Details

Time bar (total: 16.7s)

sample44.0ms

Algorithm
intervals
Results
30.0ms271×body80valid

simplify26.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
25.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.3b

localize19.0ms

Local error

Found 2 expressions with local error:

24.3b
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.3b
(fma x.re y.re (* x.im y.im))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
2 → 41
Calls
2 calls:
Slowest
8.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
0.0ms
(fma x.re y.re (* x.im y.im))

series192.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
150.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))
42.0ms
(fma x.re y.re (* x.im y.im))

simplify1.3s

Counts
31 → 47
Calls
31 calls:
Slowest
479.0ms
(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (fma y.im y.im (* y.re y.re)) (fma y.im y.im (* y.re y.re))) (fma y.im y.im (* y.re y.re))))
59.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re)))))
51.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (fma y.im y.im (* y.re y.re))))
51.0ms
(/ (sqrt (fma x.re y.re (* x.im y.im))) (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re)))))
47.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) 1)

prune590.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.9b

localize44.0ms

Local error

Found 4 expressions with local error:

28.3b
(sqrt (fma y.im y.im (* y.re y.re)))
28.3b
(sqrt (fma y.im y.im (* y.re y.re)))
14.9b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
0.3b
(fma x.re y.re (* x.im y.im))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 87
Calls
4 calls:
Slowest
9.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
0.0ms
(fma x.re y.re (* x.im y.im))

series393.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
73.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
72.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
64.0ms
(fma x.re y.re (* x.im y.im))

simplify2.0s

Counts
68 → 99
Calls
68 calls:
Slowest
326.0ms
(/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* (sqrt (fma y.im y.im (* y.re y.re))) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re)))))
87.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))
56.0ms
(/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt (sqrt (fma y.im y.im (* y.re y.re)))))
52.0ms
(/ (sqrt (fma x.re y.re (* x.im y.im))) (* (cbrt (sqrt (fma y.im y.im (* y.re y.re)))) (cbrt (sqrt (fma y.im y.im (* y.re y.re))))))
50.0ms
(- (log (fma x.re y.re (* x.im y.im))) (log (sqrt (fma y.im y.im (* y.re y.re)))))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.8b

localize31.0ms

Local error

Found 4 expressions with local error:

28.3b
(sqrt (fma y.im y.im (* y.re y.re)))
28.3b
(sqrt (fma y.im y.im (* y.re y.re)))
14.9b
(/ (* 1 (fma x.re y.re (* x.im y.im))) (sqrt (fma y.im y.im (* y.re y.re))))
0.3b
(fma x.re y.re (* x.im y.im))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
11×add-exp-log
10×*-un-lft-identity add-cube-cbrt
9×add-cbrt-cube
6×pow1 associate-/r* times-frac
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×div-exp fma-udef
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 prod-exp hypot-def
1×clear-num frac-2neg 1-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
Slowest
9.0ms
(/ (* 1 (fma x.re y.re (* x.im y.im))) (sqrt (fma y.im y.im (* y.re y.re))))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
0.0ms
(fma x.re y.re (* x.im y.im))

series335.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(/ (* 1 (fma x.re y.re (* x.im y.im))) (sqrt (fma y.im y.im (* y.re y.re))))
85.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
55.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
45.0ms
(fma x.re y.re (* x.im y.im))

simplify1.1s

Counts
45 → 88
Calls
45 calls:
Slowest
146.0ms
(/ (* (* (* 1 1) 1) (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im)))) (* (* (sqrt (fma y.im y.im (* y.re y.re))) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re)))))
127.0ms
(/ (* (* (* 1 (fma x.re y.re (* x.im y.im))) (* 1 (fma x.re y.re (* x.im y.im)))) (* 1 (fma x.re y.re (* x.im y.im)))) (* (* (sqrt (fma y.im y.im (* y.re y.re))) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re)))))
102.0ms
(- (log (* 1 (fma x.re y.re (* x.im y.im)))) (log (sqrt (fma y.im y.im (* y.re y.re)))))
78.0ms
(- (+ 0 (log (fma x.re y.re (* x.im y.im)))) (log (sqrt (fma y.im y.im (* y.re y.re)))))
44.0ms
(- (+ (log 1) (log (fma x.re y.re (* x.im y.im)))) (log (sqrt (fma y.im y.im (* y.re y.re)))))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.8b

localize20.0ms

Local error

Found 2 expressions with local error:

24.3b
(/ (/ (fma x.re y.re (* x.im y.im)) 1) (fma y.im y.im (* y.re y.re)))
0.3b
(fma x.re y.re (* x.im y.im))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
44×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×associate-/l*
9×add-exp-log
7×add-cbrt-cube
5×div-exp div-inv
3×cbrt-undiv associate-/r*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×clear-num frac-2neg 1-exp fma-udef associate-/l/
Counts
2 → 85
Calls
2 calls:
Slowest
7.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) 1) (fma y.im y.im (* y.re y.re)))
0.0ms
(fma x.re y.re (* x.im y.im))

series178.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
123.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) 1) (fma y.im y.im (* y.re y.re)))
55.0ms
(fma x.re y.re (* x.im y.im))

simplify5.0s

Counts
105 → 91
Calls
105 calls:
Slowest
193.0ms
(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (* (cbrt 1) (cbrt 1))) (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re)))))
192.0ms
(/ (* (* (/ (fma x.re y.re (* x.im y.im)) 1) (/ (fma x.re y.re (* x.im y.im)) 1)) (/ (fma x.re y.re (* x.im y.im)) 1)) (* (* (fma y.im y.im (* y.re y.re)) (fma y.im y.im (* y.re y.re))) (fma y.im y.im (* y.re y.re))))
158.0ms
(/ (/ (* (* (fma x.re y.re (* x.im y.im)) (fma x.re y.re (* x.im y.im))) (fma x.re y.re (* x.im y.im))) (* (* 1 1) 1)) (* (* (fma y.im y.im (* y.re y.re)) (fma y.im y.im (* y.re y.re))) (fma y.im y.im (* y.re y.re))))
139.0ms
(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) (sqrt 1)) (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re)))))
127.0ms
(/ (/ (* (cbrt (fma x.re y.re (* x.im y.im))) (cbrt (fma x.re y.re (* x.im y.im)))) 1) (* (cbrt (fma y.im y.im (* y.re y.re))) (cbrt (fma y.im y.im (* y.re y.re)))))

prune948.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.1b

regimes336.0ms

Accuracy

0% (2.4b remaining)

Error of 16.4b against oracle of 14.0b and baseline of 16.4b

bsearch2.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s8456×body80valid