Details

Time bar (total: 14.9s)

sample52.0ms

Algorithm
intervals
Results
14.0ms180×body80valid
12.0ms27×body2560valid
6.0ms15×body1280valid
5.0ms9×body5120valid
4.0ms14×body640valid
1.0ms6×body320valid
1.0ms5×body160valid

simplify45.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
45.0ms
(* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re))))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.1b

localize13.0ms

Local error

Found 2 expressions with local error:

1.6b
(+ (hypot re im) re)
0.0b
(hypot re im)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
5×*-un-lft-identity
4×add-log-exp
3×add-sqr-sqrt fma-def add-cube-cbrt
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×+-commutative hypot-udef sum-log flip3-+ flip-+ distribute-lft-out
Counts
2 → 29
Calls
2 calls:
Slowest
5.0ms
(+ (hypot re im) re)
0.0ms
(hypot re im)

series165.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
93.0ms
(+ (hypot re im) re)
72.0ms
(hypot re im)

simplify60.0ms

Counts
10 → 35
Calls
10 calls:
Slowest
17.0ms
(* (exp (hypot re im)) (exp re))
8.0ms
(* (cbrt (hypot re im)) (cbrt (hypot re im)))
7.0ms
(* 2 re)
6.0ms
(* -1 re)
6.0ms
(+ (hypot re im) re)

prune713.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.8b

localize23.0ms

Local error

Found 4 expressions with local error:

1.6b
(+ (hypot re im) re)
1.6b
(+ (hypot re im) re)
1.6b
(+ (hypot re im) re)
0.4b
(cbrt (+ (hypot re im) re))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
10×add-log-exp
9×fma-def
8×add-sqr-sqrt add-cube-cbrt
4×cbrt-prod expm1-log1p-u pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 log1p-expm1-u distribute-lft-out
3×+-commutative sum-log
2×cbrt-div
1×pow1/3
Counts
4 → 71
Calls
4 calls:
Slowest
4.0ms
(+ (hypot re im) re)
4.0ms
(+ (hypot re im) re)
4.0ms
(+ (hypot re im) re)
3.0ms
(cbrt (+ (hypot re im) re))

series465.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
205.0ms
(cbrt (+ (hypot re im) re))
100.0ms
(+ (hypot re im) re)
81.0ms
(+ (hypot re im) re)
79.0ms
(+ (hypot re im) re)

simplify1.3s

Counts
30 → 83
Calls
30 calls:
Slowest
370.0ms
(+ (* 1/3 (* re (pow (/ 1 (pow im 2)) 1/3))) (+ (* 1/18 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/3))) (pow im 1/3)))
257.0ms
(exp (* 1/3 (- (log 2) (log (/ 1 re)))))
235.0ms
(exp (* 1/3 (- (+ (log (/ -1 re)) (log 1/2)) (* 2 (log (/ -1 im))))))
154.0ms
(cbrt (+ (pow (hypot re im) 3) (pow re 3)))
123.0ms
(cbrt (- (* (hypot re im) (hypot re im)) (* re re)))

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.8b

localize22.0ms

Local error

Found 4 expressions with local error:

10.1b
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
0.5b
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0b
(hypot re im)
0.0b
(hypot re im)

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×pow1
18×sqrt-prod
12×*-un-lft-identity add-cube-cbrt
8×sqrt-pow1 pow1/2 swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log add-log-exp
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u unswap-sqr
3×pow-prod-down pow-sqr
2×hypot-udef
1×pow2 +-commutative sum-log rem-square-sqrt fma-def flip3-+ pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod flip-+
Counts
4 → 89
Calls
4 calls:
Slowest
8.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
8.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.0ms
(hypot re im)
0.0ms
(hypot re im)

series258.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
76.0ms
(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
70.0ms
(hypot re im)
56.0ms
(* (sqrt (hypot re im)) (sqrt (hypot re im)))
54.0ms
(hypot re im)

simplify910.0ms

Counts
73 → 101
Calls
73 calls:
Slowest
186.0ms
(* (exp (* (sqrt (hypot re im)) (sqrt (hypot re im)))) (exp re))
169.0ms
(* (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
93.0ms
(* (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))) (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))
15.0ms
(* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))))
15.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 15.7b

localize25.0ms

Local error

Found 4 expressions with local error:

12.5b
(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) re)
0.3b
(* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
0.3b
(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
0.1b
(sqrt (sqrt (hypot re im)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
55×sqrt-pow1
52×pow1
42×sqrt-prod
36×pow-prod-up
33×pow1/2
32×add-sqr-sqrt
18×associate-*l*
14×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×pow-prod-down
7×associate-*r*
6×pow-plus add-log-exp unswap-sqr
4×expm1-log1p-u cube-unmult prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×sqrt-unprod
2×rem-sqrt-square *-commutative
1×+-commutative sum-log fma-def flip3-+ flip-+
Counts
4 → 133
Calls
4 calls:
Slowest
34.0ms
(* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))
24.0ms
(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) re)
21.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
4.0ms
(sqrt (sqrt (hypot re im)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
198.0ms
(* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))
147.0ms
(sqrt (sqrt (hypot re im)))
76.0ms
(+ (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im)))) re)
54.0ms
(* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))

simplify3.3s

Counts
127 → 145
Calls
127 calls:
Slowest
574.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im))))
403.0ms
(* (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (sqrt (hypot re im)))) (* (* (* (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)))))
396.0ms
(* (exp (* (sqrt (sqrt (hypot re im))) (* (sqrt (sqrt (hypot re im))) (sqrt (hypot re im))))) (exp re))
333.0ms
(* (* (* (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)))) (* (* (sqrt (hypot re im)) (sqrt (hypot re im))) (sqrt (hypot re im)))))
201.0ms
(+ (pow im 3/4) (* 3/8 (* (pow re 2) (pow (/ 1 (pow im 5)) 1/4))))

prune1.8s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 15.7b

regimes224.0ms

Accuracy

0% (0.3b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch1.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
921.0ms6029×body80valid
888.0ms665×body2560valid
351.0ms308×body5120valid
320.0ms488×body1280valid
208.0ms288×body640valid
46.0ms131×body320valid
21.0ms91×body160valid