Details

sample41.0ms

Algorithm

intervals

Results

12.0ms	249×	body	80	valid
3.0ms	19×	body	640	valid
2.0ms	10×	body	1280	valid
2.0ms	15×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	1×	body	2560	valid

simplify6.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	46	12
3	128	12
4	360	12
5	877	12
6	2016	12
7	3586	12
done	5000	12

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.6b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite63.0ms

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:

58.0ms	(/ (- t x) (- a z))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series201.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(/ (- t x) (- a z))
144.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.2s

Counts

70 → 70

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	118	918
1	269	890
2	658	838
3	1743	834
done	5000	830

prune283.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
15.5b	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

rewrite98.0ms

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:

26.0ms	(/ 1 (- a z))
66.0ms	(* (- t x) (/ 1 (- a z)))
1.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

series227.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ 1 (- a z))
60.0ms	(* (- t x) (/ 1 (- a z)))
123.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

simplify2.0s

Counts

114 → 114

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	155	1285
1	344	1052
2	954	948
3	3231	944
done	5000	942

prune280.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
15.5b	(fma (* (- t x) (/ (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- a z)))) (- y z) x)

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod`
34×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
8×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
6×	`add-exp-log` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 102

Calls

4 calls:

8.0ms	(cbrt (- a z))
8.0ms	(cbrt (- a z))
63.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
1.0ms	(fma (* (- t x) (/ (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- a z)))) (- y z) x)

series790.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(cbrt (- a z))
245.0ms	(cbrt (- a z))
198.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
128.0ms	(fma (* (- t x) (/ (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (- a z)))) (- y z) x)

simplify2.0s

Counts

114 → 114

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	160	1601
1	319	1493
2	806	1305
3	2257	1158
done	5002	1129

prune561.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (fma (/ (- t x) (- a z)) (- y z) x)) (cbrt (fma (/ (- t x) (- a z)) (- y z) x)))
15.6b	(fma (/ (- t x) (- a z)) (- y z) x)
15.6b	(fma (/ (- t x) (- a z)) (- y z) x)
15.6b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 72

Calls

4 calls:

30.0ms	(* (cbrt (fma (/ (- t x) (- a z)) (- y z) x)) (cbrt (fma (/ (- t x) (- a z)) (- y z) x)))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series4.7s

Counts

4 → 12

Calls

4 calls:

4.3s	(* (cbrt (fma (/ (- t x) (- a z)) (- y z) x)) (cbrt (fma (/ (- t x) (- a z)) (- y z) x)))
142.0ms	(fma (/ (- t x) (- a z)) (- y z) x)
113.0ms	(fma (/ (- t x) (- a z)) (- y z) x)
149.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.4s

Counts

84 → 84

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	102	2024
1	207	1877
2	503	1695
3	1388	1404
done	5000	1376

prune482.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 6.0b

regimes480.0ms

Accuracy

9.6% (7.4b remaining)

Error of 14.0b against oracle of 6.7b and baseline of 14.8b

bsearch69.0ms

Steps

Iters	Range		Point
9	-1.7910089691738227e+194	-1.8921491898552533e+186	-1.1534381443874752e+194

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	19
1	18	19
done	18	19

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	7808×	body	80	valid
133.0ms	414×	body	320	valid
118.0ms	270×	body	1280	valid
112.0ms	481×	body	640	valid
33.0ms	284×	body	160	valid
10.0ms	25×	body	2560	valid