Details

sample42.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify4.4s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.2b

localize26.0ms

Local error

Found 3 expressions with local error:

0.3b	(fma t a (* z x))
2.0b	(fma y (- a (- b z)) (fma t a (* z x)))
25.5b	(/ (fma y (- a (- b z)) (fma t a (* z x))) (+ x (+ y t)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
15×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`distribute-lft-out`
5×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`associate-/r/` `fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

3 → 59

Calls

3 calls:

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

series433.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(fma t a (* z x))
131.0ms	(fma y (- a (- b z)) (fma t a (* z x)))
237.0ms	(/ (fma y (- a (- b z)) (fma t a (* z x))) (+ x (+ y t)))

simplify1.5s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
3	2750
2	593
1	192
0	94

prune516.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.3b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ y t) x) (fma x z (fma (- a (- b z)) y (* t a)))))
0.8b	(fma x z (fma (- a (- b z)) y (* t a)))
1.5b	(fma (- a (- b z)) y (* t a))
25.5b	(/ (+ (+ y t) x) (fma x z (fma (- a (- b z)) y (* t a))))

rewrite112.0ms

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

Counts

4 → 161

Calls

4 calls:

36.0ms	(/ 1 (/ (+ (+ y t) x) (fma x z (fma (- a (- b z)) y (* t a)))))
0.0ms	(fma x z (fma (- a (- b z)) y (* t a)))
0.0ms	(fma (- a (- b z)) y (* t a))
68.0ms	(/ (+ (+ y t) x) (fma x z (fma (- a (- b z)) y (* t a))))

series732.0ms

Counts

4 → 12

Calls

4 calls:

309.0ms	(/ 1 (/ (+ (+ y t) x) (fma x z (fma (- a (- b z)) y (* t a)))))
140.0ms	(fma x z (fma (- a (- b z)) y (* t a)))
71.0ms	(fma (- a (- b z)) y (* t a))
213.0ms	(/ (+ (+ y t) x) (fma x z (fma (- a (- b z)) y (* t a))))

simplify1.3s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
2	2568
1	474
0	192

prune803.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma x z (fma y (- (+ z a) b) (* a t)))
0.9b	(/ 1 (fma x z (fma y (- (+ z a) b) (* a t))))
1.5b	(fma y (- (+ z a) b) (* a t))
24.4b	(* (+ (+ y t) x) (/ 1 (fma x z (fma y (- (+ z a) b) (* a t)))))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
20×	`times-frac` `add-cube-cbrt`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `associate-*l/` `cbrt-unprod` `flip-+` `fma-udef` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 97

Calls

4 calls:

0.0ms	(fma x z (fma y (- (+ z a) b) (* a t)))
6.0ms	(/ 1 (fma x z (fma y (- (+ z a) b) (* a t))))
0.0ms	(fma y (- (+ z a) b) (* a t))
108.0ms	(* (+ (+ y t) x) (/ 1 (fma x z (fma y (- (+ z a) b) (* a t)))))

series578.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(fma x z (fma y (- (+ z a) b) (* a t)))
120.0ms	(/ 1 (fma x z (fma y (- (+ z a) b) (* a t))))
100.0ms	(fma y (- (+ z a) b) (* a t))
201.0ms	(* (+ (+ y t) x) (/ 1 (fma x z (fma y (- (+ z a) b) (* a t)))))

simplify3.8s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	2721
1	325
0	135

prune639.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ y t) x))
0.3b	(fma t a (* z x))
2.0b	(fma y (- a (- b z)) (fma t a (* z x)))
25.6b	(* (fma y (- a (- b z)) (fma t a (* z x))) (/ 1 (+ (+ y t) x)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

32.0ms	(/ 1 (+ (+ y t) x))
0.0ms	(fma t a (* z x))
0.0ms	(fma y (- a (- b z)) (fma t a (* z x)))
76.0ms	(* (fma y (- a (- b z)) (fma t a (* z x))) (/ 1 (+ (+ y t) x)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ 1 (+ (+ y t) x))
60.0ms	(fma t a (* z x))
134.0ms	(fma y (- a (- b z)) (fma t a (* z x)))
175.0ms	(* (fma y (- a (- b z)) (fma t a (* z x))) (/ 1 (+ (+ y t) x)))

simplify728.0ms

Counts

121 → 121

Iterations

Iter	Nodes
done	5002
2	1508
1	308
0	133

prune544.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.2b

regimes882.0ms

Accuracy

49.9% (10.7b remaining)

Error of 16.5b against oracle of 5.8b and baseline of 27.1b

bsearch158.0ms

Steps

Iters	Range		Point
10	2.14267112726571e+114	1.1383562959553758e+129	2.1720723859829747e+114
9	-1.096794704824411e+143	-1.2414299572751657e+135	-1.2601803394366536e+135

simplify4.0ms

Iterations

Iter	Nodes
done	35
1	35
0	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

759.0ms	7999×	body	80	valid
0.0ms	1×	body	1280	valid