Details

analyze1.5s (34.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.8%	98%	0.3%	13
2.4%	97.3%	0.3%	14

sample37.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	80	valid
7.0ms	148×	body	80	invalid

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	80	13
1	80	13

prune13.0ms (0.3%)

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: 0.0b

Counts

2 → 2

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y z))
0.0b	(+ (+ x (* y z)) (* t a))
0.0b	(+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))
4.4b	(* (* a z) b)

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-log-exp`
10×	`sum-log`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`+-commutative` `flip3-+` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
2×	`associate-+l+`
1×	`associate-l` `*-commutative`

Counts

4 → 56

Calls

4 calls:

8.0ms	(+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))
7.0ms	(+ (+ x (* y z)) (* t a))
5.0ms	(* (* a z) b)
3.0ms	(+ x (* y z))

series52.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))
14.0ms	(+ (+ x (* y z)) (* t a))
6.0ms	(+ x (* y z))
6.0ms	(* (* a z) b)

simplify21.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5328	695

prune96.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+ t (* z b))
0.0b	(+ x (+ (* y z) (* a (+ t (* z b)))))
0.0b	(+ (* y z) (* a (+ t (* z b))))
3.2b	(* a (+ t (* z b)))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-log-exp`
8×	`add-sqr-sqrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`sum-log`
4×	`flip3-+` `flip-+`
3×	`+-commutative` `associate-+r+` `associate-r` `associate-l`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

6.0ms	(+ x (+ (* y z) (* a (+ t (* z b)))))
5.0ms	(* a (+ t (* z b)))
4.0ms	(+ (* y z) (* a (+ t (* z b))))
3.0ms	(+ t (* z b))

series62.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ x (+ (* y z) (* a (+ t (* z b)))))
17.0ms	(+ (* y z) (* a (+ t (* z b))))
12.0ms	(* a (+ t (* z b)))
6.0ms	(+ t (* z b))

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5132	807

prune109.0ms (2.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	69	7	76

Merged error: 0.0b

Counts

76 → 7

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ t (* z b))) (cbrt (+ t (* z b))))
3.6b	(cbrt (+ t (* z b)))
3.6b	(cbrt (+ t (* z b)))
3.6b	(cbrt (+ t (* z b)))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

9.0ms	(* (cbrt (+ t (* z b))) (cbrt (+ t (* z b))))
3.0ms	(cbrt (+ t (* z b)))
3.0ms	(cbrt (+ t (* z b)))
3.0ms	(cbrt (+ t (* z b)))

series114.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (cbrt (+ t (* z b))) (cbrt (+ t (* z b))))
29.0ms	(cbrt (+ t (* z b)))
27.0ms	(cbrt (+ t (* z b)))
26.0ms	(cbrt (+ t (* z b)))

simplify74.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4873	1177
1	4873	1177

prune149.0ms (3.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	99	7	106

Merged error: 0.0b

Counts

106 → 7

localize32.0ms (0.7%)

Local error

Found 4 expressions with local error:

4.9b	(* z (* z (* b b)))
7.2b	(* a (- (* t t) (* z (* z (* b b)))))
7.6b	(* z (* b b))
22.4b	(/ (* a (- (* t t) (* z (* z (* b b))))) (- t (* z b)))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
20×	`pow1`
13×	`add-sqr-sqrt`
11×	`prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-down`
9×	`associate-l`
5×	`associate-r`
4×	`associate-*r/` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r` `-commutative` `flip--`
2×	`cbrt-undiv` `sub-neg` `div-exp` `associate-/r/` `associate-/l/` `unswap-sqr`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 87

Calls

4 calls:

9.0ms	(/ (* a (- (* t t) (* z (* z (* b b))))) (- t (* z b)))
7.0ms	(* z (* z (* b b)))
6.0ms	(* a (- (* t t) (* z (* z (* b b)))))
5.0ms	(* z (* b b))

series97.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(* a (- (* t t) (* z (* z (* b b)))))
40.0ms	(/ (* a (- (* t t) (* z (* z (* b b))))) (- t (* z b)))
7.0ms	(* z (* z (* b b)))
7.0ms	(* z (* b b))

simplify31.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5002	1037

prune123.0ms (2.8%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	99	7	106

Merged error: 0.0b

Counts

106 → 7

regimes636.0ms (14.4%)

Accuracy

Total 0.6b remaining (96%)

Threshold costs 0.6b (96%)

bsearch87.0ms (2%)

Steps

Iters	Range		Point
9	1.9033279454580884e+262	5.4990596158791114e+271	5.3953239430729174e+271
10	1.6630849969237035e-45	2.084991628164094e-31	3.666435863645927e-45
7	-2.7579038617988204e+18	-46439344256493064.0	-3.5147556571033926e+17

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	41
1	49	41

end0.0ms (0%)

sample967.0ms (22%)

Algorithm

1×

intervals

Results

383.0ms	8000×	body	80	valid
181.0ms	3828×	body	80	invalid

Details

analyze1.5s (34.7%)

sample37.0ms (0.8%)

simplify4.0ms (0.1%)

prune13.0ms (0.3%)

localize11.0ms (0.3%)

rewrite24.0ms (0.6%)

series52.0ms (1.2%)

simplify21.0ms (0.5%)

prune96.0ms (2.2%)

localize10.0ms (0.2%)

rewrite19.0ms (0.4%)

series62.0ms (1.4%)

simplify43.0ms (1%)

prune109.0ms (2.5%)

localize14.0ms (0.3%)

rewrite19.0ms (0.4%)

series114.0ms (2.6%)

simplify74.0ms (1.7%)

prune149.0ms (3.4%)

localize32.0ms (0.7%)

rewrite31.0ms (0.7%)

series97.0ms (2.2%)

simplify31.0ms (0.7%)

prune123.0ms (2.8%)

regimes636.0ms (14.4%)

bsearch87.0ms (2%)

simplify2.0ms (0%)

end0.0ms (0%)

sample967.0ms (22%)

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