Details

sample26.0ms

Algorithm

intervals

Results

11.0ms

265×

body

valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	24	16
2	43	15
3	65	15
4	96	15
5	130	15
6	163	15
7	239	15
8	396	15
9	707	15
10	1553	15
11	4269	15
done	5000	15

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.7b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (- t a))
0.8b	(fma x y (* z (- t a)))
24.0b	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 85

Calls

3 calls:

12.0ms	(* z (- t a))
0.0ms	(fma x y (* z (- t a)))
2.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

series449.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* z (- t a))
54.0ms	(fma x y (* z (- t a)))
358.0ms	(/ (fma x y (* z (- t a))) (fma z (- b y) y))

simplify1.3s

Counts

94 → 94

Iterations

Useful iterations: 3 (457.0ms)

Iter	Nodes	Cost
0	163	1562
1	288	1378
2	686	1188
3	2492	1146
done	5001	1146

prune316.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.5b	(+ (* z t) (* z (- a)))
0.8b	(fma x y (+ (* z t) (* z (- a))))
24.0b	(/ (fma x y (+ (* z t) (* z (- a)))) (fma z (- b y) y))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`distribute-rgt-neg-out`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-exp` `unsub-neg` `clear-num` `sum-log` `flip-+` `fma-udef` `div-inv` `distribute-lft-out`

Counts

3 → 56

Calls

3 calls:

3.0ms	(+ (* z t) (* z (- a)))
0.0ms	(fma x y (+ (* z t) (* z (- a))))
3.0ms	(/ (fma x y (+ (* z t) (* z (- a)))) (fma z (- b y) y))

series460.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* z t) (* z (- a)))
57.0ms	(fma x y (+ (* z t) (* z (- a))))
366.0ms	(/ (fma x y (+ (* z t) (* z (- a)))) (fma z (- b y) y))

simplify1.4s

Counts

65 → 65

Iterations

Useful iterations: 3 (464.0ms)

Iter	Nodes	Cost
0	96	1209
1	217	976
2	691	883
3	2607	879
done	5001	879

prune261.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.5b	(+ (* z t) (* z (- a)))
1.3b	(+ (* x y) (+ (* z t) (* z (- a))))
24.0b	(/ (+ (* x y) (+ (* z t) (* z (- a)))) (fma z (- b y) y))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`add-log-exp`
9×	`times-frac`
6×	`distribute-rgt-neg-out`
5×	`add-exp-log` `add-cbrt-cube`
4×	`associate-+r-` `sum-log`
3×	`pow1` `expm1-log1p-u` `flip3-+` `unsub-neg` `associate-/r` `flip-+` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `fma-def` `div-sub` `associate-/l/`
1×	`cbrt-undiv` `associate-+r+` `frac-2neg` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

3 → 68

Calls

3 calls:

3.0ms	(+ (* z t) (* z (- a)))
7.0ms	(+ (* x y) (+ (* z t) (* z (- a))))
23.0ms	(/ (+ (* x y) (+ (* z t) (* z (- a)))) (fma z (- b y) y))

series456.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ (* z t) (* z (- a)))
47.0ms	(+ (* x y) (+ (* z t) (* z (- a))))
366.0ms	(/ (+ (* x y) (+ (* z t) (* z (- a)))) (fma z (- b y) y))

simplify1.1s

Counts

77 → 77

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	114	1513
1	310	1148
2	1179	1069
done	5000	1065

prune293.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.2b	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.8b	(fma x y (* z (- t a)))
24.0b	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

rewrite26.0ms

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:

11.0ms	(* z (- t a))
5.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
0.0ms	(fma x y (* z (- t a)))
2.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

series710.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* z (- t a))
503.0ms	(/ 1 (/ (fma z (- b y) y) (fma x y (* z (- t a)))))
55.0ms	(fma x y (* z (- t a)))
114.0ms	(/ (fma z (- b y) y) (fma x y (* z (- t a))))

simplify2.1s

Counts

175 → 175

Iterations

Useful iterations: 3 (938.0ms)

Iter	Nodes	Cost
0	264	3896
1	519	3507
2	1118	3118
3	3686	3058
done	5000	3058

prune469.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.2b

regimes495.0ms

Accuracy

32.2% (8.9b remaining)

Error of 19.6b against oracle of 10.7b and baseline of 23.8b

bsearch121.0ms

Steps

Iters	Range		Point
9	2.2108085494553437e+120	6.680833282765864e+126	1.621555450877592e+125
8	-7.928120464220808e+174	-1.214019913834516e+172	-1.285204343974009e+172

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	41
1	34	35
2	37	35
3	38	35
done	38	35

end0.0ms

sample686.0ms

Algorithm

intervals

Results

389.0ms

8413×

body

valid