Details

analyze822.0ms (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

sample111.0ms (1.4%)

Algorithm

1×

intervals

Results

32.0ms	500×	body	80	nan
20.0ms	241×	body	80	invalid
19.0ms	256×	body	80	valid

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5079	16

prune16.0ms (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:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
0.6b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
0.9b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))

rewrite33.0ms (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:

13.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
7.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
7.0ms	(* (- t 1.0) (log a))
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))
9.0ms	(* (- 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

prune220.0ms (2.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	100	6	106
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	101	7	108

Merged error: 0.0b

Counts

108 → 7

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(pow (* (- t 1.0) (log a)) 3)
0.6b	(/ (* x (exp (- (+ (* y (log z)) (cbrt (pow (* (- t 1.0) (log a)) 3))) b))) y)
0.9b	(exp (- (+ (* y (log z)) (cbrt (pow (* (- t 1.0) (log a)) 3))) b))
22.7b	(cbrt (pow (* (- t 1.0) (log a)) 3))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-cbrt-cube`
11×	`add-exp-log` `add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cube-cbrt`
8×	`cbrt-prod`
7×	`pow1`
5×	`exp-prod`
4×	`cube-div` `associate-*l/`
3×	`pow-unpow` `times-frac` `associate-/r*` `rem-exp-log`
2×	`cbrt-undiv` `cube-mult` `unpow-prod-down` `cbrt-div` `flip3--` `pow-pow` `exp-diff` `diff-log` `unpow3` `cube-prod` `div-exp` `exp-sum` `pow-exp` `prod-exp` `flip--` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `frac-2neg` `pow1/3` `associate-r/` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `rem-cbrt-cube` `div-inv` `associate-/l/` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 83

Calls

4 calls:

13.0ms	(/ (* x (exp (- (+ (* y (log z)) (cbrt (pow (* (- t 1.0) (log a)) 3))) b))) y)
9.0ms	(exp (- (+ (* y (log z)) (cbrt (pow (* (- t 1.0) (log a)) 3))) b))
7.0ms	(pow (* (- t 1.0) (log a)) 3)
3.0ms	(cbrt (pow (* (- t 1.0) (log a)) 3))

series206.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (* x (exp (- (+ (* y (log z)) (cbrt (pow (* (- t 1.0) (log a)) 3))) b))) y)
69.0ms	(exp (- (+ (* y (log z)) (cbrt (pow (* (- t 1.0) (log a)) 3))) b))
24.0ms	(pow (* (- t 1.0) (log a)) 3)
12.0ms	(cbrt (pow (* (- t 1.0) (log a)) 3))

simplify42.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5117	1827

prune266.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	4	5
Picked	1	0	1
Done	1	0	1
Total	96	6	102

Merged error: 0.0b

Counts

102 → 6

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(* x (* (/ (pow 1 (+ t y)) (pow 1 1.0)) (/ (pow a (neg 1.0)) (exp (+ b (+ (* t (neg (log a))) (* y (neg (log z)))))))))
0.2b	(* t (neg (log a)))
0.3b	(* y (neg (log z)))
0.6b	(/ (* x (* (/ (pow 1 (+ t y)) (pow 1 1.0)) (/ (pow a (neg 1.0)) (exp (+ b (+ (* t (neg (log a))) (* y (neg (log z))))))))) y)

rewrite82.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

457×	`add-exp-log`
300×	`div-exp`
276×	`prod-exp`
162×	`pow-exp`
98×	`pow-to-exp`
64×	`1-exp`
51×	`add-cbrt-cube`
25×	`associate-r`
23×	`add-sqr-sqrt`
20×	`cbrt-unprod`
19×	`add-cube-cbrt` `*-un-lft-identity`
17×	`pow1`
14×	`cbrt-undiv`
12×	`log-prod` `distribute-neg-in`
9×	`associate-l`
8×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-*r/`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`pow-prod-down`
4×	`log-pow` `add-log-exp`
3×	`times-frac` `associate-/r` `-commutative` `associate-/l/`
2×	`frac-times` `neg-mul-1` `associate-*l/` `distribute-rgt-neg-out` `unswap-sqr`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 255

Calls

4 calls:

30.0ms	(/ (* x (* (/ (pow 1 (+ t y)) (pow 1 1.0)) (/ (pow a (neg 1.0)) (exp (+ b (+ (* t (neg (log a))) (* y (neg (log z))))))))) y)
24.0ms	(* x (* (/ (pow 1 (+ t y)) (pow 1 1.0)) (/ (pow a (neg 1.0)) (exp (+ b (+ (* t (neg (log a))) (* y (neg (log z)))))))))
6.0ms	(* t (neg (log a)))
6.0ms	(* y (neg (log z)))

series310.0ms (4%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (* x (* (/ (pow 1 (+ t y)) (pow 1 1.0)) (/ (pow a (neg 1.0)) (exp (+ b (+ (* t (neg (log a))) (* y (neg (log z))))))))) y)
145.0ms	(* x (* (/ (pow 1 (+ t y)) (pow 1 1.0)) (/ (pow a (neg 1.0)) (exp (+ b (+ (* t (neg (log a))) (* y (neg (log z)))))))))
7.0ms	(* t (neg (log a)))
7.0ms	(* y (neg (log z)))

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5011	3969

prune511.0ms (6.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	266	1	267
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	268	5	273

Merged error: 0.0b

Counts

273 → 5

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(* (pow a 1.0) (/ (exp b) (* (pow z y) (pow a t))))
0.4b	(/ (exp b) (* (pow z y) (pow a t)))
0.5b	(* (pow z y) (pow a t))
0.6b	(/ (/ x (* (pow a 1.0) (/ (exp b) (* (pow z y) (pow a t))))) y)

rewrite51.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

228×	`add-exp-log`
139×	`div-exp`
138×	`prod-exp`
70×	`pow-to-exp` `pow-exp`
48×	`add-sqr-sqrt`
42×	`times-frac`
40×	`add-cbrt-cube`
31×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unpow-prod-down`
15×	`cbrt-undiv`
14×	`associate-r` `associate-l`
12×	`unswap-sqr`
11×	`associate-/l*`
10×	`cbrt-unprod` `sqr-pow`
7×	`div-inv`
5×	`associate-*r/`
4×	`pow1` `associate-/r*` `associate-/r/` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 218

Calls

4 calls:

16.0ms	(/ (/ x (* (pow a 1.0) (/ (exp b) (* (pow z y) (pow a t))))) y)
11.0ms	(* (pow a 1.0) (/ (exp b) (* (pow z y) (pow a t))))
7.0ms	(/ (exp b) (* (pow z y) (pow a t)))
7.0ms	(* (pow z y) (pow a t))

series316.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (/ x (* (pow a 1.0) (/ (exp b) (* (pow z y) (pow a t))))) y)
105.0ms	(* (pow a 1.0) (/ (exp b) (* (pow z y) (pow a t))))
48.0ms	(/ (exp b) (* (pow z y) (pow a t)))
28.0ms	(* (pow z y) (pow a t))

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5069	3648

prune318.0ms (4.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	228	2	230
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	231	4	235

Merged error: 0b

Counts

235 → 4

regimes638.0ms (8.3%)

Accuracy

Total 1.1b remaining (95.2%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	94	31
1	94	31

end0.0ms (0%)

sample3.3s (42.5%)

Algorithm

1×

intervals

Results

1.1s	14374×	body	80	nan
629.0ms	8000×	body	80	valid
545.0ms	7127×	body	80	invalid

Details

analyze822.0ms (10.7%)

sample111.0ms (1.4%)

simplify43.0ms (0.6%)

prune16.0ms (0.2%)

localize17.0ms (0.2%)

rewrite33.0ms (0.4%)

series133.0ms (1.7%)

simplify30.0ms (0.4%)

prune220.0ms (2.9%)

localize24.0ms (0.3%)

rewrite34.0ms (0.4%)

series206.0ms (2.7%)

simplify42.0ms (0.5%)

prune266.0ms (3.5%)

localize28.0ms (0.4%)

rewrite82.0ms (1.1%)

series310.0ms (4%)

simplify79.0ms (1%)

prune511.0ms (6.6%)

localize16.0ms (0.2%)

rewrite51.0ms (0.7%)

series316.0ms (4.1%)

simplify76.0ms (1%)

prune318.0ms (4.1%)

regimes638.0ms (8.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.3s (42.5%)

Profiling