Details

sample79.0ms

Algorithm

intervals

Results

53.0ms

275×

body

valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
10	1582
9	731
8	425
7	258
6	185
5	149
4	115
3	75
2	43
1	24
0	14

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* z (- b y)))
0.0b	(* z (- b y))
0.7b	(+ (* x y) (* z (- t a)))
20.9b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
54×	`prod-diff`
53×	`*-un-lft-identity`
51×	`add-cube-cbrt`
44×	`associate-+r+`
33×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `sub-neg`
5×	`associate-r`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `associate-l` `associate-/l`
2×	`+-commutative` `sum-log` `associate-*r/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 157

Calls

4 calls:

7.0ms	(+ y (* z (- b y)))
18.0ms	(* z (- b y))
19.0ms	(+ (* x y) (* z (- t a)))
29.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series645.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ y (* z (- b y)))
57.0ms	(* z (- b y))
86.0ms	(+ (* x y) (* z (- t a)))
462.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify786.0ms

Counts

169 → 169

Iterations

Iter	Nodes
done	2000
2	1657
1	653
0	281

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.5b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma z (- t a) (* x y))
20.9b	(/ (fma z (- t a) (* x y)) (fma z (- b y) y))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log`
3×	`associate-/r` `associate-/l`
2×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

2 → 41

Calls

2 calls:

0.0ms	(fma z (- t a) (* x y))
6.0ms	(/ (fma z (- t a) (* x y)) (fma z (- b y) y))

series457.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(fma z (- t a) (* x y))
391.0ms	(/ (fma z (- t a) (* x y)) (fma z (- b y) y))

simplify1.0s

Counts

47 → 47

Iterations

Iter	Nodes
done	2010
3	1018
2	284
1	120
0	71

prune414.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 16.0b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma z (- t a) (* x y))
0.5b	(/ 1 (fma z (- b y) y))
20.8b	(* (fma z (- t a) (* x y)) (/ 1 (fma z (- b y) y)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `associate-/r` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 84

Calls

3 calls:

0.0ms	(fma z (- t a) (* x y))
4.0ms	(/ 1 (fma z (- b y) y))
17.0ms	(* (fma z (- t a) (* x y)) (/ 1 (fma z (- b y) y)))

series527.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(fma z (- t a) (* x y))
82.0ms	(/ 1 (fma z (- b y) y))
373.0ms	(* (fma z (- t a) (* x y)) (/ 1 (fma z (- b y) y)))

simplify676.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	2000
2	595
1	225
0	109

prune577.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 16.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
0.7b	(+ (* x y) (* z (- t a)))
20.9b	(/ (+ (* x y) (* z (- t a))) (+ y (* (* (cbrt z) (cbrt z)) (* (cbrt z) (- b y)))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
22×	`associate-+r+`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`times-frac`
6×	`cbrt-prod` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`sub-neg` `pow1/3` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 99

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
18.0ms	(+ (* x y) (* z (- t a)))
44.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* (* (cbrt z) (cbrt z)) (* (cbrt z) (- b y)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

270.0ms	(cbrt z)
278.0ms	(cbrt z)
75.0ms	(+ (* x y) (* z (- t a)))
555.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* (* (cbrt z) (cbrt z)) (* (cbrt z) (- b y)))))

simplify655.0ms

Counts

111 → 111

Iterations

Iter	Nodes
done	2000
2	1272
1	430
0	182

prune673.0ms

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 16.0b

regimes1.2s

Accuracy

-11.6% (4.8b remaining)

Error of 23.6b against oracle of 18.7b and baseline of 23.1b

bsearch163.0ms

Steps

Iters	Range		Point
10	1.213217432574003e+252	5.168756954155322e+264	6.28393270841488e+258
11	5.514109538783242e+162	6.641943257748035e+184	1.273171169071947e+184

simplify5.0ms

Iterations

Iter	Nodes
done	31
1	31
0	24

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

8428×

body

valid