Details

Time bar (total: 27.8s)

sample307.0ms

Algorithm
intervals
Results
73.0ms202×body80valid
41.0ms11×body1280valid
19.0ms19×body2560valid
16.0ms11×body5120valid
4.0ms5×body640valid
3.0ms6×body320valid
1.0ms2×body160valid

simplify190.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
190.0ms
(* 0.5 (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))))

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.5b

localize21.0ms

Local error

Found 3 expressions with local error:

0.3b
(- (hypot re im) re)
0.1b
(sqrt (* (- (hypot re im) re) 2.0))
0.0b
(* (- (hypot re im) re) 2.0)

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
12×add-cube-cbrt
9×prod-diff
8×pow1
5×add-cbrt-cube associate-*l* add-exp-log add-log-exp
4×associate-*l/
3×expm1-log1p-u flip3-- fma-neg associate-*r* insert-posit16 log1p-expm1-u flip--
2×sqrt-pow1 sqrt-div pow-prod-down distribute-lft-out-- difference-of-squares
1×sub-neg pow1/2 diff-log prod-exp *-commutative sqrt-prod cbrt-unprod unswap-sqr
Counts
3 → 70
Calls
3 calls:
Slowest
31.0ms
(* (- (hypot re im) re) 2.0)
9.0ms
(sqrt (* (- (hypot re im) re) 2.0))
8.0ms
(- (hypot re im) re)

series382.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
219.0ms
(sqrt (* (- (hypot re im) re) 2.0))
84.0ms
(* (- (hypot re im) re) 2.0)
79.0ms
(- (hypot re im) re)

simplify5.2s

Counts
93 → 79
Calls
93 calls:
Slowest
746.0ms
(* (* (* (- (hypot re im) re) 2.0) (* (- (hypot re im) re) 2.0)) (* (- (hypot re im) re) 2.0))
325.0ms
(* (* (- (hypot re im) re) (- (hypot re im) re)) (- (hypot re im) re))
315.0ms
(* (* (* (- (hypot re im) re) (- (hypot re im) re)) (- (hypot re im) re)) (* (* 2.0 2.0) 2.0))
268.0ms
(sqrt (* (- (* (hypot re im) (hypot re im)) (* re re)) 2.0))
259.0ms
(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) (- (* (sqrt re) (sqrt re))))

prune740.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 10.4b

localize45.0ms

Local error

Found 4 expressions with local error:

12.9b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
0.1b
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0b
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)
0.0b
(sqrt (hypot re im))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt pow1
7×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u sqrt-prod insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1 associate-*r* associate-*l*
2×pow1/2 pow-prod-down
1×rem-sqrt-square prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 62
Calls
4 calls:
Slowest
10.0ms
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)
7.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
2.0ms
(sqrt (hypot re im))
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series830.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
290.0ms
(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
214.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
194.0ms
(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)
132.0ms
(sqrt (hypot re im))

simplify4.1s

Counts
75 → 74
Calls
75 calls:
Slowest
793.0ms
(* (* (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0) (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)) (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
534.0ms
(* (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
377.0ms
(* (* (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (* (* 2.0 2.0) 2.0))
293.0ms
(exp (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
282.0ms
(* (* (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)) (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))) (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.3b

localize59.0ms

Local error

Found 4 expressions with local error:

12.9b
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))
0.5b
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.1b
(sqrt (sqrt (hypot re im)))
0.1b
(sqrt (sqrt (hypot re im)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
86×sqrt-prod
54×add-sqr-sqrt
40×sqrt-pow1
31×pow1
20×*-un-lft-identity pow1/2 add-cube-cbrt
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×expm1-log1p-u rem-sqrt-square insert-posit16 log1p-expm1-u add-log-exp
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 133
Calls
4 calls:
Slowest
13.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
2.0ms
(sqrt (sqrt (hypot re im)))
2.0ms
(sqrt (sqrt (hypot re im)))
0.0ms
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))

series620.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(sqrt (sqrt (hypot re im)))
167.0ms
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))
152.0ms
(sqrt (sqrt (hypot re im)))
102.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))

simplify3.4s

Counts
172 → 145
Calls
172 calls:
Slowest
238.0ms
(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
228.0ms
(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
175.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))))
150.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))))
144.0ms
(* (* (fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re)) (fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re))) (fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (- re)))

prune1.9s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.3b

localize46.0ms

Local error

Found 4 expressions with local error:

12.9b
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (- re))
0.5b
(cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
0.5b
(* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))))
0.3b
(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt sqrt-prod
18×pow1 associate-*l*
13×*-un-lft-identity add-cube-cbrt
12×sqrt-pow1
10×associate-*r*
9×unswap-sqr
8×pow1/2 add-exp-log
7×add-cbrt-cube
6×pow-prod-up
4×expm1-log1p-u cube-unmult pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-prod pow-plus prod-exp *-commutative rem-cbrt-cube cbrt-unprod
1×pow1/3 sqrt-unprod fma-udef
Counts
4 → 103
Calls
4 calls:
Slowest
21.0ms
(* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))))
20.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
6.0ms
(cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
0.0ms
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (- re))

series567.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
159.0ms
(fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (- re))
121.0ms
(cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
119.0ms
(* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))))

simplify3.2s

Counts
118 → 115
Calls
118 calls:
Slowest
304.0ms
(* (* (fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (- re)) (fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (- re))) (fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (- re)))
231.0ms
(+ (pow im 3/4) (* 3/8 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/4))))
216.0ms
(exp (fma (sqrt (hypot re im)) (* (sqrt (sqrt (hypot re im))) (cbrt (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (- re)))
216.0ms
(+ (* 1/8 (* (pow re 2) (pow (/ 1 (pow im 7)) 1/4))) (pow im 1/4))
205.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))

prune1.6s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 10.3b

regimes200.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch2.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.5s6034×body80valid
502.0ms656×body2560valid
305.0ms473×body1280valid
283.0ms324×body5120valid
239.0ms299×body640valid
53.0ms145×body320valid
17.0ms69×body160valid