Details

Time bar (total: 2.8m)

sample1.1s

Algorithm
intervals
Results
812.0ms280×body10240exit
189.0ms552×body80nan
59.0ms256×body80valid

simplify467.0ms

Calls
1 calls:
Slowest
467.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize49.0ms

Local error

Found 4 expressions with local error:

30.0b
(sqrt (+ (* re re) (* im im)))
0.6b
(* (log base) (log base))
0.3b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.3b
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
320×times-frac
244×add-sqr-sqrt
211×*-un-lft-identity
208×associate-*l*
196×log-pow
188×pow1
163×add-cube-cbrt
160×associate-*r*
110×swap-sqr
40×*-commutative unswap-sqr
23×sqrt-pow1 pow1/2
20×associate-/r* add-cbrt-cube add-exp-log
16×associate-/l*
12×log-prod
8×sqrt-prod
6×distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod
5×distribute-lft-out
4×cbrt-undiv div-exp insert-posit16 add-log-exp
2×sqrt-div pow-prod-down
1×pow2 rem-sqrt-square clear-num frac-2neg flip3-+ pow-plus pow-sqr pow-prod-up flip-+ div-inv
Calls
4 calls:
Slowest
64.0ms
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
55.0ms
(sqrt (+ (* re re) (* im im)))
19.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
15.0ms
(* (log base) (log base))

series573.0ms

Calls
4 calls:
Slowest
242.0ms
(* (log base) (log base))
148.0ms
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
119.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
63.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.3m

Calls
756 calls:
Slowest
2.4s
(/ (* (log (+ (* re re) (* im im))) (log base)) (* (sqrt (log base)) (sqrt (log base))))
2.4s
(/ (* (log (+ (* re re) (* im im))) (log base)) (* (sqrt (log base)) (sqrt (log base))))
2.3s
(/ (* (log (+ (* re re) (* im im))) (log base)) (* (sqrt (log base)) (sqrt (log base))))
2.1s
(/ (* (log (+ (* re re) (* im im))) (log base)) (* (sqrt (log base)) (sqrt (log base))))
844.0ms
(/ (* (* (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (* (log (sqrt (+ (* re re) (* im im)))) (log base))) (* (* (* (log base) (log base)) (* (log base) (log base))) (* (log base) (log base))))

prune5.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (log (/ -1 re)) (log base))
0.0b
(log (/ -1 re))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity times-frac
23×add-sqr-sqrt add-cube-cbrt
18×log-div
13×pow1 log-prod
12×associate-/l*
11×log-pow
10×associate-/r*
9×div-sub
7×add-exp-log
5×clear-num
4×add-cbrt-cube log-rec
3×frac-2neg
2×div-exp rem-log-exp distribute-frac-neg insert-posit16 div-inv add-log-exp
1×cbrt-undiv
Calls
2 calls:
Slowest
17.0ms
(/ (log (/ -1 re)) (log base))
3.0ms
(log (/ -1 re))

series346.0ms

Calls
2 calls:
Slowest
237.0ms
(log (/ -1 re))
109.0ms
(/ (log (/ -1 re)) (log base))

simplify2.6s

Calls
83 calls:
Slowest
204.0ms
(* -1 (/ (+ (log (/ 1 re)) (log -1)) (log (/ 1 base))))
177.0ms
(log (/ (* (cbrt -1) (cbrt -1)) (* (cbrt re) (cbrt re))))
162.0ms
(/ (* (* (log (/ -1 re)) (log (/ -1 re))) (log (/ -1 re))) (* (* (log base) (log base)) (log base)))
97.0ms
(/ (log (/ -1 re)) (- (log -1) (log (/ -1 base))))
84.0ms
(/ (log (/ -1 (* (cbrt re) (cbrt re)))) (log base))

prune932.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 7.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.6b
(* (log base) (log base))
0.4b
(/ (* (log (- re)) (log base)) (* (log base) (log base)))
0.3b
(* (log (- re)) (log base))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
280×times-frac
227×add-sqr-sqrt
183×*-un-lft-identity
152×pow1 associate-*r* associate-*l*
151×add-cube-cbrt
140×log-pow
96×swap-sqr
38×*-commutative unswap-sqr
20×associate-/r*
19×add-cbrt-cube add-exp-log
14×associate-/l*
12×log-prod
6×distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod
4×cbrt-undiv div-exp
3×insert-posit16 add-log-exp
2×pow-prod-down
1×pow2 clear-num frac-2neg pow-plus pow-sqr pow-prod-up div-inv
Calls
3 calls:
Slowest
26.0ms
(/ (* (log (- re)) (log base)) (* (log base) (log base)))
12.0ms
(* (log base) (log base))
8.0ms
(* (log (- re)) (log base))

series517.0ms

Calls
3 calls:
Slowest
226.0ms
(* (log base) (log base))
150.0ms
(/ (* (log (- re)) (log base)) (* (log base) (log base)))
141.0ms
(* (log (- re)) (log base))

simplify1.2m

Calls
659 calls:
Slowest
2.8s
(/ (* (log (- re)) (log base)) (* (sqrt (log base)) (sqrt (log base))))
2.6s
(/ (* (log (- re)) (log base)) (* (sqrt (log base)) (sqrt (log base))))
2.6s
(/ (* (log (- re)) (log base)) (* (sqrt (log base)) (sqrt (log base))))
2.5s
(/ (* (log (- re)) (log base)) (* (sqrt (log base)) (sqrt (log base))))
2.5s
(/ (* (log (- re)) (log base)) (* (sqrt (log base)) (sqrt (log base))))

prune4.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 7.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (log base) (log (sqrt base)))
0.6b
(* (log base) (log (sqrt base)))
0.4b
(/ (* (log (- re)) (log base)) (+ (* (log base) (log (sqrt base))) (* (log base) (log (sqrt base)))))
0.3b
(* (log (- re)) (log base))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
948×associate-*r*
938×times-frac
824×associate-*l*
809×*-un-lft-identity
746×log-pow
681×add-sqr-sqrt
634×pow1
510×distribute-rgt-out
419×add-cube-cbrt
360×distribute-lft-out
191×*-commutative
131×unswap-sqr
122×sqrt-pow1 pow1/2
67×associate-/r*
45×distribute-lft1-in distribute-rgt1-in
30×log-prod
15×distribute-rgt-in distribute-lft-in add-cbrt-cube add-exp-log
14×associate-/l*
12×sqrt-prod
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×pow-prod-down
2×cbrt-undiv div-exp associate-/r/
1×clear-num frac-2neg flip3-+ flip-+ div-inv
Calls
4 calls:
Slowest
91.0ms
(/ (* (log (- re)) (log base)) (+ (* (log base) (log (sqrt base))) (* (log base) (log (sqrt base)))))
15.0ms
(* (log base) (log (sqrt base)))
15.0ms
(* (log base) (log (sqrt base)))
9.0ms
(* (log (- re)) (log base))

series715.0ms

Calls
4 calls:
Slowest
267.0ms
(/ (* (log (- re)) (log base)) (+ (* (log base) (log (sqrt base))) (* (log base) (log (sqrt base)))))
157.0ms
(* (log (- re)) (log base))
156.0ms
(* (log base) (log (sqrt base)))
134.0ms
(* (log base) (log (sqrt base)))