Details

Time bar (total: 1.7m)

sample2.1s

Algorithm
intervals
Results
1.7s113×body10240exit
99.0ms260×body80valid
96.0ms55×body1280nan
85.0ms38×body640nan
24.0ms23×body320nan
5.0ms8×body160nan
3.0ms9×body80nan

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 3 (752.0ms)

IterNodesCost
060123
1148123
2611121
3387888
done500188

prune51.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.8b

localize128.0ms

Local error

Found 4 expressions with local error:

6.3b
(- (- 1.0 z) 1.0)
6.3b
(- (- 1.0 z) 1.0)
6.3b
(- (- 1.0 z) 1.0)
6.3b
(- (- 1.0 z) 1.0)

rewrite286.0ms

Algorithm
rewrite-expression-head
Rules
116×*-un-lft-identity
104×add-sqr-sqrt
96×prod-diff
64×add-cube-cbrt
44×associate--l+
28×distribute-lft-out--
24×add-log-exp
20×fma-neg difference-of-squares
12×diff-log
8×sub-neg
4×pow1 add-exp-log associate--l- expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
Counts
4 → 200
Calls
4 calls:
55.0ms
(- (- 1.0 z) 1.0)
88.0ms
(- (- 1.0 z) 1.0)
70.0ms
(- (- 1.0 z) 1.0)
54.0ms
(- (- 1.0 z) 1.0)

series67.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(- (- 1.0 z) 1.0)
12.0ms
(- (- 1.0 z) 1.0)
19.0ms
(- (- 1.0 z) 1.0)
23.0ms
(- (- 1.0 z) 1.0)

simplify2.8s

Counts
212 → 212
Iterations

Useful iterations: done (2.8s)

IterNodesCost
0842848
11692152
23211656
312401132
done5000904

prune3.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.8b

localize132.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))))) (exp (+ 0.5 (+ (- z) 7.0))))
1.0b
(+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z))))
1.0b
(+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z))))))))
1.0b
(sqrt (* PI 2.0))

rewrite1.5m

Algorithm
rewrite-expression-head
Rules
654×*-un-lft-identity
501×distribute-lft-out
370×frac-add
111×add-log-exp
95×times-frac
87×sum-log
86×flip3-+ flip-+
46×associate-/l/
40×add-sqr-sqrt add-cube-cbrt
26×fma-def
21×exp-sum
20×associate-/l*
7×pow1
6×add-cbrt-cube
5×add-exp-log
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×distribute-rgt-neg-in associate-/r/
2×+-commutative sqrt-pow1 div-inv
1×cbrt-undiv neg-sub0 associate-+l- associate-+r- associate-+l+ associate-+r+ frac-2neg pow1/2 exp-diff div-exp pow-prod-down clear-num sqrt-prod
Counts
4 → 318
Calls
4 calls:
1.0m
(/ (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))))) (exp (+ 0.5 (+ (- z) 7.0))))
1.6s
(+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z))))
25.3s
(+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z))))))))
6.0ms
(sqrt (* PI 2.0))

series82.0ms

Calls
1 calls:
0.0ms
(sqrt (* PI 2.0))