Details

Time bar (total: 9.4m)

sample61.0ms

Algorithm
intervals
Results
46.0ms256×body80valid

simplify19.0ms

Calls
1 calls:
Slowest
19.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize49.0ms

Local error

Found 3 expressions with local error:

30.3b
(sqrt (+ (* re re) (* im im)))
0.6b
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
0.0b
(+ (* re re) (* im im))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
24×times-frac
22×log-pow
21×pow1
17×add-sqr-sqrt
16×add-cube-cbrt
10×distribute-lft-out
8×associate-*l* sqrt-prod
6×sqrt-pow1 pow1/2 associate-/l*
5×add-cbrt-cube add-exp-log add-log-exp
4×associate-/r* sqrt-div swap-sqr
3×flip3-+ flip-+ insert-posit16
2×log-div div-sub
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log frac-2neg div-exp div-inv
Calls
3 calls:
Slowest
82.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
49.0ms
(sqrt (+ (* re re) (* im im)))
39.0ms
(+ (* re re) (* im im))

series347.0ms

Calls
3 calls:
Slowest
221.0ms
(/ (log (sqrt (+ (* re re) (* im im)))) (log 10))
81.0ms
(sqrt (+ (* re re) (* im im)))
46.0ms
(+ (* re re) (* im im))

simplify3.4s

Calls
87 calls:
Slowest
724.0ms
(/ (log (sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))) (log 10))
438.0ms
(/ (* (* (log (sqrt (+ (* re re) (* im im)))) (log (sqrt (+ (* re re) (* im im))))) (log (sqrt (+ (* re re) (* im im))))) (* (* (log 10) (log 10)) (log 10)))
313.0ms
(sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))
300.0ms
(/ (log (sqrt (+ (pow (* re re) 3) (pow (* im im) 3)))) (log 10))
250.0ms
(sqrt (- (* (* re re) (* re re)) (* (* im im) (* im im))))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.3b

localize29.0ms

Local error

Found 4 expressions with local error:

31.4b
(log (+ (* re re) (* im im)))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.3b
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.0b
(+ (* re re) (* im im))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
210×associate-/r*
182×frac-times
170×add-sqr-sqrt sqrt-prod
165×*-un-lft-identity
140×add-cube-cbrt
107×associate-/l*
89×times-frac
78×pow1
72×log-pow
33×associate-*l*
32×associate-*r*
31×clear-num
30×frac-2neg
19×add-exp-log
18×add-cbrt-cube
14×associate-*r/
13×associate-*l/
10×distribute-lft-out
9×unswap-sqr
8×log-prod
6×add-log-exp
5×cbrt-undiv div-exp
4×log-div swap-sqr prod-exp cbrt-unprod insert-posit16
3×flip3-+ un-div-inv flip-+ div-inv
2×div-sub
1×+-commutative sum-log rem-log-exp pow-prod-down *-commutative
Calls
4 calls:
Slowest
59.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
44.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
38.0ms
(+ (* re re) (* im im))
22.0ms
(log (+ (* re re) (* im im)))

series551.0ms

Calls
4 calls:
Slowest
249.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
171.0ms
(* (/ 1/2 (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
82.0ms
(log (+ (* re re) (* im im)))
48.0ms
(+ (* re re) (* im im))

simplify27.6s

Calls
575 calls:
Slowest
775.0ms
(* (* (* (/ 1/2 (sqrt (log 10))) (/ 1/2 (sqrt (log 10)))) (/ 1/2 (sqrt (log 10)))) (* (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
488.0ms
(/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10))))
357.0ms
(* (/ (* (* 1/2 1/2) 1/2) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))) (* (* (/ (log (+ (* re re) (* im im))) (sqrt (log 10))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
334.0ms
(* (/ (* (* 1/2 1/2) 1/2) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))) (/ (* (* (log (+ (* re re) (* im im))) (log (+ (* re re) (* im im)))) (log (+ (* re re) (* im im)))) (* (* (sqrt (log 10)) (sqrt (log 10))) (sqrt (log 10)))))
328.0ms
(log (+ (pow (* re re) 3) (pow (* im im) 3)))

prune4.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.1b

localize48.0ms

Local error

Found 4 expressions with local error:

31.4b
(log (+ (* re re) (* im im)))
1.0b
(sqrt (sqrt (log 10)))
1.0b
(sqrt (sqrt (log 10)))
1.0b
(* (cbrt 1/2) (cbrt 1/2))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
24×sqrt-prod
18×pow1
17×add-cube-cbrt
16×cbrt-prod
10×associate-*l*
8×log-prod sqrt-pow1 add-cbrt-cube swap-sqr
7×add-exp-log
6×pow1/3 associate-*r*
5×distribute-lft-out
4×rem-sqrt-square pow1/2 cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×log-pow
2×log-div pow-prod-down pow-sqr pow-prod-up
1×pow2 flip3-+ pow-plus rem-log-exp prod-exp *-commutative flip-+
Calls
4 calls:
Slowest
15.0ms
(log (+ (* re re) (* im im)))
8.0ms
(* (cbrt 1/2) (cbrt 1/2))
2.0ms
(sqrt (sqrt (log 10)))
2.0ms
(sqrt (sqrt (log 10)))

series73.0ms

Calls
4 calls:
Slowest
73.0ms
(log (+ (* re re) (* im im)))
0.0ms
(sqrt (sqrt (log 10)))
0.0ms
(* (cbrt 1/2) (cbrt 1/2))
0.0ms
(sqrt (sqrt (log 10)))

simplify1.4s

Calls
86 calls:
Slowest
305.0ms
(log (+ (pow (* re re) 3) (pow (* im im) 3)))
298.0ms
(log (- (* (* re re) (* re re)) (* (* im im) (* im im))))
103.0ms
(* (* (cbrt (cbrt 1/2)) (cbrt (cbrt 1/2))) (* (cbrt (cbrt 1/2)) (cbrt (cbrt 1/2))))
88.0ms
(* (* (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2)) (* (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2)))
57.0ms
(- (* 2 (log (/ -1 re))))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.0b

localize38.0ms

Local error

Found 4 expressions with local error:

31.4b
(log (+ (* re re) (* im im)))
0.5b
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
0.4b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
0.3b
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))

rewrite560.0ms

Algorithm
rewrite-expression-head
Rules
5694×sqrt-div
5486×frac-times
4543×associate-/r*
2903×sqrt-prod
2355×add-sqr-sqrt
2188×associate-/l*
2072×*-un-lft-identity
2045×add-cube-cbrt
929×pow1
918×log-pow
664×clear-num
649×frac-2neg
422×associate-*r/
257×times-frac
208×associate-*l/
141×associate-*r*
124×unswap-sqr
88×associate-*l*
45×un-div-inv
21×add-exp-log
20×add-cbrt-cube
8×log-prod
7×prod-exp cbrt-unprod
6×div-inv
5×distribute-lft-out
4×log-div pow-prod-down insert-posit16 add-log-exp
3×cbrt-undiv div-exp *-commutative
2×flip3-+ div-sub swap-sqr flip-+
1×rem-log-exp
Calls
4 calls:
Slowest
188.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
57.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
55.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
26.0ms
(log (+ (* re re) (* im im)))

series1.4s

Calls
4 calls:
Slowest
660.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10))))
360.0ms
(* (sqrt (/ 1/2 (sqrt (log 10)))) (* (sqrt (/ 1/2 (sqrt (log 10)))) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
296.0ms
(/ (log (+ (* re re) (* im im))) (sqrt (log 10)))
87.0ms
(log (+ (* re re) (* im im)))

simplify8.7m

Calls
6527 calls:
Slowest
767.0ms
(log (+ (pow (* re re) 3) (pow (* im im) 3)))
601.0ms
(* (sqrt (/ 1/2 (sqrt 1))) (* (sqrt (sqrt 1/2)) (/ (log (+ (* re re) (* im im))) (sqrt (log 10)))))
587.0ms
(* (sqrt (/ 1/2 (sqrt (sqrt (log 10))))) (* (sqrt (/ 1/2 (* (cbrt (sqrt (log 10))) (cbrt (sqrt (log 10)))))) (/ (log (+ (* re re) (* im im))) (sqrt (sqrt (log 10))))))
549.0ms
(* (sqrt (sqrt 1/2)) (* (sqrt (/ 1/2 (sqrt (sqrt (log 10))))) (/ (log (+ (* re re) (* im im))) (sqrt (* (cbrt (log 10)) (cbrt (log 10)))))))
533.0ms
(* (sqrt (/ 1/2 1)) (* (sqrt 1) (/ (log (+ (* re re) (* im im))) (sqrt 1))))