms	(expm1 (log1p (fma (* -4 a) c (* b b))))
225.0ms	(fma (fma (* -4 a) c (* b b)) (sqrt (fma (* -4 a) c (* b b))) (- (* b (* b b))))

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	2247
1	478
0	191

prune489.0ms

Pruning

59 alts after pruning (59 fresh and 0 done)

Merged error: 25.0b

regimes1.4s

Accuracy

0% (2.8b remaining)

Error of 27.1b against oracle of 24.2b and baseline of 27.1b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	34
2	34
1	30
0	22

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	4427×	body	160	valid
925.0ms	8702×	body	80	nan
892.0ms	16702×	pre	80	true
436.0ms	3573×	body	80	valid