Details

sample47.0ms

Algorithm

intervals

Results

20.0ms

263×

body

valid

simplify4.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	14	17
1	24	16
2	43	15
3	75	15
4	112	15
5	148	15
6	181	15
7	257	15
8	419	15
9	728	15
10	1525	15
11	4096	15
done	5000	15

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z (- b y) y)
0.0b	(* z (- t a))
0.3b	(fma x y (* z (- t a)))
20.8b	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

0.0ms	(fma z (- b y) y)
51.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
8.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

series588.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma z (- b y) y)
54.0ms	(* z (- t a))
74.0ms	(fma x y (* z (- t a)))
419.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

simplify2.1s

Counts

107 → 107

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	171	1678
1	309	1491
2	699	1283
3	2817	1241
done	5000	1187

prune352.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.3b	(fma x y (* z (- t a)))
0.4b	(/ 1 (fma z (- b y) y))
20.5b	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

24.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
5.0ms	(/ 1 (fma z (- b y) y))
16.0ms	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

series660.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* z (- t a))
78.0ms	(fma x y (* z (- t a)))
72.0ms	(/ 1 (fma z (- b y) y))
451.0ms	(* (fma x y (* z (- t a))) (/ 1 (fma z (- b y) y)))

simplify2.6s

Counts

139 → 139

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	200	2133
1	387	1818
2	915	1550
3	3816	1508
done	5000	1508

prune425.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 20.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.3b	(fma x y (* z (- t a)))
0.3b	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
20.7b	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
72×	`add-sqr-sqrt`
70×	`*-un-lft-identity`
68×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`prod-diff`
16×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`div-exp`
7×	`pow1`
6×	`div-inv` `associate-/l*`
5×	`associate-r`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`sub-neg` `rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num`
1×	`flip3--` `pow-flip` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 163

Calls

4 calls:

38.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
11.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
14.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

series935.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* z (- t a))
74.0ms	(fma x y (* z (- t a)))
653.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
150.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

simplify2.5s

Counts

175 → 175

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	264	3896
1	509	3507
2	1078	3118
3	4057	3058
done	5000	3058

prune502.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma x y (* z (- t a)))
0.3b	(/ 1 (* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a))))))
0.6b	(/ 1 (fma x y (* z (- t a))))
20.0b	(* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a)))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

0.0ms	(fma x y (* z (- t a)))
39.0ms	(/ 1 (* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a))))))
6.0ms	(/ 1 (fma x y (* z (- t a))))
22.0ms	(* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

81.0ms	(fma x y (* z (- t a)))
646.0ms	(/ 1 (* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a))))))
123.0ms	(/ 1 (fma x y (* z (- t a))))
151.0ms	(* (fma z (- b y) y) (/ 1 (fma x y (* z (- t a)))))

simplify3.2s

Counts

135 → 135

Iterations

Useful iterations: 2 (192.0ms)

Iter	Nodes	Cost
0	147	2456
1	303	2164
2	764	1824
3	2738	1824
done	5002	1824

prune439.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.9b

regimes518.0ms

Accuracy

35% (7.9b remaining)

Error of 19.1b against oracle of 11.2b and baseline of 23.3b

bsearch152.0ms

Steps

Iters	Range		Point
9	1.865416815092154e+123	6.123155016714887e+131	1.2335128510508918e+130
10	-3.906531860043804e+107	-5.119859547412261e+92	-4.98837196482088e+105

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	23	39
1	30	33
done	30	33

end0.0ms

sample1.5s

Algorithm

intervals

Results

741.0ms

8367×

body

valid