Details

Time bar (total: 9.4s)

analyze5.2s

Algorithm
search
sampling

Space saved by range analysis: 0.341297%

Space saved by search: 19.027303%

Guaranteed chance to sample good point: 14.753606%

sample60.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
13.0ms146×body80nan

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05017
110617
237417
3165217
4500117

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 4.2b

Counts
2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* z (sqrt (+ t a)))
0.3b
(/ 2.0 (* t 3.0))
2.6b
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.8b
(/ (* z (sqrt (+ t a))) t)

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
20×frac-sub
16×add-exp-log add-cbrt-cube
15×add-sqr-sqrt
13×*-un-lft-identity
11×add-cube-cbrt
9×flip3-- flip--
8×frac-times associate-*r/
7×associate-*r*
6×pow1 times-frac associate--r+ add-log-exp
5×flip3-+ sqrt-prod flip-+
4×cbrt-undiv sqrt-div div-exp associate-/r* associate-/l*
3×distribute-rgt-in sub-neg distribute-lft-in associate-*l* prod-exp cbrt-unprod
2×frac-2neg associate-*l/ associate--l+ clear-num div-inv associate-/l/ unswap-sqr
1×diff-log pow-prod-down *-commutative distribute-lft-out
Counts
4 → 101
Calls
4 calls:
7.0ms
(* z (sqrt (+ t a)))
5.0ms
(/ 2.0 (* t 3.0))
13.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
8.0ms
(/ (* z (sqrt (+ t a))) t)

series87.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* z (sqrt (+ t a)))
2.0ms
(/ 2.0 (* t 3.0))
54.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
17.0ms
(/ (* z (sqrt (+ t a))) t)

simplify38.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010121260
150011212

prune382.0ms

Filtered
88 candidates to 113 candidates (-28.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1094113
Fresh000
Picked101
Done000
Total1104114

Merged error: 0.5b

Counts
114 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt t)
0.6b
(cbrt t)
1.1b
(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
2.6b
(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
60×frac-sub
58×times-frac
47×*-un-lft-identity
46×associate-*r*
39×frac-times
35×add-cube-cbrt
31×cbrt-prod
28×sqrt-prod
27×associate-*r/
25×add-exp-log flip3-- flip--
21×associate-*l/
18×add-cbrt-cube
10×unswap-sqr
9×flip3-+ flip-+
8×prod-exp cbrt-unprod
7×cbrt-undiv div-exp associate-*l*
6×pow1 distribute-lft-out associate--r+ add-log-exp
3×distribute-rgt-in sub-neg distribute-lft-in
2×pow1/3 associate--l+ div-inv
1×diff-log pow-prod-down *-commutative
Counts
4 → 169
Calls
4 calls:
1.0ms
(cbrt t)
1.0ms
(cbrt t)
22.0ms
(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
21.0ms
(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

series130.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(cbrt t)
22.0ms
(cbrt t)
22.0ms
(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
62.0ms
(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
017543649
150023540

prune422.0ms

Filtered
144 candidates to 181 candidates (-25.7%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1810181
Fresh033
Picked011
Done000
Total1814185

Merged error: 0.5b

Counts
185 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2.0 (* t 3.0))
4.0b
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0)))))))
4.1b
(log (exp (/ 2.0 (* t 3.0))))
6.8b
(/ (* z (sqrt (+ t a))) t)

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
8×log-pow frac-sub
7×exp-prod flip3-- flip--
6×associate--r+ add-log-exp
5×pow1
4×cbrt-undiv frac-times associate-*r/ div-exp associate-/r* associate-/l*
3×distribute-rgt-in sub-neg log-prod distribute-lft-in div-inv
2×frac-2neg sqrt-div associate-*l/ prod-exp associate--l+ clear-num cbrt-unprod associate-/l/
1×flip3-+ diff-log rem-log-exp flip-+
Counts
4 → 89
Calls
4 calls:
7.0ms
(/ 2.0 (* t 3.0))
12.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0)))))))
4.0ms
(log (exp (/ 2.0 (* t 3.0))))
7.0ms
(/ (* z (sqrt (+ t a))) t)

series74.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(/ 2.0 (* t 3.0))
52.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (log (exp (/ 2.0 (* t 3.0)))))))
2.0ms
(log (exp (/ 2.0 (* t 3.0))))
18.0ms
(/ (* z (sqrt (+ t a))) t)

simplify87.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07631016
13784927
25001926

prune224.0ms

Filtered
79 candidates to 101 candidates (-27.8%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1001101
Fresh022
Picked011
Done011
Total1005105

Merged error: 0.2b

Counts
105 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

3.3b
(- (* b b) (* c c))
8.0b
(+ (* (* z (sqrt (+ t a))) (+ b c)) (neg (* (* t (- (* b b) (* c c))) (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0)))))))
10.2b
(* t (- (* b b) (* c c)))
22.9b
(/ (+ (* (* z (sqrt (+ t a))) (+ b c)) (neg (* (* t (- (* b b) (* c c))) (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))))))) (* t (+ b c)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
260×associate-*r/
147×flip3-+ flip-+
128×frac-times frac-add distribute-neg-frac
96×sqrt-div
66×associate-/l/
64×associate-*l/
50×flip3-- flip--
11×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
8×add-cube-cbrt *-un-lft-identity
6×pow1
4×distribute-rgt-in distribute-lft-in associate-*r*
3×sub-neg times-frac div-sub associate-*l* associate-/l*
2×cbrt-undiv neg-sub0 associate-+r- associate-+l+ associate-+r+ distribute-neg-in div-exp unsub-neg prod-exp sum-log associate-/r/ cbrt-unprod difference-of-squares
1×+-commutative frac-2neg diff-log pow-prod-down neg-log clear-num associate-/r* *-commutative div-inv unswap-sqr
Counts
4 → 213
Calls
4 calls:
4.0ms
(- (* b b) (* c c))
19.0ms
(+ (* (* z (sqrt (+ t a))) (+ b c)) (neg (* (* t (- (* b b) (* c c))) (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0)))))))
7.0ms
(* t (- (* b b) (* c c)))
26.0ms
(/ (+ (* (* z (sqrt (+ t a))) (+ b c)) (neg (* (* t (- (* b b) (* c c))) (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))))))) (* t (+ b c)))

series439.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(- (* b b) (* c c))
179.0ms
(+ (* (* z (sqrt (+ t a))) (+ b c)) (neg (* (* t (- (* b b) (* c c))) (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0)))))))
16.0ms
(* t (- (* b b) (* c c)))
237.0ms
(/ (+ (* (* z (sqrt (+ t a))) (+ b c)) (neg (* (* t (- (* b b) (* c c))) (+ a (- (/ 5.0 6.0) (/ 2.0 (* t 3.0))))))) (* t (+ b c)))

simplify104.0ms

Algorithm
egg-herbie
Counts
225 → 225
Iterations

Useful iterations: 1 (46.0ms)

IterNodesCost
022876919
150016776

prune1.1s

Filtered
201 candidates to 225 candidates (-11.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2241225
Fresh022
Picked101
Done112
Total2264230

Merged error: 0b

Counts
230 → 4

regimes702.0ms

bsearch1.0ms

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