Details

sample65.0ms

Algorithm

intervals

Results

28.0ms	255×	body	80	valid
0.0ms	1×	body	320	valid

simplify4.4s

Counts

1 → 1

Iterations

Useful iterations: 4 (139.0ms)

Iter	Nodes	Cost
0	16	21
1	33	20
2	79	20
3	201	20
4	637	19
5	2240	19
6	4952	19
done	5000	19

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (- a b))
0.5b	(fma (+ x y) z (fma a t (* y (- a b))))
24.2b	(/ (fma (+ x y) z (fma a t (* y (- a b)))) (+ (+ x t) y))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
18×	`prod-diff`
15×	`times-frac`
12×	`distribute-lft-out`
11×	`distribute-rgt-in` `distribute-lft-in`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-r` `associate-/r*`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`sub-neg` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 95

Calls

3 calls:

36.0ms	(* y (- a b))
0.0ms	(fma (+ x y) z (fma a t (* y (- a b))))
64.0ms	(/ (fma (+ x y) z (fma a t (* y (- a b)))) (+ (+ x t) y))

series571.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* y (- a b))
127.0ms	(fma (+ x y) z (fma a t (* y (- a b))))
404.0ms	(/ (fma (+ x y) z (fma a t (* y (- a b)))) (+ (+ x t) y))

simplify779.0ms

Counts

104 → 104

Iterations

Useful iterations: done (774.0ms)

Iter	Nodes	Cost
0	173	2087
1	383	1897
2	1402	1673
done	5002	1647

prune368.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma (+ x y) z (fma a t (+ (* y (- (pow (cbrt a) 3) b)) (* (+ (- b) b) y))))
0.5b	(cbrt a)
0.7b	(pow (cbrt a) 3)
24.2b	(/ (fma (+ x y) z (fma a t (+ (* y (- (pow (cbrt a) 3) b)) (* (+ (- b) b) y)))) (+ (+ x t) y))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`times-frac`
12×	`distribute-lft-out`
9×	`cbrt-prod`
7×	`add-exp-log`
6×	`unpow-prod-down` `cube-prod` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/l*`
2×	`pow-pow` `pow1/3` `associate-/r/`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `frac-2neg` `flip3-+` `unpow3` `div-exp` `pow-exp` `clear-num` `flip-+` `fma-udef` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

0.0ms	(fma (+ x y) z (fma a t (+ (* y (- (pow (cbrt a) 3) b)) (* (+ (- b) b) y))))
1.0ms	(cbrt a)
6.0ms	(pow (cbrt a) 3)
70.0ms	(/ (fma (+ x y) z (fma a t (+ (* y (- (pow (cbrt a) 3) b)) (* (+ (- b) b) y)))) (+ (+ x t) y))

series1.2s

Counts

4 → 12

Calls

4 calls:

186.0ms	(fma (+ x y) z (fma a t (+ (* y (- (pow (cbrt a) 3) b)) (* (+ (- b) b) y))))
213.0ms	(cbrt a)
308.0ms	(pow (cbrt a) 3)
470.0ms	(/ (fma (+ x y) z (fma a t (+ (* y (- (pow (cbrt a) 3) b)) (* (+ (- b) b) y)))) (+ (+ x t) y))

simplify2.1s

Counts

106 → 106

Iterations

Useful iterations: 3 (982.0ms)

Iter	Nodes	Cost
0	138	2379
1	346	1955
2	1105	1661
3	4667	1526
done	5000	1526

prune511.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x y) t) (fma z (+ x y) (fma y (+ (- a b) 0) (* a t)))))
0.3b	(fma y (+ (- a b) 0) (* a t))
0.5b	(fma z (+ x y) (fma y (+ (- a b) 0) (* a t)))
24.2b	(/ (+ (+ x y) t) (fma z (+ x y) (fma y (+ (- a b) 0) (* a t))))

rewrite147.0ms

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×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `fma-udef` `associate-/l/`
1×	`pow-flip` `flip3-+` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 161

Calls

4 calls:

47.0ms	(/ 1 (/ (+ (+ x y) t) (fma z (+ x y) (fma y (+ (- a b) 0) (* a t)))))
0.0ms	(fma y (+ (- a b) 0) (* a t))
0.0ms	(fma z (+ x y) (fma y (+ (- a b) 0) (* a t)))
92.0ms	(/ (+ (+ x y) t) (fma z (+ x y) (fma y (+ (- a b) 0) (* a t))))

series1.1s

Counts

4 → 12

Calls

4 calls:

806.0ms	(/ 1 (/ (+ (+ x y) t) (fma z (+ x y) (fma y (+ (- a b) 0) (* a t)))))
48.0ms	(fma y (+ (- a b) 0) (* a t))
138.0ms	(fma z (+ x y) (fma y (+ (- a b) 0) (* a t)))
124.0ms	(/ (+ (+ x y) t) (fma z (+ x y) (fma y (+ (- a b) 0) (* a t))))

simplify1.4s

Counts

173 → 173

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	188	5672
1	468	4823
2	2535	4579
done	5002	4420

prune466.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- a b) y)
0.0b	(/ 1 (+ (+ x y) t))
0.5b	(fma (+ x y) z (fma t a (* (- a b) y)))
24.3b	(* (/ 1 (+ (+ x y) t)) (fma (+ x y) z (fma t a (* (- a b) y))))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
32×	`times-frac`
26×	`add-cube-cbrt` `associate-l`
21×	`distribute-lft-out`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-r`
5×	`prod-exp` `associate-/r*`
4×	`expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-l/` `cbrt-unprod` `fma-udef` `associate-/l`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `pow-prod-down` `*-commutative` `flip-+` `div-inv`
1×	`distribute-rgt-in` `flip3--` `pow-flip` `frac-2neg` `distribute-lft-in` `clear-num` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 124

Calls

4 calls:

27.0ms	(* (- a b) y)
74.0ms	(/ 1 (+ (+ x y) t))
0.0ms	(fma (+ x y) z (fma t a (* (- a b) y)))
117.0ms	(* (/ 1 (+ (+ x y) t)) (fma (+ x y) z (fma t a (* (- a b) y))))

series1.2s

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (- a b) y)
70.0ms	(/ 1 (+ (+ x y) t))
160.0ms	(fma (+ x y) z (fma t a (* (- a b) y)))
905.0ms	(* (/ 1 (+ (+ x y) t)) (fma (+ x y) z (fma t a (* (- a b) y))))

simplify1.3s

Counts

136 → 136

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	168	2142
1	413	1963
2	2279	1749
done	5000	1743

prune520.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.3b

regimes464.0ms

Accuracy

22.4% (11.1b remaining)

Error of 18.1b against oracle of 7.0b and baseline of 21.3b

bsearch90.0ms

Steps

Iters	Range		Point
8	6.523274563841496e+122	1.53950547797117e+126	1.2548011133579118e+126
6	-5.198860796817705e+153	-8.036891272087674e+152	-9.934676971669404e+152

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	36
1	29	36
2	30	36
done	30	36

end0.0ms

sample1.4s

Algorithm

intervals

Results

928.0ms	7992×	body	80	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	2560	valid
0.0ms	2×	body	640	valid
0.0ms	1×	body	160	valid