Details

Time bar (total: 10.0m)

sample94.0ms

Algorithm
intervals
Results
44.0ms860×body80nan
13.0ms256×body80valid

simplify66.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03810
112210
250910
3223710
4500110

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.2b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3.0 (/ x (* y 27.0)))
1.0b
(* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
3.6b
(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
4.2b
(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

rewrite392.0ms

Algorithm
rewrite-expression-head
Rules
2284×times-frac
1696×add-sqr-sqrt
1653×associate-*r*
1274×associate-*l*
991×*-un-lft-identity
988×add-cube-cbrt
340×unswap-sqr
217×*-commutative
117×associate-/l*
95×associate-*l/
92×add-exp-log add-cbrt-cube
63×associate-/r*
54×associate-*r/
40×associate-/l/
39×prod-exp cbrt-unprod
30×div-inv
27×cbrt-undiv div-exp
12×sqrt-prod
10×pow1
9×clear-num
6×frac-2neg un-div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down
Counts
4 → 1603
Calls
4 calls:
23.0ms
(* 3.0 (/ x (* y 27.0)))
8.0ms
(* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
157.0ms
(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
47.0ms
(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

series176.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* 3.0 (/ x (* y 27.0)))
21.0ms
(* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
104.0ms
(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
30.0ms
(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

simplify209.0ms

Algorithm
egg-herbie
Counts
1615 → 1615
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
0500114907

prune6.2s

Filtered
1615 candidates to 1234 candidates (76.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New161231615
Fresh000
Picked101
Done000
Total161331616

Merged error: 0b

Counts
1616 → 3

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ x (* y 27.0))
0.2b
(* 3.0 (/ x (* y 27.0)))
3.6b
(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
4.2b
(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

rewrite420.0ms

Algorithm
rewrite-expression-head
Rules
2310×times-frac
1714×add-sqr-sqrt
1662×associate-*r*
1273×associate-*l*
1006×*-un-lft-identity
1003×add-cube-cbrt
342×unswap-sqr
220×*-commutative
117×associate-/l*
92×add-exp-log add-cbrt-cube
86×associate-*l/
72×associate-/r*
54×associate-*r/
40×associate-/l/
38×prod-exp cbrt-unprod
30×div-inv
28×cbrt-undiv div-exp
12×sqrt-prod
9×clear-num
8×pow1
6×frac-2neg un-div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down
Counts
4 → 1628
Calls
4 calls:
9.0ms
(/ x (* y 27.0))
21.0ms
(* 3.0 (/ x (* y 27.0)))
164.0ms
(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
48.0ms
(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

series202.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(/ x (* y 27.0))
24.0ms
(* 3.0 (/ x (* y 27.0)))
120.0ms
(* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))
35.0ms
(/ (* 3.0 (/ x (* y 27.0))) (* z 2.0))

simplify233.0ms

Algorithm
egg-herbie
Counts
1640 → 1640
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
0500214694

prune7.4s

Filtered
1640 candidates to 1253 candidates (76.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New163911640
Fresh112
Picked101
Done000
Total164121643

Merged error: 0b

Counts
1643 → 2

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.9b
(/ (/ (cbrt x) y) (* (cbrt z) 2.0))
1.0b
(* (/ (* 3.0 (/ (* (cbrt x) (cbrt x)) 27.0)) (* (cbrt z) (cbrt z))) (/ (/ (cbrt x) y) (* (cbrt z) 2.0)))
3.6b
(* (* (/ (* 3.0 (/ (* (cbrt x) (cbrt x)) 27.0)) (* (cbrt z) (cbrt z))) (/ (/ (cbrt x) y) (* (cbrt z) 2.0))) (sqrt t))

rewrite29.5s

Algorithm
rewrite-expression-head
Rules
67502×add-sqr-sqrt
41400×times-frac
28855×cbrt-prod
23808×associate-/l*
21916×unswap-sqr
21157×associate-*r*
21080×*-un-lft-identity
20860×add-cube-cbrt
18200×associate-*l*
17914×frac-times
9719×associate-/r*
9521×associate-*l/
7984×associate-/l/
7372×swap-sqr
4710×add-cbrt-cube
3670×associate-*r/
3079×cbrt-unprod
2442×*-commutative
2295×cbrt-undiv
1010×clear-num
1004×sqrt-prod
898×frac-2neg
627×add-exp-log
556×div-inv
332×un-div-inv
294×prod-exp
234×div-exp
11×pow1
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
1×pow1/3
Counts
4 → 29936
Calls
4 calls:
1.0ms
(cbrt x)
22.0ms
(/ (/ (cbrt x) y) (* (cbrt z) 2.0))
10.8s
(* (/ (* 3.0 (/ (* (cbrt x) (cbrt x)) 27.0)) (* (cbrt z) (cbrt z))) (/ (/ (cbrt x) y) (* (cbrt z) 2.0)))
12.5s
(* (* (/ (* 3.0 (/ (* (cbrt x) (cbrt x)) 27.0)) (* (cbrt z) (cbrt z))) (/ (/ (cbrt x) y) (* (cbrt z) 2.0))) (sqrt t))

series433.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(cbrt x)
86.0ms
(/ (/ (cbrt x) y) (* (cbrt z) 2.0))
38.0ms
(* (/ (* 3.0 (/ (* (cbrt x) (cbrt x)) 27.0)) (* (cbrt z) (cbrt z))) (/ (/ (cbrt x) y) (* (cbrt z) 2.0)))
117.0ms
(* (* (/ (* 3.0 (/ (* (cbrt x) (cbrt x)) 27.0)) (* (cbrt z) (cbrt z))) (/ (/ (cbrt x) y) (* (cbrt z) 2.0))) (sqrt t))

simplify7.5s

Algorithm
egg-herbie
Counts
29948 → 29948
Iterations

Useful iterations: 0 (573.0ms)

IterNodesCost
023291666271

prune2.9m

Filtered
29948 candidates to 21897 candidates (73.1%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New29948029948
Fresh011
Picked011
Done000
Total29948229950

Merged error: 0b

Counts
29950 → 2

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* y 27.0))
0.6b
(cbrt (* y 27.0))
1.0b
(* (/ 1.0 3.0) (acos (* (* (/ (* 3.0 (/ (* (cbrt x) (cbrt x)) (* (cbrt (* y 27.0)) (cbrt (* y 27.0))))) (* (cbrt (* z 2.0)) (cbrt (* z 2.0)))) (/ (/ (cbrt x) (cbrt (* y 27.0))) (cbrt (* z 2.0)))) (sqrt t))))
3.6b
(* (* (/ (* 3.0 (/ (* (cbrt x) (cbrt x)) (* (cbrt (* y 27.0)) (cbrt (* y 27.0))))) (* (cbrt (* z 2.0)) (cbrt (* z 2.0)))) (/ (/ (cbrt x) (cbrt (* y 27.0))) (cbrt (* z 2.0)))) (sqrt t))

rewrite6.3m

Algorithm
rewrite-expression-head