Details

sample19.0ms

Algorithm

intervals

Results

8.0ms

326×

body

valid

simplify6.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (3.0ms)

Iter	Nodes	Cost
0	7	9
1	11	9
2	20	8
3	31	8
4	46	8
5	65	8
6	88	8
7	125	8
8	189	8
9	274	8
10	417	8
11	871	8
12	4611	8
done	5000	8

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (- z x) y x)
11.1b	(/ (fma (- z x) y x) z)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 39

Calls

2 calls:

0.0ms	(fma (- z x) y x)
3.0ms	(/ (fma (- z x) y x) z)

series84.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(fma (- z x) y x)
51.0ms	(/ (fma (- z x) y x) z)

simplify1.6s

Counts

45 → 45

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	66	554
1	117	542
2	267	492
3	829	492
4	3079	492
done	5000	492

prune131.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (/ x z) y)
0.0b	(- (+ (/ x z) y) (/ (* x y) z))
5.8b	(/ (* x y) z)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `prod-diff`
24×	`times-frac`
13×	`fma-def`
10×	`distribute-lft-out` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
6×	`div-inv`
4×	`fma-neg`
3×	`pow1` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3-+` `diff-log` `div-exp` `sum-log` `frac-sub` `flip-+` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `prod-exp` `associate--l+` `clear-num` `flip--` `cbrt-unprod` `associate-/l*` `difference-of-squares`

Counts

3 → 103

Calls

3 calls:

10.0ms	(+ (/ x z) y)
87.0ms	(- (+ (/ x z) y) (/ (* x y) z))
4.0ms	(/ (* x y) z)

series78.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(+ (/ x z) y)
36.0ms	(- (+ (/ x z) y) (/ (* x y) z))
22.0ms	(/ (* x y) z)

simplify1.1s

Counts

112 → 112

Iterations

Useful iterations: 2 (183.0ms)

Iter	Nodes	Cost
0	154	2085
1	386	1744
2	1357	1457
done	5001	1457

prune225.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
144×	`*-un-lft-identity`
124×	`add-sqr-sqrt`
120×	`add-cube-cbrt`
87×	`cbrt-prod`
63×	`distribute-lft-neg-in`
48×	`fma-def`
44×	`distribute-rgt-neg-in`
41×	`distribute-rgt-out`
25×	`add-exp-log`
23×	`distribute-lft-out`
22×	`associate-l`
18×	`add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
7×	`cbrt-undiv` `div-exp` `associate-r`
6×	`pow1` `unswap-sqr`
5×	`neg-mul-1`
4×	`expm1-log1p-u` `distribute-lft1-in` `log1p-expm1-u`
2×	`pow1/3` `sum-log`
1×	`+-commutative` `neg-sub0` `frac-times` `associate-+l-` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `frac-add` `*-commutative` `flip-+` `distribute-neg-frac`

Counts

4 → 219

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
86.0ms	(+ (- (/ y (cbrt z))) (/ y (cbrt z)))
24.0ms	(* (/ y (cbrt z)) (/ x (* (cbrt z) (cbrt z))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt z)
212.0ms	(cbrt z)
3.0ms	(+ (- (/ y (cbrt z))) (/ y (cbrt z)))
56.0ms	(* (/ y (cbrt z)) (/ x (* (cbrt z) (cbrt z))))

simplify925.0ms

Counts

231 → 231

Iterations

Useful iterations: done (919.0ms)

Iter	Nodes	Cost
0	265	2305
1	650	1891
2	2035	1457
done	5001	1423

prune815.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
1.0b	(+ (- (/ y (cbrt z))) (/ y (cbrt z)))
4.4b	(* y (/ x z))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
137×	`*-un-lft-identity`
113×	`add-cube-cbrt`
106×	`add-sqr-sqrt`
76×	`cbrt-prod`
63×	`distribute-lft-neg-in`
48×	`fma-def`
44×	`distribute-rgt-neg-in`
41×	`distribute-rgt-out`
23×	`distribute-lft-out`
13×	`associate-r`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`div-inv`
6×	`pow1`
5×	`neg-mul-1`
4×	`expm1-log1p-u` `distribute-lft1-in` `log1p-expm1-u`
3×	`associate-l`
2×	`pow1/3` `prod-exp` `sum-log` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `neg-log` `frac-add` `-commutative` `flip-+` `distribute-neg-frac`

Counts

4 → 192

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
85.0ms	(+ (- (/ y (cbrt z))) (/ y (cbrt z)))
7.0ms	(* y (/ x z))

series413.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(cbrt z)
201.0ms	(cbrt z)
2.0ms	(+ (- (/ y (cbrt z))) (/ y (cbrt z)))
21.0ms	(* y (/ x z))

simplify1.5s

Counts

204 → 204

Iterations

Useful iterations: 3 (768.0ms)

Iter	Nodes	Cost
0	242	1586
1	514	1226
2	1119	1074
3	3212	571
done	5000	571

prune663.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes95.0ms

Accuracy

86.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.8b

bsearch79.0ms

Steps

Iters	Range		Point
9	1.687001986536537e-25	1.1679697638036715e-17	4.595974037957284e-24
9	-8.208193039074345e-124	-1.5908767289252482e-131	-3.808754882151643e-124

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	60
1	36	60
done	36	60

end0.0ms

sample462.0ms

Algorithm

intervals

Results

256.0ms

10044×

body

valid