Details

sample41.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify7.0s

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	9	15
1	23	14
2	52	14
3	113	14
4	229	14
5	461	14
6	822	14
7	1308	14
8	3296	14
done	5000	14

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- x y) (+ x y))
0.0b	(+ (* x x) (* y y))
19.8b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `flip3-+` `flip-+` `associate-/l/`
7×	`add-cube-cbrt`
6×	`flip3--` `flip--`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-r/` `associate-r` `associate-l/`
3×	`expm1-log1p-u` `times-frac` `associate-/r*` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `distribute-rgt-in` `fma-def` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `sum-log` `-commutative` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 80

Calls

3 calls:

42.0ms	(* (- x y) (+ x y))
9.0ms	(+ (* x x) (* y y))
41.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series191.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* (- x y) (+ x y))
46.0ms	(+ (* x x) (* y y))
90.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify2.6s

Counts

89 → 89

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	133	1302
1	423	1165
2	2082	1022
done	5000	1010

prune291.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot x y)
0.0b	(/ (+ x y) (hypot x y))
0.0b	(/ (- x y) (hypot x y))
0.1b	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

68×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
58×	`times-frac`
40×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-l`
16×	`associate-r`
9×	`associate-/l*`
7×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `hypot-udef` `flip3--` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+`

Counts

4 → 146

Calls

4 calls:

1.0ms	(hypot x y)
25.0ms	(/ (+ x y) (hypot x y))
19.0ms	(/ (- x y) (hypot x y))
57.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(hypot x y)
132.0ms	(/ (+ x y) (hypot x y))
150.0ms	(/ (- x y) (hypot x y))
128.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

simplify1.5s

Counts

158 → 158

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	172	2247
1	478	2185
2	1652	1971
done	5000	1970

prune465.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3))
0.0b	(pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3)
0.0b	(/ (- x y) (hypot x y))
0.1b	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
46×	`times-frac`
33×	`add-cube-cbrt`
31×	`add-exp-log` `add-cbrt-cube`
19×	`associate-l`
16×	`associate-r`
9×	`pow1` `cbrt-undiv` `div-exp`
8×	`cbrt-prod` `prod-exp` `cbrt-unprod`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`cube-div`
5×	`pow-exp` `associate-/l*` `rem-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-l/` `associate-/r*` `div-inv` `distribute-lft-out`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `associate-/l/` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `div-sub` `clear-num` `*-commutative` `flip--` `rem-cbrt-cube`

Counts

4 → 156

Calls

4 calls:

4.0ms	(cbrt (pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3))
36.0ms	(pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3)
22.0ms	(/ (- x y) (hypot x y))
69.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3))
139.0ms	(pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3)
146.0ms	(/ (- x y) (hypot x y))
119.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

simplify1.4s

Counts

168 → 168

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	202	2919
1	550	2582
2	2018	2363
done	5001	2342

prune590.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- x y) (hypot x y)) (+ x y))
0.0b	(cbrt (pow (/ (* (/ (- x y) (hypot x y)) (+ x y)) (hypot x y)) 3))
0.0b	(pow (/ (* (/ (- x y) (hypot x y)) (+ x y)) (hypot x y)) 3)
0.0b	(/ (- x y) (hypot x y))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
43×	`times-frac`
34×	`add-cube-cbrt`
21×	`add-exp-log` `add-cbrt-cube`
20×	`cbrt-prod`
19×	`associate-l`
14×	`unpow-prod-down` `cube-prod`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `div-exp` `div-inv`
5×	`associate-/l*`
4×	`expm1-log1p-u` `associate-r` `pow-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt`
3×	`pow-unpow` `associate-/r*`
2×	`cube-div` `cube-mult` `frac-times` `flip3-+` `unpow3` `associate-*r/` `flip-+` `associate-/l/` `unswap-sqr` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `pow1/3` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--` `rem-cbrt-cube` `distribute-lft-out`

Counts

4 → 159

Calls

4 calls:

70.0ms	(* (/ (- x y) (hypot x y)) (+ x y))
6.0ms	(cbrt (pow (/ (* (/ (- x y) (hypot x y)) (+ x y)) (hypot x y)) 3))
29.0ms	(pow (/ (* (/ (- x y) (hypot x y)) (+ x y)) (hypot x y)) 3)
19.0ms	(/ (- x y) (hypot x y))

series532.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (/ (- x y) (hypot x y)) (+ x y))
127.0ms	(cbrt (pow (/ (* (/ (- x y) (hypot x y)) (+ x y)) (hypot x y)) 3))
156.0ms	(pow (/ (* (/ (- x y) (hypot x y)) (+ x y)) (hypot x y)) 3)
138.0ms	(/ (- x y) (hypot x y))

simplify1.3s

Counts

171 → 171

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	214	3061
1	638	2727
2	2141	2517
done	5000	2509

prune571.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes64.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	13	18
done	13	18

end0.0ms

sample950.0ms

Algorithm

intervals

Results

495.0ms	8000×	body	80	valid
182.0ms	8000×	pre	80	true