Details

sample40.0ms

Algorithm

intervals

Results

14.0ms	242×	body	80	valid
3.0ms	16×	body	640	valid
2.0ms	15×	body	320	valid
2.0ms	8×	body	1280	valid
1.0ms	9×	body	160	valid

simplify10.4s

Counts

1 → 1

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	116	12
4	322	12
5	766	12
6	1555	12
7	2873	12
8	4761	12
done	5000	12

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.5b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
3.6b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite38.0ms

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-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

35.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series299.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(/ (- y z) (- a z))
224.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify1.7s

Counts

70 → 70

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	116	918
1	266	890
2	653	838
3	1707	834
done	5001	830

prune344.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
5.5b	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite112.0ms

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-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

13.0ms	(/ 1 (- a z))
94.0ms	(* (- y z) (/ 1 (- a z)))
0.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series398.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ 1 (- a z))
101.0ms	(* (- y z) (/ 1 (- a z)))
233.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify2.6s

Counts

114 → 114

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	152	1285
1	334	1052
2	930	948
3	3159	944
done	5002	942

prune449.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
9.4b	(fma (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- a z))) (- t x) x)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `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:

8.0ms	(cbrt (- a z))
8.0ms	(cbrt (- a z))
15.0ms	(cbrt (- a z))
0.0ms	(fma (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- a z))) (- t x) x)

series948.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(cbrt (- a z))
231.0ms	(cbrt (- a z))
238.0ms	(cbrt (- a z))
191.0ms	(fma (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- a z))) (- t x) x)

simplify2.6s

Counts

73 → 73

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	96	925
1	200	907
2	436	749
3	1091	676
4	3751	636
done	5000	631

prune436.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
0.5b	(cbrt (- y z))
0.5b	(cbrt (- y z))
9.4b	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `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:

7.0ms	(cbrt (- y z))
5.0ms	(cbrt (- y z))
5.0ms	(cbrt (- y z))
0.0ms	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

series890.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(cbrt (- y z))
225.0ms	(cbrt (- y z))
251.0ms	(cbrt (- y z))
212.0ms	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

simplify2.5s

Counts

73 → 73

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	96	925
1	201	907
2	435	749
3	1104	676
4	3735	636
done	5000	631

prune325.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.2b

regimes508.0ms

Accuracy

30.5% (5.8b remaining)

Error of 9.4b against oracle of 3.5b and baseline of 11.9b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	91
1	32	91
done	32	91

end0.0ms

sample1.8s

Algorithm

intervals

Results

652.0ms	7744×	body	80	valid
473.0ms	261×	body	1280	valid
177.0ms	481×	body	640	valid
74.0ms	441×	body	320	valid
33.0ms	280×	body	160	valid
4.0ms	12×	body	2560	valid