Details

sample45.0ms

Algorithm

intervals

Results

14.0ms	255×	body	80	valid
3.0ms	16×	body	640	valid
2.0ms	9×	body	1280	valid
2.0ms	10×	body	320	valid
1.0ms	6×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4619
5	1129
4	367
3	128
2	46
1	23
0	11

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
13.4b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

26.0ms	(/ (- t x) (- a z))
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series195.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (- t x) (- a z))
128.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify2.0s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	4626
2	848
1	274
0	118

prune420.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.3b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
13.4b	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-/r` `associate-l*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 105

Calls

3 calls:

10.0ms	(/ 1 (- a z))
48.0ms	(* (- t x) (/ 1 (- a z)))
0.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

series256.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ 1 (- a z))
78.0ms	(* (- t x) (/ 1 (- a z)))
135.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

simplify3.8s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	2967
1	373
0	155

prune543.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.6b	(/ 1 (/ (- a z) (- t x)))
13.3b	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
195×	`add-sqr-sqrt` `*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`flip3--` `div-inv` `flip--`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/l/`
1×	`div-sub` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 214

Calls

3 calls:

29.0ms	(/ (- a z) (- t x))
28.0ms	(/ 1 (/ (- a z) (- t x)))
1.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

series448.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ (- a z) (- t x))
220.0ms	(/ 1 (/ (- a z) (- t x)))
166.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

simplify1.4s

Counts

223 → 223

Iterations

Iter	Nodes
done	5000
2	3262
1	715
0	274

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.8b	(+ (* (/ (- y z) (- a z)) (- t x)) x)
3.3b	(* (/ (- y z) (- a z)) (- t x))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
51×	`times-frac` `add-cube-cbrt`
36×	`prod-diff`
31×	`associate-l`
23×	`distribute-lft-out--` `difference-of-squares`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `associate-r` `flip--` `associate-/l` `add-log-exp`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-times` `cbrt-undiv` `div-exp` `prod-exp` `associate-*r/` `cbrt-unprod` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `-commutative` `flip-+`

Counts

3 → 170

Calls

3 calls:

26.0ms	(/ (- y z) (- a z))
23.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
60.0ms	(* (/ (- y z) (- a z)) (- t x))

series766.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(/ (- y z) (- a z))
217.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
488.0ms	(* (/ (- y z) (- a z)) (- t x))

simplify1.5s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
2	3221
1	716
0	255

prune961.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.8b

regimes625.0ms

Accuracy

-0.1% (3.7b remaining)

Error of 7.5b against oracle of 3.8b and baseline of 7.5b

bsearch139.0ms

Steps

Iters	Range		Point
9	9.180063932475843e-204	1.0400915298588633e-197	2.406524337071742e-201
8	-5.729088054015752e-142	-1.3930320799902115e-145	-9.76162443591342e-143

simplify6.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample1.7s

Algorithm

intervals

Results

604.0ms	7765×	body	80	valid
470.0ms	409×	body	320	valid
103.0ms	509×	body	640	valid
92.0ms	261×	body	1280	valid
27.0ms	260×	body	160	valid
5.0ms	14×	body	2560	valid