Details

sample35.0ms

Algorithm

intervals

Results

12.0ms	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

simplify13.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	111	13
4	288	13
5	631	13
6	1195	13
7	2059	13
8	2903	13
9	3426	13
10	3861	13
11	4158	13
done	5000	13

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.5b	(+ x (/ (* (- y z) (- t x)) (- a z)))
18.9b	(/ (* (- y z) (- t x)) (- a z))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

49.0ms	(* (- y z) (- t x))
27.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
33.0ms	(/ (* (- y z) (- t x)) (- a z))

series419.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* (- y z) (- t x))
184.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
190.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify1.2s

Counts

90 → 90

Iterations

Useful iterations: 2 (362.0ms)

Iter	Nodes	Cost
0	162	1284
1	466	1213
2	1986	1111
done	5000	1111

prune557.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.6b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.3b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`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`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

5.0ms	(cbrt (- a z))
9.0ms	(cbrt (- a z))
154.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series922.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(cbrt (- a z))
215.0ms	(cbrt (- a z))
336.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
204.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify1.4s

Counts

146 → 146

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	255	3364
1	722	3180
2	2785	2663
done	5000	2496

prune547.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.2b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
9.3b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
36×	`cbrt-div`
26×	`add-sqr-sqrt`
22×	`add-cbrt-cube`
17×	`associate-l`
16×	`-un-lft-identity` `times-frac` `associate-r*` `associate-/r/`
15×	`prod-exp` `cbrt-unprod`
14×	`flip3--` `flip--`
13×	`cbrt-prod`
12×	`cbrt-undiv` `div-exp`
10×	`add-cube-cbrt`
9×	`frac-times`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`associate-r/` `associate-l/`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 110

Calls

4 calls:

6.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
213.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
13.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

227.0ms	(cbrt (- a z))
216.0ms	(cbrt (- a z))
465.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
222.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify1.6s

Counts

122 → 122

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	280	4294
1	779	4149
2	2856	3588
done	5002	3505

prune665.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 4.7b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.9b	(+ x (* (- y z) (/ (- t x) (- a z))))
4.0b	(* (- y z) (/ (- t x) (- a z)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 119

Calls

3 calls:

38.0ms	(/ (- t x) (- a z))
8.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
79.0ms	(* (- y z) (/ (- t x) (- a z)))

series532.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(/ (- t x) (- a z))
257.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
183.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify961.0ms

Counts

128 → 128

Iterations

Useful iterations: 2 (291.0ms)

Iter	Nodes	Cost
0	183	1813
1	469	1704
2	1736	1606
done	5000	1606

prune369.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.7b

regimes434.0ms

Accuracy

19.8% (8.5b remaining)

Error of 12.9b against oracle of 4.4b and baseline of 15.0b

bsearch207.0ms

Steps

Iters	Range		Point
8	1.3793369693960326e-72	4.61238746493178e-68	1.4125550362933808e-72
6	6.888108463244458e-131	8.355357640010509e-130	5.636122468095791e-130
7	2.530195443784478e-182	3.7544747272031375e-180	1.281345112742519e-180
9	-5.155104026169122e-187	-1.1558908166169548e-194	-7.741588738047602e-191

simplify18.0ms

Iterations

Useful iterations: 4 (8.0ms)

Iter	Nodes	Cost
0	29	81
1	37	69
2	40	57
3	46	45
4	49	44
5	52	44
6	53	44
7	54	44
done	54	44

end0.0ms

sample1.7s

Algorithm

intervals

Results

603.0ms	7744×	body	80	valid
409.0ms	261×	body	1280	valid
134.0ms	481×	body	640	valid
109.0ms	441×	body	320	valid
31.0ms	280×	body	160	valid
4.0ms	12×	body	2560	valid