Details

sample194.0ms

Algorithm

intervals

Results

68.0ms	1325×	body	80	nan
22.0ms	390×	body	80	valid
8.0ms	24×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	2×	body	1280	valid
1.0ms	6×	body	160	valid

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	31	10
1	62	10
2	137	10
3	344	10
4	1155	10
5	5001	10
done	5001	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.8b	(log (- 1.0 z))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

72×	`prod-diff`
66×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
56×	`add-cube-cbrt`
53×	`distribute-rgt-in` `distribute-lft-in`
38×	`associate-+r+`
34×	`associate-+l+`
27×	`log-prod`
26×	`pow1`
22×	`associate--l+`
20×	`log-pow`
10×	`associate-*r/`
9×	`add-log-exp`
7×	`add-exp-log`
6×	`sub-neg` `flip3--` `associate-r` `add-cbrt-cube` `flip--`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u` `difference-of-squares`
3×	`exp-prod` `associate-l`
2×	`log-div` `sum-log` `rem-exp-log`
1×	`+-commutative` `fma-def` `flip3-+` `rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 182

Calls

4 calls:

41.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
27.0ms	(* y (- (log z) t))
37.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.0ms	(log (- 1.0 z))

series450.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
73.0ms	(* y (- (log z) t))
188.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
43.0ms	(log (- 1.0 z))

simplify94.0ms

Counts

194 → 194

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	904	1913
1	3501	1501
2	5001	1500
done	5001	1500

prune636.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

168×	`prod-diff`
155×	`*-un-lft-identity`
141×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
108×	`distribute-rgt-in` `distribute-lft-in`
92×	`associate--l+`
74×	`associate-+r+`
46×	`pow1`
38×	`log-pow`
34×	`associate-+l+`
31×	`distribute-lft-out--`
24×	`log-prod`
14×	`difference-of-squares`
13×	`associate-r`
12×	`sub-neg` `associate-*r/`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `associate-l` `flip--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`exp-prod`
2×	`pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `exp-sum` `flip-+`

Counts

4 → 300

Calls

4 calls:

168.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
704.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
28.0ms	(* y (- (log z) t))
253.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series610.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
104.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
69.0ms	(* y (- (log z) t))
253.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify153.0ms

Counts

312 → 312

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	1091	5982
1	4469	4426
2	5001	4420
done	5001	4420

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (cbrt (pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3)))
0.1b	(* y (- (log z) t))
0.2b	(pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3)
26.1b	(cbrt (pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
32×	`add-cube-cbrt`
24×	`cbrt-prod` `prod-diff`
17×	`distribute-rgt-in` `distribute-lft-in`
15×	`exp-prod`
14×	`pow1`
9×	`unpow-prod-down` `cube-prod`
7×	`add-exp-log` `log-pow` `add-cbrt-cube`
6×	`log-prod` `associate-r` `associate--l+`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l` `sqr-pow`
2×	`sub-neg` `associate-*r/` `distribute-lft-out--`
1×	`pow-to-exp` `flip3--` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod` `rem-exp-log` `rem-cube-cbrt` `difference-of-squares` `unswap-sqr`

Counts

4 → 132

Calls

4 calls:

9.0ms	(exp (cbrt (pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3)))
28.0ms	(* y (- (log z) t))
2.0ms	(pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3)
2.0ms	(cbrt (pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3))

series6.6s

Counts

4 → 12

Calls

4 calls:

169.0ms	(exp (cbrt (pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3)))
70.0ms	(* y (- (log z) t))
6.1s	(pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3)
228.0ms	(cbrt (pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3))

simplify69.0ms

Counts

144 → 144

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	498	1985
1	2039	1676
2	5003	1664
done	5003	1664

prune522.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* (- (log z) t) y)))
0.0b	(cbrt (pow (exp (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* (- (log z) t) y))) 3))
0.0b	(pow (exp (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* (- (log z) t) y))) 3)
0.1b	(* (- (log z) t) y)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
14×	`cbrt-prod` `add-cube-cbrt`
8×	`pow1` `unpow-prod-down` `cube-prod`
7×	`add-cbrt-cube`
6×	`add-exp-log` `exp-prod` `associate-l`
5×	`exp-sum` `fma-udef` `add-log-exp`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`pow-unpow` `associate-r`
2×	`cube-mult` `unpow3` `associate-*l/` `distribute-lft-out--` `sqr-pow`
1×	`pow-to-exp` `flip3--` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `log-pow` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod` `rem-exp-log` `rem-cube-cbrt` `difference-of-squares` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

2.0ms	(exp (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* (- (log z) t) y)))
3.0ms	(cbrt (pow (exp (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* (- (log z) t) y))) 3))
5.0ms	(pow (exp (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* (- (log z) t) y))) 3)
31.0ms	(* (- (log z) t) y)

series692.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(exp (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* (- (log z) t) y)))
163.0ms	(cbrt (pow (exp (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* (- (log z) t) y))) 3))
275.0ms	(pow (exp (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* (- (log z) t) y))) 3)
89.0ms	(* (- (log z) t) y)

simplify45.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	324	1508
1	1173	1417
2	5002	1405
done	5002	1405

prune445.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes186.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	16
1	30	16
done	30	16

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.1s	40918×	body	80	nan
730.0ms	12540×	body	80	valid
127.0ms	378×	body	640	valid
79.0ms	394×	body	320	valid
43.0ms	61×	body	1280	valid
35.0ms	280×	body	160	valid