Details

sample57.0ms

Algorithm

intervals

Results

39.0ms

256×

body

valid

simplify4.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	4082
7	1989
6	1145
5	750
4	496
3	200
2	79
1	33
0	16

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (+ z a) b) y)
0.5b	(fma a t (* (- (+ z a) b) y))
0.5b	(fma z x (fma a t (* (- (+ z a) b) y)))
22.7b	(/ (fma z x (fma a t (* (- (+ z a) b) y))) (+ x (+ y t)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac`
13×	`distribute-lft-out`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-l`
5×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-/l*`
2×	`associate-*l/` `associate-/r/` `fma-udef` `distribute-lft-out--`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `div-inv` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

107.0ms	(* (- (+ z a) b) y)
0.0ms	(fma a t (* (- (+ z a) b) y))
0.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
34.0ms	(/ (fma z x (fma a t (* (- (+ z a) b) y))) (+ x (+ y t)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (- (+ z a) b) y)
81.0ms	(fma a t (* (- (+ z a) b) y))
146.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
238.0ms	(/ (fma z x (fma a t (* (- (+ z a) b) y))) (+ x (+ y t)))

simplify1.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	957
1	289
0	137

prune743.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (+ z a) b) y)
0.5b	(fma a t (* (- (+ z a) b) y))
0.5b	(fma z x (fma a t (* (- (+ z a) b) y)))
22.8b	(* (fma z x (fma a t (* (- (+ z a) b) y))) (/ 1 (+ x (+ y t))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
24×	`associate-r`
17×	`times-frac`
16×	`add-cube-cbrt`
15×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`distribute-lft-out`
9×	`associate-l`
8×	`pow1`
5×	`prod-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-unprod`
2×	`div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `fma-udef` `distribute-lft-out--`
1×	`cbrt-undiv` `rec-exp` `flip3-+` `flip3--` `1-exp` `associate-*r/` `un-div-inv` `flip-+` `div-inv` `flip--` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

81.0ms	(* (- (+ z a) b) y)
0.0ms	(fma a t (* (- (+ z a) b) y))
0.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
47.0ms	(* (fma z x (fma a t (* (- (+ z a) b) y))) (/ 1 (+ x (+ y t))))

series410.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (- (+ z a) b) y)
73.0ms	(fma a t (* (- (+ z a) b) y))
109.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
184.0ms	(* (fma z x (fma a t (* (- (+ z a) b) y))) (/ 1 (+ x (+ y t))))

simplify1.2s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	1408
1	382
0	162

prune633.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y)))))
0.5b	(fma a t (* (- (+ z a) b) y))
0.5b	(fma z x (fma a t (* (- (+ z a) b) y)))
22.7b	(/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
132×	`times-frac`
70×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
22×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `fma-udef` `associate-/l/`
1×	`flip3-+` `associate-/r/` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 165

Calls

4 calls:

28.0ms	(/ 1 (/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y)))))
0.0ms	(fma a t (* (- (+ z a) b) y))
0.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
45.0ms	(/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y))))

series1.1s

Counts

4 → 12

Calls

4 calls:

828.0ms	(/ 1 (/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y)))))
73.0ms	(fma a t (* (- (+ z a) b) y))
115.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
103.0ms	(/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y))))

simplify2.6s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
3	4807
2	1343
1	464
0	192

prune972.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma a t (* (- (+ z a) b) y))
0.5b	(fma z x (fma a t (* (- (+ z a) b) y)))
0.8b	(/ 1 (fma z x (fma a t (* (- (+ z a) b) y))))
21.9b	(* (+ x (+ y t)) (/ 1 (fma z x (fma a t (* (- (+ z a) b) y)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
20×	`times-frac` `add-cube-cbrt`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `associate-*l/` `cbrt-unprod` `flip-+` `fma-udef` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 101

Calls

4 calls:

0.0ms	(fma a t (* (- (+ z a) b) y))
0.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
7.0ms	(/ 1 (fma z x (fma a t (* (- (+ z a) b) y))))
56.0ms	(* (+ x (+ y t)) (/ 1 (fma z x (fma a t (* (- (+ z a) b) y)))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(fma a t (* (- (+ z a) b) y))
158.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
91.0ms	(/ 1 (fma z x (fma a t (* (- (+ z a) b) y))))
131.0ms	(* (+ x (+ y t)) (/ 1 (fma z x (fma a t (* (- (+ z a) b) y)))))

simplify1.2s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	1227
1	333
0	139

prune543.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.7b

regimes815.0ms

Accuracy

47.1% (10.6b remaining)

Error of 15.2b against oracle of 4.6b and baseline of 24.6b

bsearch121.0ms

Steps

Iters	Range		Point
8	695318447.7085649	1776871083790.3284	1752559586117.6345
9	-3.982578560469253e+86	-1.7079472454689577e+77	-1.2195156445786848e+79

simplify5.0ms

Iterations

Iter	Nodes
done	33
1	33
0	24

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.5s	7996×	body	80	valid
1.0ms	2×	body	160	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	640	valid