Details

sample30.0ms

Algorithm

intervals

Results

10.0ms	254×	body	80	valid
3.0ms	18×	body	640	valid
1.0ms	5×	body	1280	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1890
5	788
4	299
3	108
2	43
1	20
0	11

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.4b	(fma (/ (- z t) (- a t)) (- y x) x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

25.0ms	(/ (- z t) (- a t))
0.0ms	(fma (/ (- z t) (- a t)) (- y x) x)

series288.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(/ (- z t) (- a t))
202.0ms	(fma (/ (- z t) (- a t)) (- y x) x)

simplify1.9s

Counts

70 → 70

Iterations

Iter	Nodes
done	5002
3	2154
2	678
1	272
0	116

prune493.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.3b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.1b	(* (/ (- z t) (- a t)) (- y x))
1.1b	(+ (* (/ (- z t) (- a t)) (- y x)) x)

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
51×	`times-frac` `add-cube-cbrt`
36×	`prod-diff`
31×	`associate-l`
23×	`distribute-lft-out--` `difference-of-squares`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `associate-r` `flip--` `associate-/l` `add-log-exp`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-times` `cbrt-undiv` `div-exp` `prod-exp` `associate-*r/` `cbrt-unprod` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `-commutative` `flip-+`

Counts

3 → 170

Calls

3 calls:

25.0ms	(/ (- z t) (- a t))
76.0ms	(* (/ (- z t) (- a t)) (- y x))
22.0ms	(+ (* (/ (- z t) (- a t)) (- y x)) x)

series794.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (- z t) (- a t))
481.0ms	(* (/ (- z t) (- a t)) (- y x))
240.0ms	(+ (* (/ (- z t) (- a t)) (- y x)) x)

simplify1.8s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
2	2193
1	715
0	255

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- z t) (- a t))
0.0b	(/ (- z t) (- a t))
0.8b	(* (/ (- z t) (- a t)) y)
3.3b	(fma (/ (- z t) (- a t)) (- x) x)

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
76×	`times-frac`
40×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-l`
13×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r` `associate-/l`
6×	`pow1` `associate-/r/`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`clear-num` `frac-2neg` `div-sub` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`pow-prod-down` `associate-l/` `-commutative` `fma-udef`

Counts

4 → 170

Calls

4 calls:

24.0ms	(/ (- z t) (- a t))
31.0ms	(/ (- z t) (- a t))
54.0ms	(* (/ (- z t) (- a t)) y)
0.0ms	(fma (/ (- z t) (- a t)) (- x) x)

series466.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (- z t) (- a t))
73.0ms	(/ (- z t) (- a t))
165.0ms	(* (/ (- z t) (- a t)) y)
163.0ms	(fma (/ (- z t) (- a t)) (- x) x)

simplify2.3s

Counts

182 → 182

Iterations

Iter	Nodes
done	5000
3	4317
2	1159
1	406
0	162

prune926.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.8b	(* (/ (- z t) (- a t)) (* (cbrt y) (cbrt y)))
3.3b	(fma (/ (- z t) (- a t)) (- x) x)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
31×	`associate-l`
26×	`times-frac`
17×	`add-cube-cbrt`
16×	`add-exp-log`
12×	`add-cbrt-cube`
10×	`distribute-lft-out--` `difference-of-squares`
9×	`pow1`
6×	`cbrt-prod` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`cbrt-undiv` `pow1/3` `div-exp` `associate-/r/` `unswap-sqr`
1×	`flip3--` `associate-r` `associate-l/` `-commutative` `fma-udef` `div-inv` `flip--`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
49.0ms	(* (/ (- z t) (- a t)) (* (cbrt y) (cbrt y)))
0.0ms	(fma (/ (- z t) (- a t)) (- x) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

266.0ms	(cbrt y)
627.0ms	(cbrt y)
348.0ms	(* (/ (- z t) (- a t)) (* (cbrt y) (cbrt y)))
114.0ms	(fma (/ (- z t) (- a t)) (- x) x)

simplify2.5s

Counts

103 → 103

Iterations

Iter	Nodes
done	5025
3	4006
2	1046
1	370
0	139

prune716.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.3b

regimes1.0s

Accuracy

32.7% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 7.6b

bsearch2.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	40
1	40
0	29

end0.0ms

sample1.4s

Algorithm

intervals

Results

730.0ms	7870×	body	80	valid
97.0ms	458×	body	640	valid
72.0ms	263×	body	1280	valid
60.0ms	374×	body	320	valid
44.0ms	258×	body	160	valid
8.0ms	23×	body	2560	valid