Details

Time bar (total: 14.3s)

sample98.0ms

Algorithm
intervals
Results
10.0ms193×body80valid
6.0ms23×body2560valid
4.0ms11×body5120valid
3.0ms14×body1280valid
1.0ms8×body640valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify32.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize69.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.0b
(+ (* re re) (* im im))
1.0b
(- (sqrt (+ (* re re) (* im im))) re)
30.0b
(sqrt (+ (* re re) (* im im)))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×pow1 add-log-exp
7×*-un-lft-identity
5×add-cube-cbrt sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×sqrt-pow1
2×flip3-- flip3-+ pow1/2 associate-*r/ flip-- flip-+ difference-of-squares
1×+-commutative sub-neg rem-sqrt-square diff-log pow-prod-down sum-log distribute-lft-out--
Counts
4 → 54
Calls
4 calls:
50.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
25.0ms
(+ (* re re) (* im im))
80.0ms
(- (sqrt (+ (* re re) (* im im))) re)
12.0ms
(sqrt (+ (* re re) (* im im)))

series490.0ms

Counts
4 → 12
Calls
4 calls:
274.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
52.0ms
(+ (* re re) (* im im))
65.0ms
(- (sqrt (+ (* re re) (* im im))) re)
99.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts
66 → 66

prune316.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
5.7b
(exp (log (sqrt (+ (* re re) (* im im)))))
14.9b
(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
30.0b
(sqrt (+ (* re re) (* im im)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
10×*-un-lft-identity
8×add-cube-cbrt log-prod exp-sum add-log-exp
7×pow1 sqrt-prod
6×exp-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-+ log-pow flip-+ difference-of-squares
2×log-div sqrt-pow1 pow1/2 exp-diff
1×+-commutative sub-neg rem-sqrt-square flip3-- diff-log sum-log flip-- rem-exp-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
17.0ms
(+ (* re re) (* im im))
16.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
85.0ms
(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
13.0ms
(sqrt (+ (* re re) (* im im)))

series235.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(+ (* re re) (* im im))
48.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
68.0ms
(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
68.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts
76 → 76

prune282.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.6b

localize22.0ms

Local error

Found 4 expressions with local error:

5.1b
(exp (log (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
5.7b
(exp (log (sqrt (+ (* re re) (* im im)))))
14.9b
(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
30.0b
(sqrt (+ (* re re) (* im im)))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
17×log-prod exp-sum
14×*-un-lft-identity
10×add-cube-cbrt exp-prod
8×pow1 sqrt-prod
6×add-log-exp difference-of-squares
4×add-exp-log log-div exp-diff sqrt-div log-pow add-cbrt-cube
2×flip3-- sqrt-pow1 flip3-+ pow1/2 flip-- flip-+ rem-exp-log distribute-lft-out--
1×sub-neg rem-sqrt-square diff-log
Counts
4 → 74
Calls
4 calls:
64.0ms
(exp (log (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
12.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
111.0ms
(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
9.0ms
(sqrt (+ (* re re) (* im im)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(exp (log (- (exp (log (sqrt (+ (* re re) (* im im))))) re)))
70.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
61.0ms
(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
53.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts
86 → 86

prune423.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 19.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ re (sqrt (+ (* re re) (* im im))))
6.4b
(sqrt (* 2.0 (/ (pow im 2) (+ re (sqrt (+ (* re re) (* im im)))))))
22.7b
(/ (pow im 2) (+ re (sqrt (+ (* re re) (* im im)))))
30.0b
(sqrt (+ (* re re) (* im im)))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity
32×times-frac
25×add-sqr-sqrt
24×add-cube-cbrt
15×unpow-prod-down
10×distribute-lft-out
9×add-exp-log
8×pow1 associate-/l*
6×add-cbrt-cube add-log-exp
5×unpow2 sqr-pow
4×associate-/r* sqrt-prod
3×sqrt-pow1 flip3-+ sqrt-div div-exp flip-+
2×pow1/2 associate-/r/
1×cbrt-undiv +-commutative pow-to-exp rem-sqrt-square frac-2neg associate-*r/ pow-prod-down pow-exp clear-num sum-log div-inv
Counts
4 → 99
Calls
4 calls:
23.0ms
(+ re (sqrt (+ (* re re) (* im im))))
47.0ms
(sqrt (* 2.0 (/ (pow im 2) (+ re (sqrt (+ (* re re) (* im im)))))))
67.0ms
(/ (pow im 2) (+ re (sqrt (+ (* re re) (* im im)))))
9.0ms
(sqrt (+ (* re re) (* im im)))

series532.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(+ re (sqrt (+ (* re re) (* im im))))
320.0ms
(sqrt (* 2.0 (/ (pow im 2) (+ re (sqrt (+ (* re re) (* im im)))))))
91.0ms
(/ (pow im 2) (+ re (sqrt (+ (* re re) (* im im)))))
53.0ms
(sqrt (+ (* re re) (* im im)))

simplify800.0ms

Counts
111 → 111

prune477.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.3b

regimes677.0ms

Accuracy

48.6% (16.5b remaining)

Error of 23.2b against oracle of 6.7b and baseline of 38.8b

bsearch278.0ms

Steps
ItersRangePoint
10
9.073975787993055e+153
1.5239534637548497e+164
9.185171752674522e+153
4
1.1567851521465253e-78
1.945256675049522e-78
1.575660648688742e-78
8
-5.326142386021628e-164
-1.4724282309499112e-167
-5.246119333473003e-164
8
-1.051527773372545e+155
-2.3467814709880217e+151
-2.5023742436918673e+151

simplify2.1s

end0.0ms

sample2.3s

Algorithm
intervals
Results
528.0ms147×body320valid
453.0ms5987×body80valid
421.0ms702×body2560valid
253.0ms529×body1280valid
214.0ms287×body5120valid
73.0ms270×body640valid
9.0ms78×body160valid