Details

Time bar (total: 38.9s)

sample40.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
8.0ms256×pre80true

simplify207.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
207.0ms
(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize33.0ms

Local error

Found 1 expressions with local error:

20.6b
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/l/
6×add-cbrt-cube add-exp-log
4×frac-times
3×add-sqr-sqrt associate-/r* *-un-lft-identity flip3-+ times-frac flip3-- add-cube-cbrt flip-+ flip--
2×cbrt-undiv div-exp associate-*l/ associate-*r/
1×expm1-log1p-u pow1 clear-num frac-2neg prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
Counts
1 → 32
Calls
1 calls:
Slowest
35.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

series98.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
98.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

simplify4.1s

Counts
25 → 35
Calls
25 calls:
Slowest
540.0ms
(/ (* (* (* (- x y) (+ y x)) (* (- x y) (+ y x))) (* (- x y) (+ y x))) (* (* (fma x x (* y y)) (fma x x (* y y))) (fma x x (* y y))))
523.0ms
(* (- (* x x) (* y y)) (+ y x))
509.0ms
(* (- (pow x 3) (pow y 3)) (- (* y y) (* x x)))
429.0ms
(/ (* (* (* (- x y) (- x y)) (- x y)) (* (* (+ y x) (+ y x)) (+ y x))) (* (* (fma x x (* y y)) (fma x x (* y y))) (fma x x (* y y))))
358.0ms
(- (log (* (- x y) (+ y x))) (log (fma x x (* y y))))

prune400.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
93×*-un-lft-identity
90×times-frac
55×add-cube-cbrt
54×sqrt-prod
34×associate-*l*
28×associate-*r*
18×add-cbrt-cube add-exp-log
13×distribute-lft-out
9×unswap-sqr
8×pow1
6×associate-/r* distribute-lft-out-- difference-of-squares
5×cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef hypot-def associate-/l/
1×frac-times clear-num frac-2neg flip3-+ pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+
Counts
4 → 179
Calls
4 calls:
Slowest
36.0ms
(* (/ (- x y) (sqrt (fma x x (* y y)))) (/ (+ y x) (sqrt (fma x x (* y y)))))
30.0ms
(/ (+ y x) (sqrt (fma x x (* y y))))
3.0ms
(sqrt (fma x x (* y y)))
2.0ms
(sqrt (fma x x (* y y)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
131.0ms
(/ (+ y x) (sqrt (fma x x (* y y))))
89.0ms
(* (/ (- x y) (sqrt (fma x x (* y y)))) (/ (+ y x) (sqrt (fma x x (* y y)))))
70.0ms
(sqrt (fma x x (* y y)))
62.0ms
(sqrt (fma x x (* y y)))

simplify8.2s

Counts
174 → 191
Calls
174 calls:
Slowest
643.0ms
(* (/ (* (* (- x y) (- x y)) (- x y)) (* (* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y)))) (sqrt (fma x x (* y y))))) (/ (* (* (+ y x) (+ y x)) (+ y x)) (* (* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y)))) (sqrt (fma x x (* y y))))))
507.0ms
(/ (* (* (+ y x) (+ y x)) (+ y x)) (* (* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y)))) (sqrt (fma x x (* y y)))))
343.0ms
(* (* (* (/ (- x y) (sqrt (fma x x (* y y)))) (/ (- x y) (sqrt (fma x x (* y y))))) (/ (- x y) (sqrt (fma x x (* y y))))) (/ (* (* (+ y x) (+ y x)) (+ y x)) (* (* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y)))) (sqrt (fma x x (* y y))))))
336.0ms
(* (/ (* (* (- x y) (- x y)) (- x y)) (* (* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y)))) (sqrt (fma x x (* y y))))) (* (* (/ (+ y x) (sqrt (fma x x (* y y)))) (/ (+ y x) (sqrt (fma x x (* y y))))) (/ (+ y x) (sqrt (fma x x (* y y))))))
266.0ms
(* (- x y) (/ (+ y x) (sqrt (fma x x (* y y)))))

prune2.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
137×*-un-lft-identity
112×times-frac
107×add-sqr-sqrt
71×add-cube-cbrt
25×swap-sqr
22×add-cbrt-cube add-exp-log
19×associate-*r* associate-*l*
18×distribute-lft-out--
12×distribute-lft-out associate-/l* difference-of-squares
11×pow1
9×associate-/r*
7×cbrt-undiv div-exp div-inv
6×associate-/l/
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×clear-num frac-2neg flip3-+ flip-+
1×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 202
Calls
4 calls:
Slowest
34.0ms
(/ (+ y x) (hypot x y))
32.0ms
(* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y)))
14.0ms
(/ (+ y x) (hypot x y))
14.0ms
(/ (+ y x) (hypot x y))

series502.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y)))
130.0ms
(/ (+ y x) (hypot x y))
126.0ms
(/ (+ y x) (hypot x y))
103.0ms
(/ (+ y x) (hypot x y))

simplify13.4s

Counts
224 → 214
Calls
224 calls:
Slowest
983.0ms
(* (* (* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y))) (/ (- x y) (hypot x y))) (* (* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y))) (/ (- x y) (hypot x y))))
783.0ms
(/ (* (* (+ y x) (+ y x)) (+ y x)) (* (* (hypot x y) (hypot x y)) (hypot x y)))
488.0ms
(* (/ (* (cbrt (- x y)) (cbrt (- x y))) (* (cbrt (hypot x y)) (cbrt (hypot x y)))) (/ (* (cbrt (- x y)) (cbrt (- x y))) (* (cbrt (hypot x y)) (cbrt (hypot x y)))))
413.0ms
(/ (* (* (+ y x) (+ y x)) (+ y x)) (* (* (hypot x y) (hypot x y)) (hypot x y)))
395.0ms
(/ (* (* (+ y x) (+ y x)) (+ y x)) (* (* (hypot x y) (hypot x y)) (hypot x y)))

prune2.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize118.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- x y))
0.5b
(cbrt (- x y))
0.5b
(cbrt (- x y))
0.5b
(cbrt (hypot x y))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
14×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 68
Calls
4 calls:
Slowest
5.0ms
(cbrt (- x y))
5.0ms
(cbrt (- x y))
5.0ms
(cbrt (- x y))
1.0ms
(cbrt (hypot x y))

series702.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
214.0ms
(cbrt (- x y))
172.0ms
(cbrt (- x y))
169.0ms
(cbrt (- x y))
147.0ms
(cbrt (hypot x y))

simplify3.2s

Counts
36 → 80
Calls
36 calls:
Slowest
409.0ms
(- (exp (* 1/3 (+ (log -1) (log y)))) (+ (* 1/9 (* (pow x 2) (exp (* 1/3 (- (log -1) (* 5 (log y))))))) (* 1/3 (* x (exp (* 1/3 (- (log -1) (* 2 (log y)))))))))
391.0ms
(- (exp (* 1/3 (+ (log -1) (log y)))) (+ (* 1/9 (* (pow x 2) (exp (* 1/3 (- (log -1) (* 5 (log y))))))) (* 1/3 (* x (exp (* 1/3 (- (log -1) (* 2 (log y)))))))))
387.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 x)))))
386.0ms
(- (exp (* 1/3 (+ (log -1) (log y)))) (+ (* 1/9 (* (pow x 2) (exp (* 1/3 (- (log -1) (* 5 (log y))))))) (* 1/3 (* x (exp (* 1/3 (- (log -1) (* 2 (log y)))))))))
385.0ms
(exp (* 1/3 (- (log -1) (log (/ -1 x)))))

prune1.0s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes115.0ms

Accuracy

0% (0.0b remaining)

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

bsearch5.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
915.0ms8000×body80valid
345.0ms8000×pre80true