Details

sample53.0ms

Algorithm

intervals

Results

38.0ms

331×

body

valid

simplify42.0ms

Calls

1 calls:

Slowest

42.0ms

(fabs (- (/ (+ x 4) y) (* (/ x y) z)))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.3b

localize33.0ms

Local error

Found 3 expressions with local error:

4.5b	(* (/ x y) z)
0.0b	(/ (+ x 4) y)
0.0b	(- (/ (+ x 4) y) (* (/ x y) z))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-cube-cbrt`
7×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`add-log-exp`
4×	`div-inv`
4×	`prod-diff`
4×	`associate-l`
4×	`fma-neg`
3×	`associate-/l*`
3×	`log1p-expm1-u`
3×	`add-exp-log`
3×	`associate-*l/`
3×	`add-cbrt-cube`
3×	`pow1`
3×	`expm1-log1p-u`
2×	`associate-/l/`
1×	`sub-div`
1×	`flip--`
1×	`flip-+`
1×	`frac-sub`
1×	`*-commutative`
1×	`diff-log`
1×	`flip3--`
1×	`flip3-+`
1×	`frac-2neg`
1×	`sub-neg`
1×	`clear-num`

Calls

3 calls:

Slowest

13.0ms	(- (/ (+ x 4) y) (* (/ x y) z))
5.0ms	(/ (+ x 4) y)
5.0ms	(* (/ x y) z)

series73.0ms

Calls

3 calls:

Slowest

36.0ms	(- (/ (+ x 4) y) (* (/ x y) z))
22.0ms	(* (/ x y) z)
14.0ms	(/ (+ x 4) y)

simplify1.0s

Calls

31 calls:

Slowest

207.0ms	(fma (+ x 4) (/ 1 y) (- (* z (/ x y))))
123.0ms	(- (* (+ x 4) y) (* y (* x z)))
113.0ms	(- (+ (/ x y) (* 4 (/ 1 y))) (/ (* x z) y))
83.0ms	(- (+ (/ x y) (* 4 (/ 1 y))) (/ (* x z) y))
71.0ms	(- (+ (/ x y) (* 4 (/ 1 y))) (/ (* x z) y))

prune647.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

5.0b	(* (/ z y) x)
0.0b	(/ (+ 4 x) y)
0.0b	(- (/ (+ 4 x) y) (* (/ z y) x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-cube-cbrt`
7×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`add-log-exp`
4×	`div-inv`
4×	`prod-diff`
4×	`associate-l`
4×	`fma-neg`
3×	`associate-/l*`
3×	`log1p-expm1-u`
3×	`add-exp-log`
3×	`associate-*l/`
3×	`add-cbrt-cube`
3×	`pow1`
3×	`expm1-log1p-u`
2×	`associate-/l/`
1×	`sub-div`
1×	`flip--`
1×	`flip-+`
1×	`frac-sub`
1×	`*-commutative`
1×	`diff-log`
1×	`flip3--`
1×	`flip3-+`
1×	`frac-2neg`
1×	`sub-neg`
1×	`clear-num`

Calls

3 calls:

Slowest

13.0ms	(- (/ (+ 4 x) y) (* (/ z y) x))
3.0ms	(/ (+ 4 x) y)
2.0ms	(* (/ z y) x)

series55.0ms

Calls

3 calls:

Slowest

25.0ms	(- (/ (+ 4 x) y) (* (/ z y) x))
17.0ms	(* (/ z y) x)
14.0ms	(/ (+ 4 x) y)

simplify1.0s

Calls

31 calls:

Slowest

190.0ms	(fma (+ 4 x) (/ 1 y) (- (* x (/ z y))))
154.0ms	(- (* (+ 4 x) y) (* y (* z x)))
93.0ms	(- (+ (/ x y) (* 4 (/ 1 y))) (/ (* x z) y))
85.0ms	(- (+ (/ x y) (* 4 (/ 1 y))) (/ (* x z) y))
80.0ms	(- (+ (/ x y) (* 4 (/ 1 y))) (/ (* x z) y))

prune638.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize32.0ms

Local error

Found 3 expressions with local error:

5.0b	(/ x (/ y z))
0.0b	(/ (+ x 4) y)
0.0b	(- (/ (+ x 4) y) (/ x (/ y z)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`prod-diff`
17×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`div-inv`
5×	`add-log-exp`
5×	`associate-/r/`
4×	`fma-neg`
4×	`associate-/r*`
3×	`associate-/l*`
3×	`log1p-expm1-u`
3×	`add-exp-log`
3×	`add-cbrt-cube`
3×	`pow1`
3×	`expm1-log1p-u`
2×	`associate-/l/`
2×	`frac-2neg`
2×	`clear-num`
1×	`difference-of-squares`
1×	`distribute-lft-out--`
1×	`flip--`
1×	`flip-+`
1×	`frac-sub`
1×	`diff-log`
1×	`flip3--`
1×	`flip3-+`
1×	`sub-neg`

Calls

3 calls:

Slowest

12.0ms	(- (/ (+ x 4) y) (/ x (/ y z)))
5.0ms	(/ (+ x 4) y)
1.0ms	(/ x (/ y z))

series88.0ms

Calls

3 calls:

Slowest

43.0ms	(- (/ (+ x 4) y) (/ x (/ y z)))
23.0ms	(/ x (/ y z))
22.0ms	(/ (+ x 4) y)

simplify4.6s

Calls

66 calls:

Slowest

569.0ms	(fma (+ x 4) (/ 1 y) (- (* (/ x (/ y z)) 1)))
217.0ms	(fma 1 (/ (+ x 4) y) (- (* (/ 1 (/ y z)) x)))
186.0ms	(fma (- (/ 1 (/ y z))) x (* (/ 1 (/ y z)) x))
184.0ms	(fma (* (cbrt (/ (+ x 4) y)) (cbrt (/ (+ x 4) y))) (cbrt (/ (+ x 4) y)) (- (* (/ 1 (/ y z)) x)))
171.0ms	(fma (- (/ 1 (/ y z))) x (* (/ 1 (/ y z)) x))

prune889.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

5.0b	(* (/ z y) x)
5.0b	(* (/ z y) x)
0.3b	(* (sqrt (- (/ (+ 4 x) y) (* (/ z y) x))) (sqrt (- (/ (+ 4 x) y) (* (/ z y) x))))
0.1b	(sqrt (- (/ (+ 4 x) y) (* (/ z y) x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

44×	`sqrt-div`
28×	`associate-*l/`
16×	`frac-times`
14×	`associate-l`
12×	`add-sqr-sqrt`
11×	`sub-div`
11×	`flip--`
11×	`add-cube-cbrt`
11×	`frac-sub`
11×	`flip3--`
11×	`*-un-lft-identity`
9×	`sqrt-prod`
9×	`pow1`
6×	`add-exp-log`
6×	`associate-r`
6×	`add-cbrt-cube`
5×	`pow1/2`
4×	`add-log-exp`
4×	`log1p-expm1-u`
4×	`associate-*r/`
4×	`expm1-log1p-u`
3×	`*-commutative`
2×	`div-inv`
2×	`pow-prod-up`
2×	`pow-prod-down`
1×	`cbrt-unprod`
1×	`prod-exp`
1×	`sqrt-unprod`
1×	`pow-plus`
1×	`rem-square-sqrt`
1×	`rem-sqrt-square`
1×	`pow2`

Calls

4 calls:

Slowest

19.0ms	(* (sqrt (- (/ (+ 4 x) y) (* (/ z y) x))) (sqrt (- (/ (+ 4 x) y) (* (/ z y) x))))
6.0ms	(sqrt (- (/ (+ 4 x) y) (* (/ z y) x)))
5.0ms	(* (/ z y) x)
4.0ms	(* (/ z y) x)

series164.0ms

Calls

4 calls:

Slowest

99.0ms	(sqrt (- (/ (+ 4 x) y) (* (/ z y) x)))
26.0ms	(* (sqrt (- (/ (+ 4 x) y) (* (/ z y) x))) (sqrt (- (/ (+ 4 x) y) (* (/ z y) x))))
21.0ms	(* (/ z y) x)
18.0ms	(* (/ z y) x)

simplify7.9s

Calls

89 calls:

Slowest

413.0ms	(* (sqrt (- (pow (/ (+ 4 x) y) 3) (pow (* (/ z y) x) 3))) (sqrt (- (/ (+ 4 x) y) (* (/ z y) x))))
377.0ms	(* (sqrt (- (pow (/ (+ 4 x) y) 3) (pow (* (/ z y) x) 3))) (sqrt (- (+ 4 x) (* z x))))
377.0ms	(* (sqrt (- (+ 4 x) (* z x))) (sqrt (- (pow (/ (+ 4 x) y) 3) (pow (* (/ z y) x) 3))))
347.0ms	(* (sqrt (- (* (/ (+ 4 x) y) (/ (+ 4 x) y)) (* (* (/ z y) x) (* (/ z y) x)))) (sqrt (- (* (/ (+ 4 x) y) (/ (+ 4 x) y)) (* (* (/ z y) x) (* (/ z y) x)))))
344.0ms	(sqrt (- (pow (/ (+ 4 x) y) 3) (pow (* (/ z y) x) 3)))

prune1.5s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes267.0ms

Accuracy

96.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.9b

bsearch6.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

10166×

body

valid