Details

sample40.0ms

Algorithm

intervals

Results

12.0ms	264×	body	80	valid
3.0ms	16×	body	640	valid
2.0ms	8×	body	1280	valid
1.0ms	7×	body	320	valid
1.0ms	10×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	3252
5	844
4	292
3	111
2	45
1	20
0	11

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.8b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.7b	(+ x (* (/ (- y z) (- a z)) (- t x)))
3.8b	(* (/ (- y z) (- a z)) (- t x))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-l`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `associate-r` `flip--` `associate-/l` `add-log-exp`
4×	`distribute-rgt-in` `associate-+r+` `sub-neg` `distribute-lft-in` `associate-/r/`
2×	`frac-times` `cbrt-undiv` `div-exp` `prod-exp` `associate-*r/` `cbrt-unprod` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `-commutative` `flip-+`

Counts

3 → 127

Calls

3 calls:

19.0ms	(/ (- y z) (- a z))
6.0ms	(+ x (* (/ (- y z) (- a z)) (- t x)))
74.0ms	(* (/ (- y z) (- a z)) (- t x))

series729.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/ (- y z) (- a z))
257.0ms	(+ x (* (/ (- y z) (- a z)) (- t x)))
404.0ms	(* (/ (- y z) (- a z)) (- t x))

simplify1.2s

Counts

136 → 136

Iterations

Iter	Nodes
done	5001
2	2148
1	536
0	195

prune678.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
3.4b	(+ x (* (* (- y z) (/ 1 (- a z))) (- t x)))
3.8b	(* (* (- y z) (/ 1 (- a z))) (- t x))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`times-frac` `add-exp-log`
26×	`associate-r`
25×	`add-cube-cbrt`
20×	`frac-times` `add-cbrt-cube`
17×	`flip3--` `flip--`
14×	`associate-*l/`
13×	`prod-exp`
12×	`pow1`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `associate-l` `associate-*r/` `add-log-exp`
5×	`associate-/r*`
4×	`distribute-rgt-in` `associate-+r+` `sub-neg` `distribute-lft-in` `pow-prod-down` `associate-/r/` `un-div-inv`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 154

Calls

4 calls:

21.0ms	(/ 1 (- a z))
50.0ms	(* (- y z) (/ 1 (- a z)))
13.0ms	(+ x (* (* (- y z) (/ 1 (- a z))) (- t x)))
85.0ms	(* (* (- y z) (/ 1 (- a z))) (- t x))

series910.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ 1 (- a z))
95.0ms	(* (- y z) (/ 1 (- a z)))
235.0ms	(+ x (* (* (- y z) (/ 1 (- a z))) (- t x)))
532.0ms	(* (* (- y z) (/ 1 (- a z))) (- t x))

simplify429.0ms

Counts

166 → 166

Iterations

Iter	Nodes
done	5001
1	693
0	231

prune850.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.2b

localize37.0ms

Local error

Found 4 expressions with local error:

3.8b	(* (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (cbrt (/ (- y z) (- a z)))) (- t x))
5.0b	(cbrt (/ (- y z) (- a z)))
5.0b	(cbrt (/ (- y z) (- a z)))
5.0b	(cbrt (/ (- y z) (- a z)))

rewrite551.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
39×	`cbrt-div`
38×	`add-cube-cbrt`
31×	`distribute-lft-out--` `difference-of-squares`
29×	`frac-times`
22×	`associate-*l/`
13×	`pow1` `add-exp-log`
11×	`flip3--` `associate-*r/` `flip--`
9×	`add-cbrt-cube`
6×	`pow-prod-down` `prod-exp` `associate-/r/` `cbrt-unprod`
5×	`associate-r`
4×	`add-log-exp`
3×	`pow1/3` `div-inv`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`associate-l` `*-commutative`

Counts

4 → 170

Calls

4 calls:

513.0ms	(* (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (cbrt (/ (- y z) (- a z)))) (- t x))
7.0ms	(cbrt (/ (- y z) (- a z)))
8.0ms	(cbrt (/ (- y z) (- a z)))
8.0ms	(cbrt (/ (- y z) (- a z)))

series1.8s

Counts

4 → 12

Calls

4 calls:

441.0ms	(* (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (cbrt (/ (- y z) (- a z)))) (- t x))
457.0ms	(cbrt (/ (- y z) (- a z)))
461.0ms	(cbrt (/ (- y z) (- a z)))
460.0ms	(cbrt (/ (- y z) (- a z)))

simplify1.3s

Counts

182 → 182

Iterations

Iter	Nodes
done	5001
2	2297
1	623
0	254

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
0.5b	(cbrt (- y z))
3.8b	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x))
7.1b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

91×	`times-frac`
69×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
51×	`associate-l`
36×	`cbrt-prod`
27×	`add-cube-cbrt`
22×	`add-exp-log`
16×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
7×	`prod-exp` `cbrt-unprod`
6×	`pow1` `cbrt-undiv` `cbrt-div` `div-exp` `add-log-exp`
5×	`flip3--` `associate-r` `flip--`
4×	`distribute-rgt-in` `associate-+r+` `sub-neg` `distribute-lft-in` `unswap-sqr`
3×	`associate-/r/`
2×	`frac-times` `pow1/3` `associate-*r/` `div-inv`
1×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `associate-l/` `-commutative` `flip-+`

Counts

4 → 133

Calls

4 calls:

4.0ms	(cbrt (- y z))
3.0ms	(cbrt (- y z))
100.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x))
6.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x)))

series1.2s

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt (- y z))
230.0ms	(cbrt (- y z))
501.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x))
244.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x)))

simplify1.9s

Counts

145 → 145

Iterations

Iter	Nodes
done	5000
2	3352
1	711
0	267

prune907.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.2b

regimes737.0ms

Accuracy

23.7% (6.6b remaining)

Error of 10.1b against oracle of 3.5b and baseline of 12.1b

bsearch138.0ms

Steps

Iters	Range		Point
9	1.507532718961738e+201	3.8461080361265226e+208	2.3107008637180498e+203
7	-2.964212764581606e+198	-8.157833908662871e+196	-4.1975781468616386e+197

simplify3.0ms

Iterations

Iter	Nodes
done	32
1	32
0	25

end0.0ms

sample1.7s

Algorithm

intervals

Results

735.0ms	7739×	body	80	valid
107.0ms	474×	body	640	valid
106.0ms	413×	body	320	valid
83.0ms	282×	body	1280	valid
30.0ms	269×	body	160	valid
5.0ms	17×	body	2560	valid