Details

sample73.0ms

Algorithm

intervals

Results

20.0ms	236×	body	80	nan
19.0ms	256×	body	80	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	50	17
1	106	17
2	374	17
3	1652	17
4	5001	17

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 3.0b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.3b	(/ 2.0 (* t 3.0))
1.6b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.1b	(/ (* z (sqrt (+ t a))) t)

rewrite786.0ms

Algorithm

rewrite-expression-head

Rules

5600×	`frac-sub`
2442×	`associate-/l*`
2163×	`associate-/r*`
2068×	`add-sqr-sqrt`
1900×	`frac-times`
1495×	`*-un-lft-identity`
1468×	`flip3-+` `flip-+`
1309×	`associate-r`
1246×	`add-cube-cbrt`
1186×	`associate-*r/`
1051×	`flip3--` `flip--`
827×	`associate-l`
607×	`sqrt-prod`
404×	`unswap-sqr`
275×	`*-commutative`
268×	`frac-2neg` `clear-num`
236×	`sqrt-div`
234×	`associate-/l/`
121×	`distribute-lft-out`
93×	`times-frac`
50×	`associate-*l/`
16×	`add-exp-log` `add-cbrt-cube`
8×	`associate--r+` `difference-of-squares`
6×	`pow1` `add-log-exp`
4×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate--l+` `distribute-lft-out--`
3×	`sub-neg` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `div-inv`
1×	`diff-log` `pow-prod-down`

Counts

4 → 3108

Calls

4 calls:

7.0ms	(* z (sqrt (+ t a)))
7.0ms	(/ 2.0 (* t 3.0))
229.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
12.0ms	(/ (* z (sqrt (+ t a))) t)

series382.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* z (sqrt (+ t a)))
17.0ms	(/ 2.0 (* t 3.0))
201.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
94.0ms	(/ (* z (sqrt (+ t a))) t)

simplify1.6s

Algorithm

egg-herbie

Counts

3120 → 3120

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	7951	158447

prune19.9s

Filtered

3120 candidates to 2260 candidates (27.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	3117	3	3120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	3118	3	3121

Merged error: 0.0b

Counts

3121 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
1.0b	(/ (* (cbrt z) (cbrt z)) (/ t (* (cbrt z) (sqrt (+ t a)))))
1.6b	(- (/ (* (cbrt z) (cbrt z)) (/ t (* (cbrt z) (sqrt (+ t a))))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

rewrite5.2s

Algorithm

rewrite-expression-head

Rules

22848×	`frac-sub`
16426×	`add-sqr-sqrt`
15790×	`associate-/r*`
11646×	`times-frac`
10506×	`*-un-lft-identity`
9633×	`add-cube-cbrt`
7752×	`frac-times`
6001×	`associate-r`
5652×	`flip3-+` `flip-+`
5570×	`associate-l`
5303×	`cbrt-prod`
4998×	`associate-/l*`
4285×	`flip3--` `flip--`
4164×	`associate-*r/`
3275×	`unswap-sqr`
2634×	`sqrt-prod`
1246×	`*-commutative`
1158×	`swap-sqr`
730×	`frac-2neg` `clear-num`
433×	`distribute-lft-out`
316×	`associate-/r/`
288×	`sqrt-div`
204×	`associate-*l/`
145×	`div-inv`
110×	`difference-of-squares`
64×	`add-cbrt-cube`
35×	`cbrt-undiv`
26×	`cbrt-unprod`
25×	`add-exp-log`
10×	`div-exp`
8×	`associate--r+`
6×	`add-log-exp`
5×	`prod-exp`
4×	`pow1` `distribute-rgt-in` `distribute-lft-in` `associate--l+` `distribute-lft-out--`
3×	`sub-neg`
2×	`+-commutative` `pow1/3`
1×	`diff-log`

Counts

4 → 14094

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
76.0ms	(/ (* (cbrt z) (cbrt z)) (/ t (* (cbrt z) (sqrt (+ t a)))))
2.0s	(- (/ (* (cbrt z) (cbrt z)) (/ t (* (cbrt z) (sqrt (+ t a))))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

series710.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt z)
174.0ms	(cbrt z)
113.0ms	(/ (* (cbrt z) (cbrt z)) (/ t (* (cbrt z) (sqrt (+ t a)))))
241.0ms	(- (/ (* (cbrt z) (cbrt z)) (/ t (* (cbrt z) (sqrt (+ t a))))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

simplify8.7s

Algorithm

egg-herbie

Counts

14106 → 14106

Iterations

Useful iterations: 0 (696.0ms)

Iter	Nodes	Cost
0	30466	820134

prune1.7m

Filtered

14106 candidates to 9785 candidates (30.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	14104	2	14106
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	14106	3	14109

Merged error: 0.0b

Counts

14109 → 3

localize43.0ms

Local error

Found 4 expressions with local error:

4.4b	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
5.6b	(* (/ (* (cbrt z) (cbrt z)) (/ (* (cbrt t) (cbrt t)) 1)) (* (- a (/ 5.0 6.0)) (* t 3.0)))
7.4b	(* (/ (cbrt t) (* (cbrt z) (sqrt (+ t a)))) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
14.5b	(/ (- (* (/ (* (cbrt z) (cbrt z)) (/ (* (cbrt t) (cbrt t)) 1)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (/ (cbrt t) (* (cbrt z) (sqrt (+ t a)))) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* (/ (cbrt t) (* (cbrt z) (sqrt (+ t a)))) (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite7.8m

Algorithm

rewrite-expression-head

Calls

4 calls:

63.0ms	(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
902.0ms	(* (/ (* (cbrt z) (cbrt z)) (/ (* (cbrt t) (cbrt t)) 1)) (* (- a (/ 5.0 6.0)) (* t 3.0)))
243.0ms	(* (/ (cbrt t) (* (cbrt z) (sqrt (+ t a)))) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
1.9m	(/ (- (* (/ (* (cbrt z) (cbrt z)) (/ (* (cbrt t) (cbrt t)) 1)) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* (/ (cbrt t) (* (cbrt z) (sqrt (+ t a)))) (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* (/ (cbrt t) (* (cbrt z) (sqrt (+ t a)))) (* (- a (/ 5.0 6.0)) (* t 3.0))))