Details

sample29.0ms

Algorithm

intervals

Results

10.0ms	259×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	4×	body	1280	valid
0.0ms	6×	body	160	valid
0.0ms	1×	body	2560	valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
6	2502
5	895
4	343
3	126
2	46
1	23
0	11

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.4b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
11.4b	(fma (- y z) (/ (- t x) (- a z)) 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/` `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:

28.0ms	(/ (- t x) (- a z))
0.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series202.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(/ (- t x) (- a z))
138.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify1.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
3	2173
2	663
1	274
0	118

prune418.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
11.4b	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

rewrite51.0ms

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:

9.0ms	(/ 1 (- a z))
38.0ms	(* (- t x) (/ 1 (- a z)))
0.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

series314.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ 1 (- a z))
96.0ms	(* (- t x) (/ 1 (- a z)))
156.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

simplify2.9s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
3	3515
2	1184
1	369
0	155

prune765.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.6b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.1b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.0b	(* (- y z) (/ (- t x) (- a z)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 128

Calls

3 calls:

19.0ms	(/ (- t x) (- a z))
12.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
58.0ms	(* (- y z) (/ (- t x) (- a z)))

series534.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(/ (- t x) (- a z))
258.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
185.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify1.5s

Counts

137 → 137

Iterations

Iter	Nodes
done	5000
2	1817
1	515
0	189

prune792.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
5.3b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
28×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-l/` `associate-r/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 145

Calls

4 calls:

7.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
196.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
12.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

230.0ms	(cbrt (- a z))
186.0ms	(cbrt (- a z))
440.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
262.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify2.5s

Counts

157 → 157

Iterations

Iter	Nodes
done	5004
2	2977
1	761
0	261

prune1.1s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 2.6b

regimes1.2s

Accuracy

54.2% (4.3b remaining)

Error of 7.5b against oracle of 3.2b and baseline of 12.7b

bsearch5.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	36
1	36
0	29

end0.0ms

sample1.9s

Algorithm

intervals

Results

618.0ms	465×	body	640	valid
603.0ms	7883×	body	80	valid
76.0ms	245×	body	1280	valid
66.0ms	377×	body	320	valid
58.0ms	243×	body	160	valid
6.0ms	16×	body	2560	valid