Details

Time bar (total: 17.3s)

sample46.0ms

Algorithm
intervals
Results
14.0ms256×pre80true
13.0ms256×body80valid

simplify48.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077
1187
2397
3657
done657

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (+ b c) d)
0.1b
(* a (+ (+ b c) d))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
7×add-log-exp
6×add-sqr-sqrt distribute-lft-out
5×associate-*r*
4×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×associate-*l* sum-log
2×flip3-+ associate-*r/ flip-+
1×+-commutative distribute-rgt-in associate-+l+ distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
2 → 39
Calls
2 calls:
60.0ms
(+ (+ b c) d)
151.0ms
(* a (+ (+ b c) d))

series67.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(+ (+ b c) d)
38.0ms
(* a (+ (+ b c) d))

simplify2.6s

Counts
45 → 45
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
066400
1177380
2683346
33966340
done5001340

prune113.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ b c) a)
0.0b
(+ (* (+ b c) a) (* d a))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity
4×pow1 add-exp-log add-cube-cbrt associate-*l* add-cbrt-cube add-log-exp
3×associate-*r*
2×flip3-+ associate-*l/ flip-+
1×+-commutative distribute-rgt-out pow-prod-down prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
2 → 33
Calls
2 calls:
46.0ms
(* (+ b c) a)
21.0ms
(+ (* (+ b c) a) (* d a))

series84.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(* (+ b c) a)
51.0ms
(+ (* (+ b c) a) (* d a))

simplify3.4s

Counts
39 → 39
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
068387
1191329
2768303
33716301
done5000301

prune106.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (sqrt (* (+ b c) a)) (sqrt (* (+ b c) a))) (* d a))
0.1b
(sqrt (* (+ b c) a))
0.1b
(sqrt (* (+ b c) a))
0.5b
(* (sqrt (* (+ b c) a)) (sqrt (* (+ b c) a)))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
59×pow1
32×sqrt-pow1
22×pow-prod-down
18×associate-*l/
16×sqrt-div
12×pow1/2
10×add-sqr-sqrt pow-prod-up
9×flip3-+ flip-+
8×add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod pow-sqr add-cbrt-cube add-log-exp
4×frac-times swap-sqr associate-*r* associate-*l*
2×associate-*r/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod unswap-sqr
Counts
4 → 94
Calls
4 calls:
88.0ms
(+ (* (sqrt (* (+ b c) a)) (sqrt (* (+ b c) a))) (* d a))
12.0ms
(sqrt (* (+ b c) a))
16.0ms
(sqrt (* (+ b c) a))
87.0ms
(* (sqrt (* (+ b c) a)) (sqrt (* (+ b c) a)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(+ (* (sqrt (* (+ b c) a)) (sqrt (* (+ b c) a))) (* d a))
153.0ms
(sqrt (* (+ b c) a))
124.0ms
(sqrt (* (+ b c) a))
41.0ms
(* (sqrt (* (+ b c) a)) (sqrt (* (+ b c) a)))

simplify4.4s

Counts
106 → 106
Iterations

Useful iterations: done (4.4s)

IterNodesCost
01221518
12821002
21004910
34917863
done5001856

prune305.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ b c))
0.0b
(+ (* (sqrt (+ b c)) (* (sqrt (+ b c)) a)) (* d a))
0.2b
(* (sqrt (+ b c)) a)
0.4b
(* (sqrt (+ b c)) (* (sqrt (+ b c)) a))

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity sqrt-div
15×add-sqr-sqrt
14×associate-*l*
13×sqrt-prod
12×pow1
11×add-exp-log add-cbrt-cube
10×add-cube-cbrt associate-*l/
9×flip3-+ flip-+
6×add-log-exp
4×frac-times associate-*r* pow-prod-down prod-exp cbrt-unprod
3×distribute-lft-out
2×associate-*r/ *-commutative unswap-sqr
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 82
Calls
4 calls:
9.0ms
(sqrt (+ b c))
81.0ms
(+ (* (sqrt (+ b c)) (* (sqrt (+ b c)) a)) (* d a))
47.0ms
(* (sqrt (+ b c)) a)
95.0ms
(* (sqrt (+ b c)) (* (sqrt (+ b c)) a))

series330.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(sqrt (+ b c))
111.0ms
(+ (* (sqrt (+ b c)) (* (sqrt (+ b c)) a)) (* d a))
112.0ms
(* (sqrt (+ b c)) a)
62.0ms
(* (sqrt (+ b c)) (* (sqrt (+ b c)) a))

simplify4.3s

Counts
94 → 94
Iterations

Useful iterations: 3 (1.7s)

IterNodesCost
01521320
1400987
21143865
33872842
done5001842

prune342.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes3.0ms