Details

sample68.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
18.0ms	256×	body	80	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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 (0.0%)

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: 5.0b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))
0.2b	(/ 2.0 (* t 3.0))
3.3b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.3b	(/ (* z (sqrt (+ t a))) t)

rewrite845.0ms

Algorithm

rewrite-expression-head

Rules

5600×	`frac-sub`
2445×	`associate-/l*`
2168×	`associate-/r*`
2071×	`add-sqr-sqrt`
1900×	`frac-times`
1516×	`*-un-lft-identity`
1468×	`flip3-+` `flip-+`
1302×	`associate-r`
1253×	`add-cube-cbrt`
1184×	`associate-*r/`
1051×	`flip3--` `flip--`
828×	`associate-l`
602×	`sqrt-prod`
402×	`unswap-sqr`
274×	`*-commutative`
269×	`frac-2neg` `clear-num`
234×	`sqrt-div` `associate-/l/`
128×	`distribute-lft-out`
108×	`times-frac`
50×	`associate-*l/`
16×	`add-exp-log` `add-cbrt-cube`
8×	`associate--r+` `difference-of-squares`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `distribute-rgt-in` `distribute-lft-in` `associate--l+` `distribute-lft-out--`
3×	`sub-neg` `div-inv`
2×	`+-commutative` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`diff-log`

Counts

4 → 3120

Calls

4 calls:

79.0ms	(/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))
7.0ms	(/ 2.0 (* t 3.0))
210.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
11.0ms	(/ (* z (sqrt (+ t a))) t)

series569.0ms

Counts

4 → 12

Calls

4 calls:

302.0ms	(/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))
15.0ms	(/ 2.0 (* t 3.0))
170.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
82.0ms	(/ (* z (sqrt (+ t a))) t)

simplify1.7s

Algorithm

egg-herbie

Counts

3132 → 3132

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	7992	159209

prune21.4s

Filtered

3132 candidates to 2265 candidates (72.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	3127	5	3132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	3128	5	3133

Merged error: 0.7b

Counts

3133 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt t)
3.3b	(- (* (/ (sqrt (+ t a)) (* (cbrt t) (cbrt t))) (/ z (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

rewrite18.5s

Algorithm

rewrite-expression-head

Rules

116704×	`frac-sub`
106068×	`associate-/r*`
93884×	`frac-times`
61971×	`add-sqr-sqrt`
46165×	`*-un-lft-identity`
43019×	`add-cube-cbrt`
38167×	`cbrt-prod`
33970×	`associate-/l*`
29642×	`flip3-+` `flip-+`
21883×	`flip3--` `flip--`
21190×	`associate-*r/`
18433×	`associate-l`
18426×	`associate-r`
9390×	`clear-num`
9378×	`unswap-sqr`
9274×	`frac-2neg`
9072×	`swap-sqr`
6086×	`sqrt-prod`
5566×	`associate-*l/`
4646×	`*-commutative`
3016×	`sqrt-div` `associate-/l/`
1508×	`distribute-lft-out`
232×	`un-div-inv`
184×	`times-frac`
116×	`difference-of-squares`
8×	`associate--r+` `distribute-lft-out--`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `distribute-rgt-in` `distribute-lft-in` `associate--l+` `add-cbrt-cube`
3×	`sub-neg` `pow1/3`
2×	`+-commutative`
1×	`diff-log`

Counts

4 → 60611

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
1.0ms	(cbrt t)
2.7s	(- (* (/ (sqrt (+ t a)) (* (cbrt t) (cbrt t))) (/ z (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

series747.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt t)
168.0ms	(cbrt t)
175.0ms	(cbrt t)
231.0ms	(- (* (/ (sqrt (+ t a)) (* (cbrt t) (cbrt t))) (/ z (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

simplify41.6s

Algorithm

egg-herbie

Counts

60623 → 60623

Iterations

Useful iterations: 0 (2.3s)

Iter	Nodes	Cost
0	115532	3989184

prune7.5m

Filtered

60623 candidates to 40038 candidates (66.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	60621	2	60623
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	60623	5	60628

Merged error: 0.7b

Counts

60628 → 5

localize37.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (* b b) (* c c))
4.9b	(* (/ (* (cbrt t) (cbrt t)) (sqrt (+ t a))) (* (- (* b b) (* c c)) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.1b	(- (* (* (sqrt 1) (/ z (cbrt t))) (+ b c)) (* (/ (* (cbrt t) (cbrt t)) (sqrt (+ t a))) (* (- (* b b) (* c c)) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))
14.6b	(/ (- (* (* (sqrt 1) (/ z (cbrt t))) (+ b c)) (* (/ (* (cbrt t) (cbrt t)) (sqrt (+ t a))) (* (- (* b b) (* c c)) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))) (* (/ (* (cbrt t) (cbrt t)) (sqrt (+ t a))) (+ b c)))

rewrite1.1m

Algorithm

rewrite-expression-head

Calls

4 calls:

16.0ms	(- (* b b) (* c c))
272.0ms	(* (/ (* (cbrt t) (cbrt t)) (sqrt (+ t a))) (* (- (* b b) (* c c)) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
8.2s	(- (* (* (sqrt 1) (/ z (cbrt t))) (+ b c)) (* (/ (* (cbrt t) (cbrt t)) (sqrt (+ t a))) (* (- (* b b) (* c c)) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))
21.8s	(/ (- (* (* (sqrt 1) (/ z (cbrt t))) (+ b c)) (* (/ (* (cbrt t) (cbrt t)) (sqrt (+ t a))) (* (- (* b b) (* c c)) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))) (* (/ (* (cbrt t) (cbrt t)) (sqrt (+ t a))) (+ b c)))