Details

Time bar (total: 20.2s)

sample489.0ms

Algorithm
intervals
Results
123.0ms65×body1280valid
109.0ms48×body640valid
84.0ms258×body80valid
14.0ms23×body320valid
4.0ms9×body160valid

simplify1.1s

Counts
1 → 1

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize125.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
17.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
42.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (atan2 x.im x.re) y.im)
51.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
49.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
238.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
68 → 68

prune502.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 21.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×add-exp-log add-cbrt-cube
7×add-log-exp
6×associate-*r*
3×exp-prod sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg rem-sqrt-square flip3-+ exp-diff diff-log flip-+
Counts
4 → 69
Calls
4 calls:
27.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
19.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
123.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
34.0ms
(* (atan2 x.im x.re) y.im)
47.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify2.1s

Counts
81 → 81

prune398.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.6b
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×cbrt-prod
14×add-cube-cbrt *-un-lft-identity
10×pow1
9×sqrt-prod
8×add-exp-log associate-*l* add-cbrt-cube
6×unpow-prod-down cube-prod associate-*r*
4×sqrt-div add-log-exp
2×cube-div cbrt-div flip3-+ pow1/3 pow-prod-down prod-exp log-pow *-commutative cbrt-unprod flip-+ unswap-sqr
1×cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 82
Calls
4 calls:
26.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
25.0ms
(* (atan2 x.im x.re) y.im)
9.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

series280.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(* (log (cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)
70.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
48.0ms
(cbrt (pow (sqrt (+ (* x.re x.re) (* x.im x.im))) 3))

simplify1.2s

Counts
94 → 94

prune505.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.1b

localize44.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (atan2 x.im x.re) y.im)
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.6b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (atan2 x.im x.re) y.im)
58.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
65.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
228.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts
68 → 68

prune561.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.1b

regimes379.0ms

Accuracy

68% (6.9b remaining)

Error of 10.6b against oracle of 3.8b and baseline of 25.2b

bsearch163.0ms

Steps
ItersRangePoint
9
-9.214276440891805e-306
2.072267979179663e-306
5.5875289921881e-311

simplify541.0ms

end0.0ms

sample8.1s

Algorithm
intervals
Results
3.2s2005×body1280valid
1.6s7987×body80valid
1.4s1432×body640valid
989.0ms665×body320valid
108.0ms311×body160valid