Details

sample141.0ms

Algorithm

intervals

Results

46.0ms	552×	pre	80	true
32.0ms	147×	body	160	valid
30.0ms	296×	body	80	nan
12.0ms	109×	body	80	valid

simplify104.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma -3 (* c a) (* b b)))
0.3b	(fma -3 (* c a) (* b b))
0.4b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
29.7b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

1.0ms	(sqrt (fma -3 (* c a) (* b b)))
0.0ms	(fma -3 (* c a) (* b b))
30.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
8.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series422.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt (fma -3 (* c a) (* b b)))
66.0ms	(fma -3 (* c a) (* b b))
124.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
105.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify2.1s

Counts

114 → 114

Iterations

Iter	Nodes
3	3402
2	935
1	329
0	152

prune1.0s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 27.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))))
0.4b	(/ (- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b)) (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
0.4b	(/ (/ (- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b)) (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b))))) (* 3 a))
28.6b	(- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
48×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `add-cube-cbrt`
23×	`pow3`
20×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
11×	`difference-cubes`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`div-sub` `associate-l` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `pow-prod-up` `flip--` `unswap-sqr`
1×	`sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `*-commutative`

Counts

4 → 139

Calls

4 calls:

9.0ms	(* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))))
47.0ms	(/ (- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b)) (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
75.0ms	(/ (/ (- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b)) (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b))))) (* 3 a))
33.0ms	(- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b))

series3.7s

Counts

4 → 12

Calls

4 calls:

1.5s	(* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))))
599.0ms	(/ (- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b)) (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
541.0ms	(/ (/ (- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b)) (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b))))) (* 3 a))
1.1s	(- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b))

simplify5.1s

Counts

151 → 151

Iterations

Iter	Nodes
3	7431
2	1658
1	566
0	231

prune1.9s

Pruning

41 alts after pruning (41 fresh and 0 done)

Merged error: 26.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* b b) b)
0.4b	(/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
0.4b	(/ (/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b))))) (* 3 a))
28.2b	(fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
28×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `add-cube-cbrt`
23×	`pow1` `add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`pow-plus` `pow-prod-up`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-r` `pow-prod-down`
2×	`pow2` `clear-num` `frac-2neg` `pow-sqr`
1×	`associate-l` `pow3` `*-commutative` `fma-udef` `unswap-sqr` `associate-/l/`

Counts

4 → 121

Calls

4 calls:

24.0ms	(* (* b b) b)
8.0ms	(/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
16.0ms	(/ (/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b))))) (* 3 a))
0.0ms	(fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b)))

series1.4s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* b b) b)
709.0ms	(/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
446.0ms	(/ (/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b))))) (* 3 a))
228.0ms	(fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b)))

simplify3.5s

Counts

133 → 133

Iterations

Iter	Nodes
3	5786
2	1227
1	423
0	186

prune1.6s

Pruning

52 alts after pruning (52 fresh and 0 done)

Merged error: 25.9b

localize104.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
0.5b	(cbrt (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
0.5b	(cbrt (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
28.2b	(fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
1.0ms	(cbrt (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
1.0ms	(cbrt (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
1.0ms	(fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b)))

series1.2s

Counts

4 → 12

Calls

4 calls:

298.0ms	(cbrt (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
305.0ms	(cbrt (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
353.0ms	(cbrt (fma b (sqrt (fma -3 (* a c) (* b b))) (+ (* b b) (fma -3 (* a c) (* b b)))))
260.0ms	(fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b)))

simplify3.1s

Counts

65 → 65

Iterations

Iter	Nodes
4	6407
3	1443
2	426
1	170
0	81

prune994.0ms

Pruning

57 alts after pruning (57 fresh and 0 done)

Merged error: 25.9b

regimes1.6s

Accuracy

0% (2.8b remaining)

Error of 27.7b against oracle of 24.9b and baseline of 27.7b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
3	35
2	35
1	31
0	22

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.4s	8407×	body	80	nan
1.2s	4503×	body	160	valid
1.1s	16407×	pre	80	true
559.0ms	3497×	body	80	valid