Details

Time bar (total: 35.9s)

sample41.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
6.0ms256×pre80true

simplify6.9s

Counts
1 → 1
Iterations
IterNodes
done5004
71738
6803
5457
4220
3107
250
123
09

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize46.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma x x (* y y))
18.8b
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/l/
7×add-cbrt-cube add-exp-log
4×add-sqr-sqrt frac-times *-un-lft-identity add-cube-cbrt
3×associate-/r* flip3-+ times-frac flip3-- flip-+ flip--
2×expm1-log1p-u pow1 cbrt-undiv div-exp associate-*l/ associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
1×clear-num frac-2neg prod-exp cbrt-unprod fma-udef div-inv associate-/l*
Counts
2 → 43
Calls
2 calls:
1.0ms
(fma x x (* y y))
43.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

series189.0ms

Counts
2 → 6
Calls
2 calls:
76.0ms
(fma x x (* y y))
112.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

simplify2.2s

Counts
49 → 49
Iterations
IterNodes
done5001
21116
1250
084

prune582.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y))))
18.3b
(sqrt (fma x x (* y y)))
18.3b
(sqrt (fma x x (* y y)))
18.8b
(/ (* (- x y) (+ y x)) (* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y)))))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
18×add-cbrt-cube add-exp-log
14×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1 pow1/2
8×swap-sqr associate-/l/
6×associate-*r* associate-*l*
5×prod-exp pow-prod-up cbrt-unprod
4×expm1-log1p-u frac-times cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×flip3-+ flip3-- pow-prod-down pow-sqr flip-+ flip--
2×rem-sqrt-square associate-*l/ associate-*r/ fma-udef hypot-def
1×pow2 clear-num associate-/r* rem-square-sqrt frac-2neg times-frac pow-plus sqrt-unprod *-commutative div-inv associate-/l*
Counts
4 → 118
Calls
4 calls:
36.0ms
(* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y))))
5.0ms
(sqrt (fma x x (* y y)))
5.0ms
(sqrt (fma x x (* y y)))
83.0ms
(/ (* (- x y) (+ y x)) (* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y)))))

series352.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y))))
91.0ms
(sqrt (fma x x (* y y)))
84.0ms
(sqrt (fma x x (* y y)))
113.0ms
(/ (* (- x y) (+ y x)) (* (sqrt (fma x x (* y y))) (sqrt (fma x x (* y y)))))

simplify3.2s

Counts
130 → 130
Iterations
IterNodes
done5000
21663
1379
0126

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- x y) (hypot y x))
0.0b
(* (/ (+ y x) (hypot y x)) (/ (- x y) (hypot y x)))
0.0b
(/ (+ y x) (hypot y x))
0.4b
(expm1 (* (/ (+ y x) (hypot y x)) (/ (- x y) (hypot y x))))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
66×add-sqr-sqrt
58×times-frac
40×add-cube-cbrt
20×add-cbrt-cube add-exp-log
19×associate-*r*
16×associate-*l*
9×associate-/l*
7×distribute-lft-out distribute-lft-out-- difference-of-squares
6×pow1 cbrt-undiv associate-/r* div-exp
5×log1p-expm1-u
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 div-inv add-log-exp unswap-sqr associate-/l/
2×clear-num frac-2neg
1×frac-times expm1-log1p flip3-+ flip3-- div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+ flip-- expm1-udef
Counts
4 → 151
Calls
4 calls:
51.0ms
(/ (- x y) (hypot y x))
103.0ms
(* (/ (+ y x) (hypot y x)) (/ (- x y) (hypot y x)))
36.0ms
(/ (+ y x) (hypot y x))
1.0ms
(expm1 (* (/ (+ y x) (hypot y x)) (/ (- x y) (hypot y x))))

series678.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (- x y) (hypot y x))
149.0ms
(* (/ (+ y x) (hypot y x)) (/ (- x y) (hypot y x)))
153.0ms
(/ (+ y x) (hypot y x))
230.0ms
(expm1 (* (/ (+ y x) (hypot y x)) (/ (- x y) (hypot y x))))

simplify3.8s

Counts
163 → 163
Iterations
IterNodes
done5000
21618
1528
0187

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize141.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ y (hypot y x))
0.0b
(* (/ (+ y x) (hypot y x)) (- (/ x (hypot y x)) (/ y (hypot y x))))
0.0b
(/ (+ y x) (hypot y x))
0.4b
(expm1 (* (/ (+ y x) (hypot y x)) (- (/ x (hypot y x)) (/ y (hypot y x)))))

rewrite520.0ms

Algorithm
rewrite-expression-head
Rules
512×times-frac
418×*-un-lft-identity
413×add-sqr-sqrt
396×add-cube-cbrt
338×prod-diff
171×distribute-rgt-in distribute-lft-in
57×div-inv
16×associate-*l*
13×add-cbrt-cube add-exp-log
12×associate-*r*
7×distribute-lft-out associate-/l*
6×pow1 associate-/r*
5×log1p-expm1-u
4×expm1-log1p-u frac-times associate-*r/ insert-posit16 distribute-lft-out-- add-log-exp difference-of-squares
3×cbrt-undiv div-exp
2×clear-num sub-neg frac-2neg flip3-- prod-exp frac-sub cbrt-unprod flip-- sub-div unswap-sqr associate-/l/
1×expm1-log1p flip3-+ distribute-rgt-out-- pow-prod-down associate-*l/ *-commutative flip-+ expm1-udef
Counts
4 → 475
Calls
4 calls:
13.0ms
(/ y (hypot y x))
301.0ms
(* (/ (+ y x) (hypot y x)) (- (/ x (hypot y x)) (/ y (hypot y x))))
52.0ms
(/ (+ y x) (hypot y x))
2.0ms
(expm1 (* (/ (+ y x) (hypot y x)) (- (/ x (hypot y x)) (/ y (hypot y x)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ y (hypot y x))
346.0ms
(* (/ (+ y x) (hypot y x)) (- (/ x (hypot y x)) (/ y (hypot y x))))
148.0ms
(/ (+ y x) (hypot y x))
411.0ms
(expm1 (* (/ (+ y x) (hypot y x)) (- (/ x (hypot y x)) (/ y (hypot y x)))))

simplify5.0s

Counts
487 → 487
Iterations
IterNodes
done5001
12552
0799

prune5.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes307.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify19.0ms

Iterations
IterNodes
done27
127
019

end0.0ms

sample1.4s

Algorithm
intervals
Results
886.0ms8000×body80valid
203.0ms8000×pre80true