Details

sample56.0ms

Algorithm

intervals

Results

21.0ms

453×

body

valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	7
1	48	7
2	81	7
3	98	7
4	98	7

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.1b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x y) (* z t))
0.0b	(+ (+ (* x y) (* z t)) (* a b))
0.0b	(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
10×	`sum-log`
3×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`associate-+l+`

Counts

3 → 38

Calls

3 calls:

3.0ms	(+ (* x y) (* z t))
5.0ms	(+ (+ (* x y) (* z t)) (* a b))
8.0ms	(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))

series139.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(+ (* x y) (* z t))
19.0ms	(+ (+ (* x y) (* z t)) (* a b))
110.0ms	(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))

simplify36.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	276	348
1	1151	333
2	5001	333

prune70.0ms

Filtered

37 candidates to 47 candidates (-27.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	4	48

Merged error: 0.0b

Counts

48 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))
0.0b	(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.0b	(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
0.2b	(* (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-log-exp`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `sum-log` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `associate-+l+` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

8.0ms	(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))
6.0ms	(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
6.0ms	(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
17.0ms	(* (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))

series2.8s

Counts

4 → 12

Calls

4 calls:

119.0ms	(+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))
1.3s	(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
1.3s	(sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))
116.0ms	(* (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))) (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))

simplify58.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	353	1507
1	1570	1389
2	5003	1353

prune109.0ms

Filtered

68 candidates to 113 candidates (-66.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	112	5	117

Merged error: 0.0b

Counts

117 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
0.1b	(sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
0.1b	(* (pow (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))) 3) (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))))
0.3b	(pow (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))) 3)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

107×	`sqrt-prod`
74×	`add-sqr-sqrt`
36×	`sqrt-div`
27×	`unpow-prod-down` `cube-prod`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l` `unswap-sqr`
12×	`pow1` `sqrt-pow1`
10×	`add-exp-log`
9×	`flip3-+` `associate-r` `flip-+`
8×	`cube-div`
7×	`add-cbrt-cube`
6×	`pow1/2`
5×	`pow-pow` `sqr-pow`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`cube-mult` `pow-to-exp` `unpow3` `associate-r/` `associate-l/` `pow-exp`
1×	`pow-plus` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 163

Calls

4 calls:

7.0ms	(sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
9.0ms	(sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
24.0ms	(* (pow (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))) 3) (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))))
9.0ms	(pow (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))) 3)

series303.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
50.0ms	(sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i))))
115.0ms	(* (pow (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))) 3) (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))))
87.0ms	(pow (sqrt (sqrt (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))) 3)

simplify82.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	447	2966
1	2022	2662
2	5002	2394

prune148.0ms

Filtered

89 candidates to 175 candidates (-96.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	175	5	180

Merged error: 0.0b

Counts

180 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

2.5b	(+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3))
2.6b	(+ (* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b)))) (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))))
4.0b	(* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b))))
43.2b	(/ (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)) (+ (* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b)))) (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b)))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

42×	`associate-*r/`
32×	`frac-add`
28×	`flip3-+` `flip-+`
25×	`*-un-lft-identity`
18×	`associate-/r/`
17×	`flip3--` `flip--`
16×	`frac-times`
15×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`associate-*l/` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `sum-cubes` `distribute-lft-out` `associate-/l*`
4×	`sub-neg` `associate-+l+`
3×	`associate-r` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`+-commutative` `associate-+r+` `sum-log` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative` `div-inv`

Counts

4 → 125

Calls

4 calls:

13.0ms	(+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3))
18.0ms	(+ (* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b)))) (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))))
10.0ms	(* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b))))
28.0ms	(/ (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)) (+ (* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b)))) (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b)))))

series2.4min

Calls

3 calls:

1.4min

(+ (* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b)))) (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b))))

128.0ms

(* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b))))

1.1s

(/ (+ (pow (+ (+ (* x y) (* z t)) (* a b)) 3) (pow (* c i) 3)) (+ (* (* c i) (- (* c i) (+ (+ (* x y) (* z t)) (* a b)))) (* (+ (+ (* x y) (* z t)) (* a b)) (+ (+ (* x y) (* z t)) (* a b)))))

Details

sample56.0ms

simplify8.0ms

prune5.0ms

localize12.0ms

rewrite17.0ms

series139.0ms

simplify36.0ms

prune70.0ms

localize17.0ms

rewrite40.0ms

series2.8s

simplify58.0ms

prune109.0ms

localize17.0ms

rewrite56.0ms

series303.0ms

simplify82.0ms

prune148.0ms

localize25.0ms

rewrite79.0ms

series2.4min

Profiling