Details

sample40.0ms

Algorithm

intervals

Results

14.0ms

263×

body

valid

simplify74.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	65
5	65
4	61
3	51
2	38
1	26
0	15

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.4b

localize16.0ms

Local error

Found 3 expressions with local error:

2.9b	(fma y (/ b t) (+ a 1.0))
3.7b	(fma (/ z t) y x)
8.1b	(/ (fma (/ z t) y x) (fma y (/ b t) (+ a 1.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma y (/ b t) (+ a 1.0))
0.0ms	(fma (/ z t) y x)
4.0ms	(/ (fma (/ z t) y x) (fma y (/ b t) (+ a 1.0)))

series366.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(fma y (/ b t) (+ a 1.0))
67.0ms	(fma (/ z t) y x)
234.0ms	(/ (fma (/ z t) y x) (fma y (/ b t) (+ a 1.0)))

simplify842.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
3	1228
2	307
1	125
0	77

prune439.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* b (/ y t)) (+ a 1.0))
3.6b	(* b (/ y t))
3.7b	(fma (/ z t) y x)
8.1b	(/ (fma (/ z t) y x) (+ (* b (/ y t)) (+ a 1.0)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
13×	`associate-r`
11×	`add-cbrt-cube` `add-exp-log`
9×	`add-log-exp`
6×	`pow1`
5×	`associate-*r/`
4×	`expm1-log1p-u` `flip3-+` `frac-add` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`associate-/r` `sum-log` `associate-l` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `clear-num` `fma-def` `frac-2neg` `pow-prod-down` `*-commutative` `fma-udef`

Counts

4 → 95

Calls

4 calls:

20.0ms	(+ (* b (/ y t)) (+ a 1.0))
22.0ms	(* b (/ y t))
0.0ms	(fma (/ z t) y x)
57.0ms	(/ (fma (/ z t) y x) (+ (* b (/ y t)) (+ a 1.0)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ (* b (/ y t)) (+ a 1.0))
26.0ms	(* b (/ y t))
62.0ms	(fma (/ z t) y x)
318.0ms	(/ (fma (/ z t) y x) (+ (* b (/ y t)) (+ a 1.0)))

simplify937.0ms

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	1647
1	458
0	179

prune849.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ a 1.0) (/ (* y b) t))
6.1b	(/ (* y b) t)
6.3b	(/ (* y z) t)
8.1b	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
26×	`times-frac`
25×	`distribute-lft-out`
20×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/r*`
9×	`add-log-exp`
6×	`associate-/l*`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`expm1-log1p-u` `pow1` `fma-def` `frac-add` `associate-/r/` `log1p-expm1-u`
3×	`clear-num` `sum-log` `frac-2neg` `div-inv`
2×	`prod-exp` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `associate-+l+`

Counts

4 → 118

Calls

4 calls:

35.0ms	(+ (+ a 1.0) (/ (* y b) t))
15.0ms	(/ (* y b) t)
15.0ms	(/ (* y z) t)
86.0ms	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (+ a 1.0) (/ (* y b) t))
39.0ms	(/ (* y b) t)
33.0ms	(/ (* y z) t)
158.0ms	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))

simplify1.1s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	2625
1	512
0	195

prune896.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (/ (/ t y) b))
3.7b	(/ (/ t y) b)
6.3b	(/ (* y z) t)
8.1b	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ 1 (/ (/ t y) b))))

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

499×	`times-frac`
301×	`*-un-lft-identity`
245×	`add-sqr-sqrt` `add-cube-cbrt`
56×	`associate-/r*`
38×	`distribute-lft-out`
37×	`add-exp-log`
34×	`div-inv`
25×	`add-cbrt-cube`
21×	`div-exp` `associate-/l*`
12×	`cbrt-undiv`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `flip3-+` `1-exp` `flip-+` `associate-/l/`
2×	`frac-add`
1×	`prod-exp` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 356

Calls

4 calls:

32.0ms	(/ 1 (/ (/ t y) b))
18.0ms	(/ (/ t y) b)
14.0ms	(/ (* y z) t)
236.0ms	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ 1 (/ (/ t y) b))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1 (/ (/ t y) b))
28.0ms	(/ (/ t y) b)
20.0ms	(/ (* y z) t)
167.0ms	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ 1 (/ (/ t y) b))))

simplify845.0ms

Counts

368 → 368

Iterations

Iter	Nodes
done	5000
1	1560
0	556

prune2.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.0b

regimes1.3s

Accuracy

41.7% (2.5b remaining)

Error of 13.2b against oracle of 10.7b and baseline of 14.9b

bsearch150.0ms

Steps

Iters	Range		Point
8	2.5371791648247652e-45	6.718392364159933e-43	6.661904461324814e-43
8	-2.377518062730008e+47	-2.734380216735275e+44	-1.456503524337498e+46

simplify4.0ms

Iterations

Iter	Nodes
done	43
1	43
0	30

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.3s

8259×

body

valid