Details

Time bar (total: 22.7s)

sample57.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
16.0ms256×pre80true

simplify4.7s

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

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/ log1p-expm1-u add-log-exp
1×clear-num frac-2neg prod-exp cbrt-unprod fma-udef div-inv associate-/l*
Counts
2 → 41
Calls
2 calls:
0.0ms
(fma x x (* y y))
18.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

series185.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(fma x x (* y y))
117.0ms
(/ (* (- x y) (+ y x)) (fma x x (* y y)))

simplify1.2s

Counts
47 → 47
Iterations
IterNodes
done5002
21107
1248
082

prune316.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- x y) (sqrt (fma x x (* y y))))
0.0b
(* (/ (- x y) (sqrt (fma x x (* y y)))) (/ (+ y x) (sqrt (fma x x (* y y)))))
19.0b
(sqrt (fma x x (* y y)))
19.0b
(sqrt (fma x x (* y y)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
115×add-sqr-sqrt
96×times-frac
95×*-un-lft-identity
57×add-cube-cbrt sqrt-prod
34×associate-*l*
28×associate-*r*
18×add-cbrt-cube add-exp-log
13×distribute-lft-out-- difference-of-squares
9×unswap-sqr
8×pow1
6×associate-/r* distribute-lft-out
5×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u 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-- div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 183
Calls
4 calls:
17.0ms
(/ (- x y) (sqrt (fma x x (* y y))))
120.0ms
(* (/ (- x y) (sqrt (fma x x (* y y)))) (/ (+ y x) (sqrt (fma x x (* y y)))))
3.0ms
(sqrt (fma x x (* y y)))
3.0ms
(sqrt (fma x x (* y y)))

series666.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(/ (- x y) (sqrt (fma x x (* y y))))
355.0ms
(* (/ (- x y) (sqrt (fma x x (* y y)))) (/ (+ y x) (sqrt (fma x x (* y y)))))
85.0ms
(sqrt (fma x x (* y y)))
60.0ms
(sqrt (fma x x (* y y)))

simplify1.9s

Counts
195 → 195
Iterations
IterNodes
done5001
22470
1571
0188

prune889.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize92.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
1034×add-cbrt-cube add-exp-log
563×prod-exp cbrt-unprod
322×cbrt-undiv div-exp
179×*-un-lft-identity
155×times-frac
148×frac-times
143×add-sqr-sqrt
106×associate-*r/
89×add-cube-cbrt
68×associate-*l/
59×pow1
55×associate-*l*
47×swap-sqr
37×associate-*r*
32×pow-prod-down
21×distribute-lft-out--
18×distribute-lft-out
15×difference-of-squares
9×div-inv
8×unswap-sqr
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp
2×pow2 pow-plus pow-sqr pow-prod-up
Counts
4 → 582
Calls
4 calls:
766.0ms
(* (* (/ (- x y) (hypot x y)) (* (/ (+ y x) (hypot x y)) (* (/ (+ y x) (hypot x y)) (/ (+ y x) (hypot x y))))) (* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y))))
41.0ms
(* (/ (+ y x) (hypot x y)) (/ (+ y x) (hypot x y)))
81.0ms
(* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y)))
205.0ms
(* (/ (- x y) (hypot x y)) (* (/ (+ y x) (hypot x y)) (* (/ (+ y x) (hypot x y)) (/ (+ y x) (hypot x y)))))

series649.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(* (* (/ (- x y) (hypot x y)) (* (/ (+ y x) (hypot x y)) (* (/ (+ y x) (hypot x y)) (/ (+ y x) (hypot x y))))) (* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y))))
137.0ms
(* (/ (+ y x) (hypot x y)) (/ (+ y x) (hypot x y)))
109.0ms
(* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y)))
179.0ms
(* (/ (- x y) (hypot x y)) (* (/ (+ y x) (hypot x y)) (* (/ (+ y x) (hypot x y)) (/ (+ y x) (hypot x y)))))

simplify3.1s

Counts
594 → 594
Iterations
IterNodes
done5000
12275
0648

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize95.0ms

Local error

Found 4 expressions with local error:

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

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
265×*-un-lft-identity
247×add-sqr-sqrt
243×times-frac
157×add-cbrt-cube add-exp-log
133×add-cube-cbrt
76×associate-*l*
75×swap-sqr
70×prod-exp cbrt-unprod
58×associate-*r*
57×distribute-lft-out--
49×cbrt-undiv div-exp
39×difference-of-squares
34×pow1
20×frac-times associate-*r/
13×div-inv
12×unswap-sqr
10×associate-*l/
9×pow-prod-down
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp
3×pow2 pow-plus pow-sqr pow-prod-up
Counts
4 → 371
Calls
4 calls:
59.0ms
(* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y)))
43.0ms
(* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y)))
50.0ms
(* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y)))
164.0ms
(* (/ (- x y) (hypot x y)) (* (/ (+ y x) (hypot x y)) (* (/ (+ y x) (hypot x y)) (/ (+ y x) (hypot x y)))))

series547.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y)))
123.0ms
(* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y)))
133.0ms
(* (/ (- x y) (hypot x y)) (/ (- x y) (hypot x y)))
183.0ms
(* (/ (- x y) (hypot x y)) (* (/ (+ y x) (hypot x y)) (* (/ (+ y x) (hypot x y)) (/ (+ y x) (hypot x y)))))

simplify2.1s

Counts
383 → 383
Iterations
IterNodes
done5012
23663
1957
0273

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes87.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done21
121
016

end0.0ms

sample860.0ms

Algorithm
intervals
Results
449.0ms8000×body80valid
205.0ms8000×pre80true