Details

sample105.0ms

Algorithm

intervals

Results

28.0ms	521×	pre	80	true
23.0ms	265×	body	80	nan
22.0ms	126×	body	160	valid
12.0ms	130×	body	80	valid

simplify93.0ms

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma -3 (* c a) (* b b)))
0.2b	(fma -3 (* c a) (* b b))
0.3b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
25.4b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite52.0ms

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` `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 → 98

Calls

4 calls:

2.0ms	(sqrt (fma -3 (* c a) (* b b)))
0.0ms	(fma -3 (* c a) (* b b))
34.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
14.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series420.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(sqrt (fma -3 (* c a) (* b b)))
76.0ms	(fma -3 (* c a) (* b b))
122.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
97.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify2.1s

Counts

110 → 110

Iterations

Iter	Nodes
3	3547
2	949
1	324
0	148

prune1.3s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 23.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))))
0.3b	(/ (/ (- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b)) (+ (fma (sqrt (fma -3 (* a c) (* b b))) b (* b b)) (fma -3 (* a c) (* b b)))) (* 3 a))
0.4b	(/ (- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b)) (+ (fma (sqrt (fma -3 (* a c) (* b b))) b (* b b)) (fma -3 (* a c) (* b b))))
24.3b	(- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

70×	`times-frac`
61×	`*-un-lft-identity`
54×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
29×	`pow3`
26×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
14×	`difference-cubes`
13×	`distribute-lft-out`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r` `associate-/r/` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u` `div-inv`
3×	`flip3-+` `div-sub` `associate-l` `prod-exp` `cbrt-unprod` `flip-+` `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 → 154

Calls

4 calls:

9.0ms	(* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))))
52.0ms	(/ (/ (- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b)) (+ (fma (sqrt (fma -3 (* a c) (* b b))) b (* b b)) (fma -3 (* a c) (* b b)))) (* 3 a))
84.0ms	(/ (- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b)) (+ (fma (sqrt (fma -3 (* a c) (* b b))) b (* b b)) (fma -3 (* a c) (* b b))))
14.0ms	(- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b))

series4.2s

Counts

4 → 12

Calls

4 calls:

1.6s	(* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))))
640.0ms	(/ (/ (- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b)) (+ (fma (sqrt (fma -3 (* a c) (* b b))) b (* b b)) (fma -3 (* a c) (* b b)))) (* 3 a))
552.0ms	(/ (- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b)) (+ (fma (sqrt (fma -3 (* a c) (* b b))) b (* b b)) (fma -3 (* a c) (* b b))))
1.4s	(- (* (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b)))) (* (* b b) b))

simplify1.3s

Counts

166 → 166

Iterations

Iter	Nodes
2	2195
1	637
0	244

prune2.5s

Pruning

44 alts after pruning (44 fresh and 0 done)

Merged error: 22.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma -3 (* a c) (* b b))
0.3b	(/ (/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (+ (fma (sqrt (fma -3 (* a c) (* b b))) b (* b b)) (fma -3 (* a c) (* b b)))) (* 3 a))
0.4b	(/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (+ (fma (sqrt (fma -3 (* a c) (* b b))) b (* b b)) (fma -3 (* a c) (* b b))))
24.1b	(fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
49×	`*-un-lft-identity`
29×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`associate-/l*`
18×	`add-cbrt-cube` `add-exp-log`
10×	`distribute-lft-out`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `fma-udef`
1×	`associate-/l/`

Counts

4 → 113

Calls

4 calls:

0.0ms	(fma -3 (* a c) (* b b))
15.0ms	(/ (/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (+ (fma (sqrt (fma -3 (* a c) (* b b))) b (* b b)) (fma -3 (* a c) (* b b)))) (* 3 a))
7.0ms	(/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (+ (fma (sqrt (fma -3 (* a c) (* b b))) b (* b b)) (fma -3 (* a c) (* b b))))
0.0ms	(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:

73.0ms	(fma -3 (* a c) (* b b))
486.0ms	(/ (/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (+ (fma (sqrt (fma -3 (* a c) (* b b))) b (* b b)) (fma -3 (* a c) (* b b)))) (* 3 a))
406.0ms	(/ (fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b))) (+ (fma (sqrt (fma -3 (* a c) (* b b))) b (* b b)) (fma -3 (* a c) (* b b))))
238.0ms	(fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b)))

simplify6.2s

Counts

125 → 125

Iterations

Iter	Nodes
3	7401
2	1405
1	438
0	181

prune1.9s

Pruning

55 alts after pruning (55 fresh and 0 done)

Merged error: 21.9b

localize60.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma -3 (* a c) (* b b)))
0.6b	(cbrt (fma -3 (* a c) (* b b)))
0.6b	(cbrt (fma -3 (* a c) (* b b)))
24.1b	(fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b)))

rewrite4.0ms

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` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (fma -3 (* a c) (* b b)))
1.0ms	(cbrt (fma -3 (* a c) (* b b)))
1.0ms	(cbrt (fma -3 (* a c) (* b b)))
0.0ms	(fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b)))

series1.1s

Counts

4 → 12

Calls

4 calls:

249.0ms	(cbrt (fma -3 (* a c) (* b b)))
278.0ms	(cbrt (fma -3 (* a c) (* b b)))
294.0ms	(cbrt (fma -3 (* a c) (* b b)))
288.0ms	(fma (fma -3 (* a c) (* b b)) (sqrt (fma -3 (* a c) (* b b))) (- (* (* b b) b)))

simplify2.7s

Counts

61 → 61

Iterations

Iter	Nodes
4	5226
3	1330
2	396
1	159
0	77

prune1.0s

Pruning

56 alts after pruning (55 fresh and 1 done)

Merged error: 21.9b

regimes1.3s

Accuracy

0% (2.6b remaining)

Error of 27.4b against oracle of 24.8b and baseline of 27.4b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
3	33
2	33
1	29
0	20

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.5s	4502×	body	160	valid
1.1s	8584×	body	80	nan
1.1s	16584×	pre	80	true
412.0ms	3498×	body	80	valid