Details

Time bar (total: 2.5m)

sample55.0ms

Algorithm
intervals
Results
20.0ms376×body80valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0328
1698
21348
32258
43788
55988
68158
710358
811438
912118
1012118

prune5.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* z t) 16.0)
0.0b
(+ (* x y) (/ (* z t) 16.0))
0.0b
(+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c)
0.0b
(- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
20×add-log-exp
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
6×add-cube-cbrt sum-log
4×pow1 diff-log
3×associate-+l+ flip3-+ times-frac associate-/r* flip-+
2×cbrt-undiv +-commutative sub-neg div-exp associate--l+ frac-sub distribute-lft-out distribute-lft-out--
1×associate-+l- flip3-- frac-2neg prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l* difference-of-squares
Counts
4 → 69
Calls
4 calls:
4.0ms
(/ (* z t) 16.0)
4.0ms
(+ (* x y) (/ (* z t) 16.0))
10.0ms
(+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c)
8.0ms
(- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))

series85.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ (* z t) 16.0)
12.0ms
(+ (* x y) (/ (* z t) 16.0))
43.0ms
(+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c)
27.0ms
(- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))

simplify39.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0376628
11475597
25001590

prune103.0ms

Filtered
81 candidates to 60 candidates (25.9%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New79281
Fresh000
Picked011
Done000
Total79382

Merged error: 0.0b

Counts
82 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))
0.0b
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
0.0b
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
0.2b
(* (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))) (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
48×sqrt-div
42×add-sqr-sqrt
40×sqrt-prod
34×*-un-lft-identity
26×frac-sub
21×pow1
16×frac-times
14×add-cube-cbrt
13×flip3-- flip3-+ flip-- flip-+
12×swap-sqr
10×sqrt-pow1 pow1/2
9×distribute-lft-out-- add-log-exp
8×associate-*r* associate-*l*
7×difference-of-squares
6×add-exp-log add-cbrt-cube
5×pow-prod-up
4×associate-*r/ associate-*l/ unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square diff-log
1×pow2 sub-neg pow-plus sqrt-unprod prod-exp associate--l+ sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 137
Calls
4 calls:
8.0ms
(- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))
7.0ms
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
7.0ms
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
20.0ms
(* (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))) (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))

series366.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))
144.0ms
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
159.0ms
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
38.0ms
(* (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))) (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))

simplify72.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04332676
117912554
250022518

prune236.0ms

Filtered
149 candidates to 91 candidates (38.9%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1481149
Fresh011
Picked011
Done011
Total1484152

Merged error: 0.0b

Counts
152 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (fabs (cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) (sqrt (cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))))
0.2b
(* (fabs (cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
0.6b
(cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
0.6b
(cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
44×sqrt-div
28×cbrt-div associate-*r/
26×frac-sub
24×add-sqr-sqrt
20×*-un-lft-identity
19×associate-*r*
16×frac-times
15×cbrt-prod
14×sqrt-prod
13×flip3-- flip3-+ flip-- flip-+
12×add-cube-cbrt
11×pow1 add-exp-log add-cbrt-cube
4×associate-*l* pow-prod-down associate-*l/ prod-exp cbrt-unprod distribute-lft-out-- add-log-exp difference-of-squares
2×pow1/3 *-commutative unswap-sqr
Counts
4 → 112
Calls
4 calls:
25.0ms
(* (* (fabs (cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) (sqrt (cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))))
13.0ms
(* (fabs (cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
8.0ms
(cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
10.0ms
(cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))

series597.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(* (* (fabs (cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) (sqrt (cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))))
324.0ms
(* (fabs (cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
61.0ms
(cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
65.0ms
(cbrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))

simplify93.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
07473803
130093605
250013584

prune440.0ms

Filtered
124 candidates to 101 candidates (18.5%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1240124
Fresh011
Picked011
Done022
Total1244128

Merged error: 0.0b

Counts
128 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x y) (/ (* z t) 16.0))
0.0b
(- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))
0.1b
(pow (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c) 3)
44.6b
(cbrt (pow (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c) 3))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity
16×cbrt-prod
12×add-sqr-sqrt
11×add-log-exp
10×add-cube-cbrt unpow-prod-down cube-prod
8×distribute-lft-out
5×pow1 add-exp-log add-cbrt-cube distribute-lft-out--
4×cube-div flip3-+ flip-+
3×pow-unpow
2×cube-mult cbrt-div diff-log unpow3 sum-log frac-sub sqr-pow
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow pow1/3 pow-exp associate--l+ flip-- rem-cbrt-cube rem-cube-cbrt difference-of-squares
Counts
4 → 85
Calls
4 calls:
5.0ms
(+ (* x y) (/ (* z t) 16.0))
8.0ms
(- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))
11.0ms
(pow (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c) 3)
11.0ms
(cbrt (pow (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c) 3))

series2.5m

Calls
1 calls:
49.0ms
(cbrt (pow (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c) 3))

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