Details

Time bar (total: 14.9s)

sample154.0ms

Algorithm
intervals
Results
52.0ms278×body80nan
26.0ms145×body160valid
24.0ms534×pre80true
12.0ms44×body320valid
6.0ms67×body80valid

simplify143.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01217
12117
24116
37516
48816
59616
done9616

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 3.0 a) c))
0.3b
(* (* 3.0 a) c)
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
39.2b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×add-log-exp
9×pow1
7×add-sqr-sqrt add-cube-cbrt
6×distribute-lft-out
5×times-frac associate-/l*
4×prod-exp cbrt-unprod
3×distribute-rgt-neg-in associate-*r* pow-prod-down
2×cbrt-undiv neg-sub0 associate-+l- flip3-+ div-exp sum-log flip-+ associate-/l/
1×+-commutative sub-neg flip3-- frac-2neg diff-log div-sub associate-*l* neg-log clear-num associate-/r* *-commutative flip-- div-inv
Counts
4 → 73
Calls
4 calls:
17.0ms
(- (* b b) (* (* 3.0 a) c))
40.0ms
(* (* 3.0 a) c)
115.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
46.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series412.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (* b b) (* (* 3.0 a) c))
35.0ms
(* (* 3.0 a) c)
180.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
131.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.5s

Counts
85 → 85
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01541437
14101361
215471139
done50001125

prune328.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.3b
(* (* 3.0 a) c)
0.3b
(* 3.0 (* a c))
0.4b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite318.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt *-un-lft-identity
40×add-cube-cbrt
30×associate-/l*
28×add-exp-log add-cbrt-cube
20×distribute-lft-out-- difference-of-squares
14×pow1
10×distribute-rgt-neg-in sqrt-prod
8×prod-exp associate-/r* cbrt-unprod
7×cbrt-undiv div-exp
6×pow-prod-down associate-/r/
4×associate-*r* associate-*l* div-inv add-log-exp
3×flip3-- flip-- associate-/l/
2×frac-2neg clear-num *-commutative
1×flip3-+ flip-+
Counts
4 → 157
Calls
4 calls:
98.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
36.0ms
(* (* 3.0 a) c)
28.0ms
(* 3.0 (* a c))
141.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series546.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.0ms
(* (* 3.0 a) c)
33.0ms
(* 3.0 (* a c))
257.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify2.3s

Counts
169 → 169
Iterations

Useful iterations: 2 (729.0ms)

IterNodesCost
02434718
16034240
225923862
done50013862

prune621.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c)))
0.3b
(* (* 3.0 a) c)
0.3b
(* (* 3.0 a) c)
0.4b
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))) (* 3.0 a))

rewrite320.0ms

Algorithm
rewrite-expression-head
Rules
207×times-frac
157×add-exp-log
102×add-sqr-sqrt *-un-lft-identity
77×div-exp
73×add-cbrt-cube
62×add-cube-cbrt
46×prod-exp
41×associate-/l*
31×cbrt-undiv
20×cbrt-unprod distribute-lft-out-- difference-of-squares
15×pow1
14×div-inv
12×rec-exp 1-exp associate-/r*
10×distribute-rgt-neg-in sqrt-prod
6×associate-*r* pow-prod-down
4×add-log-exp
3×associate-/r/
2×frac-2neg associate-*l* clear-num *-commutative
1×pow-flip associate-/l/ inv-pow
Counts
4 → 236
Calls
4 calls:
90.0ms
(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c)))
20.0ms
(* (* 3.0 a) c)
21.0ms
(* (* 3.0 a) c)
163.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))) (* 3.0 a))

series522.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c)))
25.0ms
(* (* 3.0 a) c)
44.0ms
(* (* 3.0 a) c)
204.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (* 3.0 a) c))) (* 3.0 a))

simplify1.9s

Counts
248 → 248
Iterations

Useful iterations: 2 (818.0ms)

IterNodesCost
03277129
18186638
227755311
done50005311

prune540.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
0.3b
(* (* 3.0 a) c)
0.4b
(* (* 3.0 a) (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)))
0.4b
(/ (* (* 3.0 a) (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))) (* 3.0 a))

rewrite351.0ms

Algorithm
rewrite-expression-head
Rules
298×times-frac
218×add-sqr-sqrt *-un-lft-identity
202×add-exp-log
134×add-cube-cbrt
100×add-cbrt-cube
83×associate-*r*
81×prod-exp
79×div-exp
42×distribute-lft-out-- difference-of-squares
37×cbrt-unprod
35×cbrt-undiv
26×associate-/r*
21×distribute-rgt-neg-in sqrt-prod
15×pow1
14×rec-exp 1-exp
10×div-inv
6×pow-prod-down
4×associate-/l* add-log-exp
2×frac-2neg associate-*r/ associate-*l* clear-num associate-/r/ un-div-inv *-commutative associate-/l/
1×pow-flip inv-pow
Counts
4 → 314
Calls
4 calls:
76.0ms
(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
20.0ms
(* (* 3.0 a) c)
126.0ms
(* (* 3.0 a) (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)))
91.0ms
(/ (* (* 3.0 a) (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))) (* 3.0 a))

series745.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
37.0ms
(* (* 3.0 a) c)
286.0ms
(* (* 3.0 a) (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)))
244.0ms
(/ (* (* 3.0 a) (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c))) (* 3.0 a))

simplify3.1s

Counts
326 → 326
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
03859117
110657998
237756243
done50016243

prune760.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes5.0ms