Details

sample60.0ms

Algorithm

intervals

Results

21.0ms	248×	body	80	valid
5.0ms	15×	body	640	valid
4.0ms	9×	body	1280	valid
3.0ms	14×	body	320	valid
2.0ms	9×	body	160	valid
1.0ms	2×	body	2560	valid

simplify13.4s

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.5b	(+ x (/ (* (- y z) (- t x)) (- a z)))
20.6b	(/ (* (- y z) (- t x)) (- a z))

rewrite128.0ms

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:

56.0ms	(* (- y z) (- t x))
26.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
41.0ms	(/ (* (- y z) (- t x)) (- a z))

series537.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(* (- y z) (- t x))
247.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
233.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify1.3s

Counts

90 → 90

Iterations

Useful iterations: 2 (292.0ms)

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

prune306.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.5b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.6b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite274.0ms

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:

8.0ms	(cbrt (- a z))
11.0ms	(cbrt (- a z))
234.0ms	(* (/ (- 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)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

189.0ms	(cbrt (- a z))
232.0ms	(cbrt (- a z))
444.0ms	(* (/ (- 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)))))

simplify1.7s

Counts

146 → 146

Iterations

Useful iterations: done (1.7s)

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

prune733.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
1.0b	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.7b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
35×	`add-cbrt-cube`
32×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
15×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
14×	`associate-l`
9×	`pow1` `add-cube-cbrt`
8×	`times-frac`
6×	`cbrt-div` `add-log-exp`
5×	`frac-times` `associate-*r/`
3×	`flip3--` `pow-prod-down` `associate-*l/` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `associate-/r/`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 103

Calls

4 calls:

7.0ms	(cbrt (- y z))
7.0ms	(cbrt (- y z))
197.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
9.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (- y z))
222.0ms	(cbrt (- y z))
445.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
259.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify1.7s

Counts

115 → 115

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	225	3755
1	600	3566
2	2220	2466
done	5001	2157

prune504.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
1.0b	(* (* (cbrt (- t x)) (cbrt (- t x))) (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
8.6b	(+ x (* (* (* (cbrt (- t x)) (cbrt (- t x))) (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

5.0ms	(cbrt (- t x))
6.0ms	(cbrt (- t x))
169.0ms	(* (* (cbrt (- t x)) (cbrt (- t x))) (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
8.0ms	(+ x (* (* (* (cbrt (- t x)) (cbrt (- t x))) (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

222.0ms	(cbrt (- t x))
206.0ms	(cbrt (- t x))
1.1s	(* (* (cbrt (- t x)) (cbrt (- t x))) (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
276.0ms	(+ x (* (* (* (cbrt (- t x)) (cbrt (- t x))) (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify1.8s

Counts

112 → 112

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	273	3004
1	749	2856
2	2476	2413
done	5001	2323

prune586.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.3b

regimes570.0ms

Accuracy

15.5% (7.6b remaining)

Error of 10.9b against oracle of 3.4b and baseline of 12.3b

bsearch126.0ms

Steps

Iters	Range		Point
8	2.2455987213562883e-119	3.3151492280354115e-115	1.9876705662071354e-115
8	-3.8032487866059233e-25	-6.0695810582136045e-28	-6.14323213192593e-28

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	103
1	46	103
done	46	103

end0.0ms

sample1.5s

Algorithm

intervals

Results

729.0ms	7718×	body	80	valid
137.0ms	494×	body	640	valid
113.0ms	287×	body	1280	valid
72.0ms	399×	body	320	valid
32.0ms	270×	body	160	valid
9.0ms	23×	body	2560	valid