Details

analyze855.0ms (10.7%)

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
6.2%	90.4%	3.4%	6
6.2%	90.4%	3.4%	7
6.2%	88.8%	5%	8
7.8%	77.9%	14.3%	9
7.8%	56.5%	35.7%	10
7.8%	56.5%	35.7%	11
8.1%	41.5%	50.3%	12
8.3%	41.4%	50.3%	13
8.4%	40.2%	51.4%	14

sample109.0ms (1.4%)

Algorithm

1×

intervals

Results

33.0ms	440×	body	80	nan
21.0ms	256×	body	80	valid
17.0ms	211×	body	80	invalid

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5079	16

prune17.0ms (0.2%)

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: 0.3b

Counts

2 → 2

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.6b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
1.0b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod`
10×	`pow1` `add-log-exp`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `div-exp` `exp-sum` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `associate-r/` `associate--l+` `clear-num` `sum-log` `flip--` `div-inv` `associate-/l/` `associate-/l`

Counts

4 → 94

Calls

4 calls:

11.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
9.0ms	(* (- t 1.0) (log a))
7.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
4.0ms	(* y (log z))

series133.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
45.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
10.0ms	(* (- t 1.0) (log a))
7.0ms	(* y (log z))

simplify30.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5016	1237

prune218.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	102	6	108

Merged error: 0.0b

Counts

108 → 6

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/ y (* (pow z y) (pow a (- t 1.0))))
0.1b	(pow a (- t 1.0))
1.5b	(/ x (* (/ y (* (pow z y) (pow a (- t 1.0)))) (exp b)))
1.9b	(* (/ y (* (pow z y) (pow a (- t 1.0)))) (exp b))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-exp-log`
49×	`prod-exp`
42×	`div-exp`
32×	`add-cbrt-cube`
19×	`pow-to-exp` `pow-exp`
17×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
10×	`cbrt-undiv`
9×	`times-frac` `cbrt-unprod`
8×	`associate-l`
7×	`pow1`
6×	`associate-/l*`
5×	`pow-unpow`
4×	`add-log-exp`
3×	`unpow-prod-down` `associate-r` `associate-/r/` `div-inv` `pow-sub`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r*`
1×	`unpow-prod-up` `sub-neg` `pow-pow` `pow-prod-down` `*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 121

Calls

4 calls:

14.0ms	(/ x (* (/ y (* (pow z y) (pow a (- t 1.0)))) (exp b)))
11.0ms	(* (/ y (* (pow z y) (pow a (- t 1.0)))) (exp b))
7.0ms	(/ y (* (pow z y) (pow a (- t 1.0))))
4.0ms	(pow a (- t 1.0))

series203.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ x (* (/ y (* (pow z y) (pow a (- t 1.0)))) (exp b)))
68.0ms	(* (/ y (* (pow z y) (pow a (- t 1.0)))) (exp b))
47.0ms	(/ y (* (pow z y) (pow a (- t 1.0))))
13.0ms	(pow a (- t 1.0))

simplify53.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4968	1865
1	4968	1865

prune275.0ms (3.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	134	5	139

Merged error: 0.0b

Counts

139 → 5

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(* (exp b) (pow a 1.0))
0.0b	(/ y (* (pow z y) (pow a t)))
0.0b	(* (/ y (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0)))
1.5b	(/ x (* (/ y (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0))))

rewrite62.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

333×	`add-exp-log`
238×	`prod-exp`
135×	`div-exp`
77×	`pow-to-exp` `pow-exp`
61×	`add-cbrt-cube`
24×	`cbrt-unprod`
18×	`add-sqr-sqrt`
17×	`cbrt-undiv`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
9×	`times-frac`
8×	`associate-r`
6×	`pow1` `associate-/l*`
4×	`unpow-prod-down` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `*-commutative` `sqr-pow`
1×	`pow-prod-down` `associate-/r/`

Counts

4 → 192

Calls

4 calls:

27.0ms	(/ x (* (/ y (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0))))
12.0ms	(* (/ y (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0)))
6.0ms	(* (exp b) (pow a 1.0))
6.0ms	(/ y (* (pow z y) (pow a t)))

series343.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ x (* (/ y (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0))))
105.0ms	(* (/ y (* (pow z y) (pow a t))) (* (exp b) (pow a 1.0)))
40.0ms	(/ y (* (pow z y) (pow a t)))
35.0ms	(* (exp b) (pow a 1.0))

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4974	3108
1	4974	3108

prune326.0ms (4.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	203	6	209

Merged error: 0b

Counts

209 → 6

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(* (/ (pow z y) y) (pow a t))
0.0b	(* (pow a 1.0) (exp b))
0.1b	(/ (* (/ (pow z y) y) (pow a t)) (* (pow a 1.0) (exp b)))
1.5b	(* x (/ (* (/ (pow z y) y) (pow a t)) (* (pow a 1.0) (exp b))))

rewrite62.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

380×	`add-exp-log`
242×	`prod-exp`
185×	`div-exp`
90×	`pow-to-exp` `pow-exp`
61×	`add-cbrt-cube`
58×	`add-sqr-sqrt`
35×	`associate-l`
32×	`times-frac`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`cbrt-unprod`
23×	`unpow-prod-down`
17×	`cbrt-undiv`
16×	`unswap-sqr`
15×	`associate-r`
13×	`sqr-pow`
6×	`pow1`
4×	`add-log-exp`
3×	`*-commutative` `div-inv`
2×	`associate-*l/`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `associate-/l/` `associate-/l*`

Counts

4 → 243

Calls

4 calls:

16.0ms	(* x (/ (* (/ (pow z y) y) (pow a t)) (* (pow a 1.0) (exp b))))
12.0ms	(/ (* (/ (pow z y) y) (pow a t)) (* (pow a 1.0) (exp b)))
11.0ms	(* (/ (pow z y) y) (pow a t))
6.0ms	(* (pow a 1.0) (exp b))

series317.0ms (4%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(* x (/ (* (/ (pow z y) y) (pow a t)) (* (pow a 1.0) (exp b))))
118.0ms	(/ (* (/ (pow z y) y) (pow a t)) (* (pow a 1.0) (exp b)))
36.0ms	(* (pow a 1.0) (exp b))
33.0ms	(* (/ (pow z y) y) (pow a t))

simplify86.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5014	3906

prune421.0ms (5.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	255	0	255
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	255	6	261

Merged error: 0b

Counts

261 → 6

regimes983.0ms (12.3%)

Accuracy

Total 2.1b remaining (99.3%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	18
1	39	18

end0.0ms (0%)

sample3.2s (40.1%)

Algorithm

1×

intervals

Results

981.0ms	14361×	body	80	nan
647.0ms	8000×	body	80	valid
564.0ms	7145×	body	80	invalid

Details

analyze855.0ms (10.7%)

sample109.0ms (1.4%)

simplify44.0ms (0.6%)

prune17.0ms (0.2%)

localize17.0ms (0.2%)

rewrite35.0ms (0.4%)

series133.0ms (1.7%)

simplify30.0ms (0.4%)

prune218.0ms (2.7%)

localize15.0ms (0.2%)

rewrite41.0ms (0.5%)

series203.0ms (2.5%)

simplify53.0ms (0.7%)

prune275.0ms (3.5%)

localize30.0ms (0.4%)

rewrite62.0ms (0.8%)

series343.0ms (4.3%)

simplify79.0ms (1%)

prune326.0ms (4.1%)

localize15.0ms (0.2%)

rewrite62.0ms (0.8%)

series317.0ms (4%)

simplify86.0ms (1.1%)

prune421.0ms (5.3%)

regimes983.0ms (12.3%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample3.2s (40.1%)

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