Details

sample47.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify9.3s

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

prune57.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (+ z a) b) y)
0.3b	(fma z x (fma a t (* (- (+ z a) b) y)))
0.5b	(fma a t (* (- (+ z a) b) y))
24.6b	(/ (fma z x (fma a t (* (- (+ z a) b) y))) (+ x (+ y t)))

rewrite230.0ms

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:

176.0ms	(* (- (+ z a) b) y)
1.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
1.0ms	(fma a t (* (- (+ z a) b) y))
47.0ms	(/ (fma z x (fma a t (* (- (+ z a) b) y))) (+ x (+ y t)))

series800.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (- (+ z a) b) y)
228.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
100.0ms	(fma a t (* (- (+ z a) b) y))
423.0ms	(/ (fma z x (fma a t (* (- (+ z a) b) y))) (+ x (+ y t)))

simplify2.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	975
1	289
0	137

prune1.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.7b

localize89.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y)))))
0.3b	(fma z x (fma a t (* (- (+ z a) b) y)))
0.5b	(fma a t (* (- (+ z a) b) y))
24.6b	(/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y))))

rewrite161.0ms

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:

58.0ms	(/ 1 (/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y)))))
1.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
1.0ms	(fma a t (* (- (+ z a) b) y))
86.0ms	(/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y))))

series1.7s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ 1 (/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y)))))
203.0ms	(fma z x (fma a t (* (- (+ z a) b) y)))
98.0ms	(fma a t (* (- (+ z a) b) y))
166.0ms	(/ (+ x (+ y t)) (fma z x (fma a t (* (- (+ z a) b) y))))

simplify6.2s

Counts

177 → 177

Iterations

Iter	Nodes
done	5000
3	4658
2	1201
1	465
0	192

prune2.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.0b

localize162.0ms

Local error

Found 4 expressions with local error:

6.5b	(* (/ (* (cbrt (fma z x (fma a t (* (- (+ z a) b) y)))) (cbrt (fma z x (fma a t (* (- (+ z a) b) y))))) 1) (/ (cbrt (fma z x (fma a t (* (- (+ z a) b) y)))) (+ x (+ y t))))
25.2b	(cbrt (fma z x (fma a t (* (- (+ z a) b) y))))
25.2b	(cbrt (fma z x (fma a t (* (- (+ z a) b) y))))
25.2b	(cbrt (fma z x (fma a t (* (- (+ z a) b) y))))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
47×	`add-sqr-sqrt`
45×	`times-frac`
37×	`add-exp-log`
36×	`associate-r`
27×	`cbrt-prod`
26×	`add-cube-cbrt`
18×	`add-cbrt-cube` `distribute-lft-out`
14×	`prod-exp`
13×	`div-exp`
9×	`unswap-sqr`
8×	`cbrt-unprod`
7×	`cbrt-undiv` `associate-l`
6×	`pow1`
4×	`expm1-log1p-u` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`associate-/r/` `div-inv`
1×	`frac-times` `flip3-+` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip-+`

Counts

4 → 125

Calls

4 calls:

185.0ms	(* (/ (* (cbrt (fma z x (fma a t (* (- (+ z a) b) y)))) (cbrt (fma z x (fma a t (* (- (+ z a) b) y))))) 1) (/ (cbrt (fma z x (fma a t (* (- (+ z a) b) y)))) (+ x (+ y t))))
3.0ms	(cbrt (fma z x (fma a t (* (- (+ z a) b) y))))
3.0ms	(cbrt (fma z x (fma a t (* (- (+ z a) b) y))))
2.0ms	(cbrt (fma z x (fma a t (* (- (+ z a) b) y))))

series2.3s

Counts

4 → 12

Calls

4 calls:

430.0ms	(* (/ (* (cbrt (fma z x (fma a t (* (- (+ z a) b) y)))) (cbrt (fma z x (fma a t (* (- (+ z a) b) y))))) 1) (/ (cbrt (fma z x (fma a t (* (- (+ z a) b) y)))) (+ x (+ y t))))
654.0ms	(cbrt (fma z x (fma a t (* (- (+ z a) b) y))))
603.0ms	(cbrt (fma z x (fma a t (* (- (+ z a) b) y))))
606.0ms	(cbrt (fma z x (fma a t (* (- (+ z a) b) y))))

simplify3.6s

Counts

137 → 137

Iterations

Iter	Nodes
done	5001
2	1742
1	641
0	204

prune1.7s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x (+ y t)))
0.6b	(cbrt (+ x (+ y t)))
9.4b	(/ (cbrt (+ x (+ y t))) (fma z x (fma a t (* (- (+ z a) b) y))))
14.7b	(/ (/ 1 (/ (* (cbrt (+ x (+ y t))) (cbrt (+ x (+ y t)))) 1)) (/ (cbrt (+ x (+ y t))) (fma z x (fma a t (* (- (+ z a) b) y)))))

rewrite417.0ms

Algorithm

rewrite-expression-head

Rules

2270×	`times-frac`
1269×	`*-un-lft-identity`
834×	`add-sqr-sqrt` `add-cube-cbrt`
435×	`cbrt-prod`
261×	`distribute-lft-out`
145×	`div-inv`
120×	`add-exp-log`
93×	`div-exp`
34×	`associate-/l*`
31×	`associate-/r*`
30×	`associate-/r/`
29×	`add-cbrt-cube`
23×	`cbrt-undiv`
22×	`1-exp`
12×	`prod-exp`
10×	`rec-exp`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l/`
2×	`clear-num` `frac-2neg` `pow1/3` `cbrt-unprod`

Counts

4 → 925

Calls

4 calls:

17.0ms	(cbrt (+ x (+ y t)))
18.0ms	(cbrt (+ x (+ y t)))
54.0ms	(/ (cbrt (+ x (+ y t))) (fma z x (fma a t (* (- (+ z a) b) y))))
153.0ms	(/ (/ 1 (/ (* (cbrt (+ x (+ y t))) (cbrt (+ x (+ y t)))) 1)) (/ (cbrt (+ x (+ y t))) (fma z x (fma a t (* (- (+ z a) b) y)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

221.0ms	(cbrt (+ x (+ y t)))
222.0ms	(cbrt (+ x (+ y t)))
411.0ms	(/ (cbrt (+ x (+ y t))) (fma z x (fma a t (* (- (+ z a) b) y))))
956.0ms	(/ (/ 1 (/ (* (cbrt (+ x (+ y t))) (cbrt (+ x (+ y t)))) 1)) (/ (cbrt (+ x (+ y t))) (fma z x (fma a t (* (- (+ z a) b) y)))))

simplify5.0s

Counts

937 → 937

Iterations

Iter	Nodes
done	5003
1	4126
0	1165

prune10.3s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.0b

regimes1.8s

Accuracy

48.5% (11.6b remaining)

Error of 16.1b against oracle of 4.5b and baseline of 27.0b

bsearch101.0ms

Steps

Iters	Range		Point
8	2.4453942514097082e+73	1.1646077756330867e+77	2.5679851439195343e+75
6	-4.556345573702227e+73	-4.217802647696024e+72	-2.6725091383027097e+73

simplify8.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample1.0s

Algorithm

intervals

Results

638.0ms	7999×	body	80	valid
0.0ms	1×	body	320	valid