Details

sample64.0ms

Algorithm

intervals

Results

27.0ms

256×

body

valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	4350
5	2090
4	637
3	201
2	79
1	33
0	16

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (+ y t))
1.3b	(fma (+ y x) z (* a (+ y t)))
2.4b	(- (fma (+ y x) z (* a (+ y t))) (* b y))
23.0b	(/ (- (fma (+ y x) z (* a (+ y t))) (* b y)) (+ x (+ y t)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

29.0ms	(* a (+ y t))
0.0ms	(fma (+ y x) z (* a (+ y t)))
9.0ms	(- (fma (+ y x) z (* a (+ y t))) (* b y))
66.0ms	(/ (- (fma (+ y x) z (* a (+ y t))) (* b y)) (+ x (+ y t)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* a (+ y t))
73.0ms	(fma (+ y x) z (* a (+ y t)))
152.0ms	(- (fma (+ y x) z (* a (+ y t))) (* b y))
258.0ms	(/ (- (fma (+ y x) z (* a (+ y t))) (* b y)) (+ x (+ y t)))

simplify1.3s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1655
1	414
0	156

prune850.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ x (+ y t)) (- (fma (+ y x) z (* a (+ y t))) (* b y))))
1.3b	(fma (+ y x) z (* a (+ y t)))
2.4b	(- (fma (+ y x) z (* a (+ y t))) (* b y))
23.0b	(/ (+ x (+ y t)) (- (fma (+ y x) z (* a (+ y t))) (* b y)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

154×	`*-un-lft-identity`
138×	`times-frac`
74×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
24×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`div-exp` `associate-/l*`
6×	`flip3--` `div-inv` `flip--` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `fma-udef` `associate-/l/`
1×	`sub-neg` `flip3-+` `diff-log` `associate--l+` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 182

Calls

4 calls:

52.0ms	(/ 1 (/ (+ x (+ y t)) (- (fma (+ y x) z (* a (+ y t))) (* b y))))
0.0ms	(fma (+ y x) z (* a (+ y t)))
9.0ms	(- (fma (+ y x) z (* a (+ y t))) (* b y))
88.0ms	(/ (+ x (+ y t)) (- (fma (+ y x) z (* a (+ y t))) (* b y)))

series1.2s

Counts

4 → 12

Calls

4 calls:

884.0ms	(/ 1 (/ (+ x (+ y t)) (- (fma (+ y x) z (* a (+ y t))) (* b y))))
77.0ms	(fma (+ y x) z (* a (+ y t)))
140.0ms	(- (fma (+ y x) z (* a (+ y t))) (* b y))
107.0ms	(/ (+ x (+ y t)) (- (fma (+ y x) z (* a (+ y t))) (* b y)))

simplify1.9s

Counts

194 → 194

Iterations

Iter	Nodes
done	5000
2	2952
1	583
0	224

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.7b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ y x) t))
1.0b	(fma (+ y x) z (- (* (+ y t) a) (* b y)))
1.6b	(- (* (+ y t) a) (* b y))
23.1b	(* (/ 1 (+ (+ y x) t)) (fma (+ y x) z (- (* (+ y t) a) (* b y))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
32×	`times-frac`
31×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
21×	`associate-l` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `associate-/r/` `log1p-expm1-u`
3×	`associate-r` `fma-udef` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `div-inv`
1×	`distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3--` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-l/` `-commutative` `pow-flip` `flip--` `inv-pow`

Counts

4 → 116

Calls

4 calls:

27.0ms	(/ 1 (+ (+ y x) t))
0.0ms	(fma (+ y x) z (- (* (+ y t) a) (* b y)))
12.0ms	(- (* (+ y t) a) (* b y))
95.0ms	(* (/ 1 (+ (+ y x) t)) (fma (+ y x) z (- (* (+ y t) a) (* b y))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ 1 (+ (+ y x) t))
119.0ms	(fma (+ y x) z (- (* (+ y t) a) (* b y)))
42.0ms	(- (* (+ y t) a) (* b y))
243.0ms	(* (/ 1 (+ (+ y x) t)) (fma (+ y x) z (- (* (+ y t) a) (* b y))))

simplify1.4s

Counts

128 → 128

Iterations

Iter	Nodes
done	5000
2	2443
1	415
0	157

prune632.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ 1 (- (fma (+ y x) z (* a (+ y t))) (* b y)))
1.3b	(fma (+ y x) z (* a (+ y t)))
2.4b	(- (fma (+ y x) z (* a (+ y t))) (* b y))
22.0b	(/ (/ 1 (+ x (+ y t))) (/ 1 (- (fma (+ y x) z (* a (+ y t))) (* b y))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

762×	`times-frac`
552×	`*-un-lft-identity`
312×	`add-sqr-sqrt` `add-cube-cbrt`
144×	`distribute-lft-out`
79×	`associate-/r/`
48×	`add-exp-log`
40×	`div-inv`
34×	`div-exp`
24×	`flip3--` `flip--` `associate-/l*`
18×	`associate-/r*` `add-cbrt-cube`
16×	`flip3-+` `flip-+`
9×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`clear-num` `frac-2neg` `fma-udef`
1×	`sub-neg` `diff-log` `associate--l+` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 451

Calls

4 calls:

12.0ms	(/ 1 (- (fma (+ y x) z (* a (+ y t))) (* b y)))
0.0ms	(fma (+ y x) z (* a (+ y t)))
7.0ms	(- (fma (+ y x) z (* a (+ y t))) (* b y))
81.0ms	(/ (/ 1 (+ x (+ y t))) (/ 1 (- (fma (+ y x) z (* a (+ y t))) (* b y))))

series1.1s

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ 1 (- (fma (+ y x) z (* a (+ y t))) (* b y)))
61.0ms	(fma (+ y x) z (* a (+ y t)))
153.0ms	(- (fma (+ y x) z (* a (+ y t))) (* b y))
783.0ms	(/ (/ 1 (+ x (+ y t))) (/ 1 (- (fma (+ y x) z (* a (+ y t))) (* b y))))

simplify1.9s

Counts

463 → 463

Iterations

Iter	Nodes
done	5000
1	1951
0	557

prune2.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.7b

regimes906.0ms

Accuracy

48.4% (11.6b remaining)

Error of 16.0b against oracle of 4.5b and baseline of 26.8b

bsearch229.0ms

Steps

Iters	Range		Point
11	4.0721326822252617e+40	1.022342862720565e+63	3.3861281284597196e+60
9	-2.0076717784505904e+49	-6.499354134947939e+42	-2.3109830578270404e+48
10	-2.2840861367093013e+101	-1.408724127355391e+91	-2.073956642809604e+98
5	-7.0159311393260055e+140	-1.9128038684460106e+140	-1.9674995841746742e+140

simplify862.0ms

Iterations

Iter	Nodes
done	5000
14	2061
13	1331
12	601
11	413
10	223
9	167
8	112
7	88
6	72
5	59
4	53
3	50
2	44
1	41
0	30

end0.0ms

sample1.5s

Algorithm

intervals

Results

772.0ms	7996×	body	80	valid
1.0ms	2×	body	640	valid
0.0ms	2×	body	320	valid