Details

sample28.0ms

Algorithm

intervals

Results

15.0ms

432×

body

valid

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 8 (2.5s)

Iter	Nodes	Cost
0	11	15
1	23	14
2	58	14
3	106	14
4	191	14
5	341	14
6	704	14
7	1628	13
8	4939	12
done	5000	12

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (/ (+ x z) y) (- x z) y)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (/ (+ x z) y) (- x z) y)

series57.0ms

Counts

1 → 3

Calls

1 calls:

57.0ms

(fma (/ (+ x z) y) (- x z) y)

simplify674.0ms

Counts

13 → 13

Iterations

Useful iterations: 4 (100.0ms)

Iter	Nodes	Cost
0	24	180
1	45	180
2	108	160
3	261	160
4	960	157
done	5000	157

prune43.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (/ (+ x z) y) (- x z) y))
0.5b	(cbrt (fma (/ (+ x z) y) (- x z) y))
0.5b	(cbrt (fma (/ (+ x z) y) (- x z) y))
0.5b	(* (cbrt (fma (/ (+ x z) y) (- x z) y)) (cbrt (fma (/ (+ x z) y) (- x z) y)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

0.0ms	(cbrt (fma (/ (+ x z) y) (- x z) y))
0.0ms	(cbrt (fma (/ (+ x z) y) (- x z) y))
0.0ms	(cbrt (fma (/ (+ x z) y) (- x z) y))
6.0ms	(* (cbrt (fma (/ (+ x z) y) (- x z) y)) (cbrt (fma (/ (+ x z) y) (- x z) y)))

series837.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(cbrt (fma (/ (+ x z) y) (- x z) y))
152.0ms	(cbrt (fma (/ (+ x z) y) (- x z) y))
358.0ms	(cbrt (fma (/ (+ x z) y) (- x z) y))
167.0ms	(* (cbrt (fma (/ (+ x z) y) (- x z) y)) (cbrt (fma (/ (+ x z) y) (- x z) y)))

simplify1.0s

Counts

93 → 93

Iterations

Useful iterations: 3 (366.0ms)

Iter	Nodes	Cost
0	108	2087
1	229	1944
2	669	1775
3	2162	1496
done	5000	1496

prune291.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (/ (+ x z) y) (- x z) y))
0.5b	(cbrt (fma (/ (+ x z) y) (- x z) y))
0.5b	(* (cbrt (cbrt (fma (/ (+ x z) y) (- x z) y))) (cbrt (cbrt (fma (/ (+ x z) y) (- x z) y))))
0.5b	(* (cbrt (fma (/ (+ x z) y) (- x z) y)) (cbrt (fma (/ (+ x z) y) (- x z) y)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

76×	`cbrt-prod`
52×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
15×	`swap-sqr` `associate-r` `associate-l`
14×	`pow1/3`
13×	`unswap-sqr`
8×	`add-exp-log`
4×	`expm1-log1p-u` `pow-prod-down` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

1.0ms	(cbrt (fma (/ (+ x z) y) (- x z) y))
1.0ms	(cbrt (fma (/ (+ x z) y) (- x z) y))
12.0ms	(* (cbrt (cbrt (fma (/ (+ x z) y) (- x z) y))) (cbrt (cbrt (fma (/ (+ x z) y) (- x z) y))))
6.0ms	(* (cbrt (fma (/ (+ x z) y) (- x z) y)) (cbrt (fma (/ (+ x z) y) (- x z) y)))

series636.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (fma (/ (+ x z) y) (- x z) y))
157.0ms	(cbrt (fma (/ (+ x z) y) (- x z) y))
167.0ms	(* (cbrt (cbrt (fma (/ (+ x z) y) (- x z) y))) (cbrt (cbrt (fma (/ (+ x z) y) (- x z) y))))
161.0ms	(* (cbrt (fma (/ (+ x z) y) (- x z) y)) (cbrt (fma (/ (+ x z) y) (- x z) y)))

simplify1.5s

Counts

136 → 136

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	167	3745
1	337	3478
2	1035	3219
3	3388	2640
done	5000	2636

prune448.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

3.9b	(- (+ (* x x) (* y y)) (* z z))
30.8b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`times-frac` `associate-/l*`
3×	`fma-neg` `prod-diff` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3--` `diff-log` `div-exp` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`sub-neg` `frac-2neg` `div-sub` `prod-exp` `associate--l+` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `div-inv`

Counts

2 → 51

Calls

2 calls:

19.0ms	(- (+ (* x x) (* y y)) (* z z))
34.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series125.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(- (+ (* x x) (* y y)) (* z z))
84.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify676.0ms

Counts

57 → 57

Iterations

Useful iterations: done (674.0ms)

Iter	Nodes	Cost
0	108	1089
1	298	967
2	1078	841
done	5000	829

prune150.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes78.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	10	12
done	10	12

end0.0ms

sample755.0ms

Algorithm

intervals

Results

470.0ms

13731×

body

valid