Details

Time bar (total: 13.8s)

sample229.0ms

Algorithm
intervals
Results
95.0ms319×body80nan
43.0ms68×body10240exit
25.0ms256×body80valid

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
079
1139
2229
3459
41159
52689
68349
731979
done50019

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow (sqrt (atan2 b b)) (- b a))
0.0b
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
*-un-lft-identity
add-cube-cbrt
pow1 unpow-prod-down sqrt-prod
pow-unpow
add-exp-log
pow-pow add-cbrt-cube add-log-exp
unpow-prod-up sqrt-pow1 pow1/2
pow-to-exp sub-neg rem-sqrt-square pow-exp sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
3 → 48
Calls
3 calls:
10.0ms
(pow (sqrt (atan2 b b)) (- b a))
10.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms
(sqrt (atan2 b b))

series188.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(pow (sqrt (atan2 b b)) (- b a))
123.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
25.0ms
(sqrt (atan2 b b))

simplify2.6s

Counts
57 → 57
Iterations

Useful iterations: 3 (296.0ms)

IterNodesCost
075614
1147571
2337536
3843527
42738527
done5000527

prune221.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b
(sin (pow (atan2 b b) (* (- b a) 1/2)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
Counts
1 → 7
Calls
1 calls:
17.0ms
(sin (pow (atan2 b b) (* (- b a) 1/2)))

series94.0ms

Counts
1 → 3
Calls
1 calls:
94.0ms
(sin (pow (atan2 b b) (* (- b a) 1/2)))

simplify5.2s

Counts
10 → 10
Iterations

Useful iterations: 4 (348.0ms)

IterNodesCost
031160
165160
2159140
3394119
4710116
51404116
64860116
done5001116

prune36.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (- b a) (log (atan2 b b)))
0.6b
(* (* 1/2 (cos 1)) (* (- b a) (log (atan2 b b))))
1.6b
(log (atan2 b b))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
21×log-prod
19×pow1
18×add-exp-log
17×add-cbrt-cube
16×add-sqr-sqrt
15×distribute-rgt-in distribute-lft-in
14×*-un-lft-identity
12×add-cube-cbrt
pow-prod-down prod-exp cbrt-unprod
associate-*l*
associate-*r*
associate-*l/
add-log-exp
flip3-- associate-*r/ log-pow *-commutative flip--
rem-log-exp distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 77
Calls
3 calls:
24.0ms
(* (- b a) (log (atan2 b b)))
53.0ms
(* (* 1/2 (cos 1)) (* (- b a) (log (atan2 b b))))
1.0ms
(log (atan2 b b))

series342.0ms

Counts
3 → 9
Calls
3 calls:
66.0ms
(* (- b a) (log (atan2 b b)))
209.0ms
(* (* 1/2 (cos 1)) (* (- b a) (log (atan2 b b))))
67.0ms
(log (atan2 b b))

simplify863.0ms

Counts
86 → 86
Iterations

Useful iterations: done (860.0ms)

IterNodesCost
01251384
13361327
213111099
done50001078

prune178.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes1.0ms