Details

sample466.0ms

Algorithm

intervals

Results

229.0ms	1413×	body	80	nan
59.0ms	465×	body	80	valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	17	18
1	33	17
2	73	17
3	189	16
4	514	16
5	1747	16
done	5000	16

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (log z))
0.3b	(* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))
1.2b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.2b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite797.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
24×	`exp-sum`
19×	`associate-r`
18×	`prod-diff`
13×	`add-cbrt-cube`
11×	`add-exp-log`
10×	`add-log-exp`
9×	`pow1`
6×	`log-prod` `associate-l`
5×	`exp-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `exp-diff` `prod-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate--l+` `-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `sum-log` `log-pow` `div-inv` `associate-/l/` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 114

Calls

4 calls:

9.0ms	(* y (log z))
390.0ms	(* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))
121.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
273.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series735.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* y (log z))
229.0ms	(* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b)))
189.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
263.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify1.3s

Counts

126 → 126

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	239	2543
1	502	2261
2	1305	1821
done	5000	1666

prune717.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ 0 (log z)) y)
0.3b	(* x (exp (- (+ (* (+ 0 (log z)) y) (* (- t 1.0) (log a))) b)))
1.2b	(exp (- (+ (* (+ 0 (log z)) y) (* (- t 1.0) (log a))) b))
1.2b	(/ (* x (exp (- (+ (* (+ 0 (log z)) y) (* (- t 1.0) (log a))) b))) y)

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
24×	`exp-sum`
23×	`add-cube-cbrt`
18×	`associate-r` `prod-diff`
13×	`add-cbrt-cube`
11×	`add-exp-log`
10×	`add-log-exp`
9×	`pow1`
8×	`associate-l`
5×	`exp-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac` `exp-diff` `prod-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `associate--l+` `*-commutative` `distribute-lft-out` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `clear-num` `sum-log` `log-pow` `flip-+` `div-inv` `associate-/l/` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 111

Calls

4 calls:

27.0ms	(* (+ 0 (log z)) y)
656.0ms	(* x (exp (- (+ (* (+ 0 (log z)) y) (* (- t 1.0) (log a))) b)))
233.0ms	(exp (- (+ (* (+ 0 (log z)) y) (* (- t 1.0) (log a))) b))
577.0ms	(/ (* x (exp (- (+ (* (+ 0 (log z)) y) (* (- t 1.0) (log a))) b))) y)

series894.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (+ 0 (log z)) y)
243.0ms	(* x (exp (- (+ (* (+ 0 (log z)) y) (* (- t 1.0) (log a))) b)))
228.0ms	(exp (- (+ (* (+ 0 (log z)) y) (* (- t 1.0) (log a))) b))
308.0ms	(/ (* x (exp (- (+ (* (+ 0 (log z)) y) (* (- t 1.0) (log a))) b))) y)

simplify1.6s

Counts

123 → 123

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	234	2789
1	523	2220
2	1483	1788
done	5000	1631

prune597.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma y (- (log z)) (fma (- (log a)) t b))
0.1b	(fma (- (log a)) t b)
1.2b	(/ (/ (/ x (pow a 1.0)) (exp (fma y (- (log z)) (fma (- (log a)) t b)))) y)
6.2b	(/ (/ x (pow a 1.0)) (exp (fma y (- (log z)) (fma (- (log a)) t b))))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

1253×	`times-frac`
533×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
189×	`unpow-prod-down`
129×	`associate-/l*`
128×	`fma-udef`
126×	`exp-sum`
63×	`sqr-pow`
27×	`div-inv`
22×	`add-exp-log`
19×	`div-exp`
18×	`add-cbrt-cube`
9×	`cbrt-undiv`
7×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `associate-/l/`

Counts

4 → 608

Calls

4 calls:

1.0ms	(fma y (- (log z)) (fma (- (log a)) t b))
1.0ms	(fma (- (log a)) t b)
91.0ms	(/ (/ (/ x (pow a 1.0)) (exp (fma y (- (log z)) (fma (- (log a)) t b)))) y)
21.0ms	(/ (/ x (pow a 1.0)) (exp (fma y (- (log z)) (fma (- (log a)) t b))))

series1.3s

Counts

4 → 12

Calls

4 calls:

142.0ms	(fma y (- (log z)) (fma (- (log a)) t b))
132.0ms	(fma (- (log a)) t b)
502.0ms	(/ (/ (/ x (pow a 1.0)) (exp (fma y (- (log z)) (fma (- (log a)) t b)))) y)
556.0ms	(/ (/ x (pow a 1.0)) (exp (fma y (- (log z)) (fma (- (log a)) t b))))

simplify1.5s

Counts

620 → 620

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	1070	22444
1	2375	21673
done	5001	20405

prune5.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log a) t)
0.2b	(/ 1 (pow a (/ 1.0 2)))
0.4b	(/ (/ (/ 1 (pow a (/ 1.0 2))) 1) (/ y (/ (/ x (exp (- b (fma (log z) y (* (log a) t))))) (pow a (/ 1.0 2)))))
0.8b	(/ y (/ (/ x (exp (- b (fma (log z) y (* (log a) t))))) (pow a (/ 1.0 2))))

rewrite31.0s

Algorithm

rewrite-expression-head

Rules

450958×	`times-frac`
180086×	`add-sqr-sqrt`
180084×	`add-cube-cbrt` `*-un-lft-identity`
61551×	`unpow-prod-down`
56364×	`exp-sum`
46116×	`prod-diff`
20517×	`sqr-pow`
6055×	`div-inv`
5124×	`sub-neg`
1790×	`associate-/r/`
1708×	`exp-diff`
1344×	`associate-/r*`
782×	`div-exp`
680×	`add-exp-log`
131×	`1-exp`
95×	`pow-to-exp` `pow-exp`
85×	`associate-/l*`
71×	`add-cbrt-cube`
51×	`rec-exp`
49×	`cbrt-undiv`
7×	`pow1`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num`
1×	`pow-flip` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `associate-/l/` `inv-pow` `unswap-sqr`

Counts

4 → 82027

Calls

4 calls:

8.0ms	(* (log a) t)
11.0ms	(/ 1 (pow a (/ 1.0 2)))
2.9s	(/ (/ (/ 1 (pow a (/ 1.0 2))) 1) (/ y (/ (/ x (exp (- b (fma (log z) y (* (log a) t))))) (pow a (/ 1.0 2)))))
152.0ms	(/ y (/ (/ x (exp (- b (fma (log z) y (* (log a) t))))) (pow a (/ 1.0 2))))

series1.7s

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (log a) t)
483.0ms	(/ 1 (pow a (/ 1.0 2)))
608.0ms	(/ (/ (/ 1 (pow a (/ 1.0 2))) 1) (/ y (/ (/ x (exp (- b (fma (log z) y (* (log a) t))))) (pow a (/ 1.0 2)))))
501.0ms	(/ y (/ (/ x (exp (- b (fma (log z) y (* (log a) t))))) (pow a (/ 1.0 2))))

simplify1.2m

Counts

82039 → 82039

Iterations

Useful iterations: 0 (20.0s)

Iter	Nodes	Cost
0	104295	8023025
done	104295	8023025

Details

sample466.0ms

simplify2.6s

prune11.0ms

localize21.0ms

rewrite797.0ms

series735.0ms

simplify1.3s

prune717.0ms

localize45.0ms

rewrite1.5s

series894.0ms

simplify1.6s

prune597.0ms

localize37.0ms

rewrite194.0ms

series1.3s

simplify1.5s

prune5.3s

localize62.0ms

rewrite31.0s

series1.7s

simplify1.2m

prune7.9m