Details

sample57.0ms

Algorithm

intervals

Results

19.0ms	242×	body	80	valid
16.0ms	12×	body	640	valid
2.0ms	10×	body	320	valid
2.0ms	6×	body	1280	valid
2.0ms	11×	body	160	valid

simplify5.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	3658
7	2634
6	1295
5	547
4	222
3	110
2	52
1	22
0	11

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.2b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
3.5b	(fma y (/ (- t z) (- a t)) (+ y x))

rewrite31.0ms

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/` `insert-posit16` `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 → 66

Calls

2 calls:

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

series273.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ (- t z) (- a t))
199.0ms	(fma y (/ (- t z) (- a t)) (+ y x))

simplify2.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	5006
3	2184
2	652
1	265
0	116

prune416.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- t z) (/ 1 (- a t)))
3.9b	(fma y (* (- t z) (/ 1 (- a t))) (+ y x))

rewrite45.0ms

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` `insert-posit16` `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 → 108

Calls

3 calls:

9.0ms	(/ 1 (- a t))
34.0ms	(* (- t z) (/ 1 (- a t)))
0.0ms	(fma y (* (- t z) (/ 1 (- a t))) (+ y x))

series250.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ 1 (- a t))
52.0ms	(* (- t z) (/ 1 (- a t)))
158.0ms	(fma y (* (- t z) (/ 1 (- a t))) (+ y x))

simplify2.5s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
3	4123
2	1260
1	357
0	153

prune586.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- t z))
1.7b	(/ y (/ (- a t) (- t z)))
3.0b	(+ (/ y (/ (- a t) (- t z))) (+ y x))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

386×	`times-frac`
325×	`*-un-lft-identity`
320×	`add-sqr-sqrt`
156×	`add-cube-cbrt`
98×	`fma-def`
82×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
18×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log` `div-inv`
9×	`flip3--` `flip--`
8×	`associate-/l*` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `sum-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
2×	`clear-num` `frac-2neg` `flip3-+` `frac-add` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+r+` `div-sub`

Counts

3 → 318

Calls

3 calls:

28.0ms	(/ (- a t) (- t z))
20.0ms	(/ y (/ (- a t) (- t z)))
65.0ms	(+ (/ y (/ (- a t) (- t z))) (+ y x))

series403.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ (- a t) (- t z))
207.0ms	(/ y (/ (- a t) (- t z)))
139.0ms	(+ (/ y (/ (- a t) (- t z))) (+ y x))

simplify1.7s

Counts

327 → 327

Iterations

Iter	Nodes
done	5000
2	3523
1	917
0	327

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- t z))
0.5b	(cbrt (- t z))
0.7b	(/ y (/ (- a t) (cbrt (- t z))))
10.3b	(fma (/ 1 (/ 1 (* (cbrt (- t z)) (cbrt (- t z))))) (/ y (/ (- a t) (cbrt (- t z)))) (+ y x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

298×	`times-frac`
237×	`add-sqr-sqrt` `*-un-lft-identity`
129×	`add-cube-cbrt`
110×	`cbrt-prod`
54×	`distribute-lft-out--` `difference-of-squares`
46×	`associate-/r*`
12×	`cbrt-div`
9×	`add-exp-log` `associate-/r/`
8×	`add-cbrt-cube`
6×	`flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`pow1/3`
1×	`clear-num` `frac-2neg` `fma-udef`

Counts

4 → 252

Calls

4 calls:

6.0ms	(cbrt (- t z))
5.0ms	(cbrt (- t z))
30.0ms	(/ y (/ (- a t) (cbrt (- t z))))
1.0ms	(fma (/ 1 (/ 1 (* (cbrt (- t z)) (cbrt (- t z))))) (/ y (/ (- a t) (cbrt (- t z)))) (+ y x))

series1.1s

Counts

4 → 12

Calls

4 calls:

264.0ms	(cbrt (- t z))
281.0ms	(cbrt (- t z))
277.0ms	(/ y (/ (- a t) (cbrt (- t z))))
325.0ms	(fma (/ 1 (/ 1 (* (cbrt (- t z)) (cbrt (- t z))))) (/ y (/ (- a t) (cbrt (- t z)))) (+ y x))

simplify2.3s

Counts

264 → 264

Iterations

Iter	Nodes
done	5003
2	3267
1	1036
0	403

prune1.6s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.2b

regimes683.0ms

Accuracy

32.6% (5.1b remaining)

Error of 8.4b against oracle of 3.3b and baseline of 10.9b

bsearch161.0ms

Steps

Iters	Range		Point
10	6.229866488820149e-124	5.163141678576117e-110	1.0196092676127147e-123
9	-2.0477058230588415e-118	-1.5355849018748885e-123	-1.0092107391768066e-119

simplify5.0ms

Iterations

Iter	Nodes
done	23
1	23
0	21

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.3s	7403×	body	80	valid
212.0ms	430×	body	640	valid
135.0ms	236×	body	1280	valid
98.0ms	390×	body	320	valid
45.0ms	264×	body	160	valid
9.0ms	19×	body	2560	valid