Details

sample42.0ms

Algorithm

intervals

Results

15.0ms	258×	body	80	valid
3.0ms	13×	body	640	valid
2.0ms	7×	body	1280	valid
1.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.7b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
11.8b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite40.0ms

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:

37.0ms	(/ (- t x) (- a z))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series198.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(/ (- t x) (- a z))
114.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.9s

Counts

70 → 70

Iterations

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

prune542.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
11.8b	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

rewrite89.0ms

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:

18.0ms	(/ 1 (- a z))
64.0ms	(* (- t x) (/ 1 (- a z)))
0.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

series218.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ 1 (- a z))
62.0ms	(* (- t x) (/ 1 (- a z)))
106.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

simplify4.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	2967
1	373
0	155

prune675.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
11.7b	(fma (/ (/ (/ (- t x) (cbrt (- a z))) (cbrt (- a z))) (cbrt (- a z))) (- y z) x)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
7.0ms	(cbrt (- a z))
1.0ms	(fma (/ (/ (/ (- t x) (cbrt (- a z))) (cbrt (- a z))) (cbrt (- a z))) (- y z) x)

series689.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(cbrt (- a z))
208.0ms	(cbrt (- a z))
168.0ms	(cbrt (- a z))
112.0ms	(fma (/ (/ (/ (- t x) (cbrt (- a z))) (cbrt (- a z))) (cbrt (- a z))) (- y z) x)

simplify935.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	1665
2	504
1	200
0	97

prune580.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.5b

localize75.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (/ (- t x) (- a z)) (- y z) x))
11.8b	(fma (/ (- t x) (- a z)) (- y z) x)
11.8b	(fma (/ (- t x) (- a z)) (- y z) x)
11.8b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (fma (/ (- t x) (- a z)) (- y z) x))
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series1.5s

Counts

4 → 12

Calls

4 calls:

1.1s	(cbrt (fma (/ (- t x) (- a z)) (- y z) x))
118.0ms	(fma (/ (- t x) (- a z)) (- y z) x)
147.0ms	(fma (/ (- t x) (- a z)) (- y z) x)
146.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify752.0ms

Counts

55 → 55

Iterations

Iter	Nodes
done	5002
3	1498
2	327
1	131
0	69

prune403.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.5b

regimes903.0ms

Accuracy

9.7% (7.7b remaining)

Error of 13.9b against oracle of 6.2b and baseline of 14.8b

bsearch52.0ms

Steps

Iters	Range		Point
9	6.232674112580621e+208	4.457444719923058e+213	4.4149995707834223e+213

simplify3.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample1.8s

Algorithm

intervals

Results

968.0ms	7795×	body	80	valid
114.0ms	488×	body	640	valid
79.0ms	287×	body	1280	valid
70.0ms	249×	body	160	valid
68.0ms	393×	body	320	valid
5.0ms	16×	body	2560	valid