Details

sample219.0ms

Algorithm

intervals

Results

76.0ms	1568×	body	80	nan
30.0ms	511×	body	80	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 3 (25.0ms)

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
1.0b	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.8b	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log` `log-prod` `exp-sum`
10×	`pow1` `add-log-exp`
9×	`prod-diff`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`exp-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `rem-exp-log`
2×	`cbrt-undiv` `exp-diff` `diff-log` `div-exp` `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 → 112

Calls

4 calls:

23.0ms	(* (- t 1.0) (log a))
10.0ms	(* y (log z))
76.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
179.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series404.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (- t 1.0) (log a))
37.0ms	(* y (log z))
125.0ms	(exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
184.0ms	(/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify1.0s

Counts

124 → 124

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	275	2031
1	580	1829
2	1652	1505
done	5001	1399

prune399.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- t 1.0) (log a))
0.3b	(* y (log z))
1.1b	(pow E (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
1.8b	(/ (* x (pow E (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
21×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`unpow-prod-up` `log-prod`
11×	`pow1`
9×	`prod-diff`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in` `prod-exp`
5×	`pow-unpow` `div-exp`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `times-frac` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `pow-to-exp` `e-exp-1` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `distribute-lft-out--` `pow-sub` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `flip3--` `pow-pow` `frac-2neg` `associate-r/` `associate--l+` `clear-num` `flip--` `div-inv` `associate-/l/` `associate-/l` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

25.0ms	(* (- t 1.0) (log a))
8.0ms	(* y (log z))
27.0ms	(pow E (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
32.0ms	(/ (* x (pow E (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

series435.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (- t 1.0) (log a))
37.0ms	(* y (log z))
133.0ms	(pow E (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))
202.0ms	(/ (* x (pow E (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)

simplify1.1s

Counts

132 → 132

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	294	2364
1	659	2072
2	1814	1827
done	5001	1713

prune442.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.5b	(* (cbrt y) (cbrt y))
1.1b	(pow E (- (fma y (log z) (* (- t 1.0) (log a))) b))
5.2b	(* (/ x (* (cbrt y) (cbrt y))) (/ (pow E (- (fma y (log z) (* (- t 1.0) (log a))) b)) (cbrt y)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-sqr-sqrt`
136×	`times-frac`
124×	`associate-r`
112×	`*-un-lft-identity`
110×	`add-cube-cbrt`
84×	`unpow-prod-up`
82×	`cbrt-prod`
63×	`prod-diff`
58×	`add-exp-log`
25×	`unpow-prod-down`
22×	`div-exp`
21×	`prod-exp`
18×	`add-cbrt-cube` `unswap-sqr`
14×	`pow1`
13×	`associate-l`
11×	`sqr-pow`
9×	`cbrt-unprod`
8×	`pow-exp`
7×	`cbrt-undiv` `sub-neg` `pow1/3` `associate--l+` `fma-udef`
6×	`swap-sqr`
5×	`pow-unpow`
4×	`expm1-log1p-u` `pow-to-exp` `e-exp-1` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`pow2` `frac-times` `pow-pow` `pow-plus` `associate-r/` `associate-l/` `distribute-lft-out--` `pow-sub` `difference-of-squares`

Counts

4 → 264

Calls

4 calls:

1.0ms	(cbrt y)
12.0ms	(* (cbrt y) (cbrt y))
8.0ms	(pow E (- (fma y (log z) (* (- t 1.0) (log a))) b))
84.0ms	(* (/ x (* (cbrt y) (cbrt y))) (/ (pow E (- (fma y (log z) (* (- t 1.0) (log a))) b)) (cbrt y)))

series770.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt y)
210.0ms	(* (cbrt y) (cbrt y))
132.0ms	(pow E (- (fma y (log z) (* (- t 1.0) (log a))) b))
235.0ms	(* (/ x (* (cbrt y) (cbrt y))) (/ (pow E (- (fma y (log z) (* (- t 1.0) (log a))) b)) (cbrt y)))

simplify2.3s

Counts

276 → 276

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	504	7764
1	1319	6655
2	4569	5920
done	5000	5909

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.5b	(cbrt y)
0.5b	(* (cbrt y) (cbrt y))
5.2b	(* (/ x (* (cbrt y) (cbrt y))) (/ (/ (pow a (- 1.0)) (exp (fma y (- (log z)) (fma (- (log a)) t b)))) (cbrt y)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

400×	`times-frac`
245×	`add-sqr-sqrt`
202×	`associate-r`
177×	`add-cube-cbrt` `*-un-lft-identity`
126×	`cbrt-prod`
76×	`unpow-prod-down`
60×	`add-exp-log`
42×	`exp-sum` `fma-udef`
31×	`div-exp`
28×	`add-cbrt-cube` `sqr-pow`
22×	`unswap-sqr`
21×	`prod-exp`
15×	`cbrt-undiv`
13×	`pow1` `associate-l` `cbrt-unprod`
8×	`pow1/3` `div-inv`
6×	`swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-prod-down` `pow-exp`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/`

Counts

4 → 327

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
13.0ms	(* (cbrt y) (cbrt y))
116.0ms	(* (/ x (* (cbrt y) (cbrt y))) (/ (/ (pow a (- 1.0)) (exp (fma y (- (log z)) (fma (- (log a)) t b)))) (cbrt y)))

series964.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(cbrt y)
185.0ms	(cbrt y)
199.0ms	(* (cbrt y) (cbrt y))
389.0ms	(* (/ x (* (cbrt y) (cbrt y))) (/ (/ (pow a (- 1.0)) (exp (fma y (- (log z)) (fma (- (log a)) t b)))) (cbrt y)))

simplify915.0ms

Counts

339 → 339

Iterations

Useful iterations: done (904.0ms)

Iter	Nodes	Cost
0	657	9487
1	1951	8369
done	5000	7826

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes426.0ms

Accuracy

27.5% (3.4b remaining)

Error of 3.6b against oracle of 0.3b and baseline of 4.9b

bsearch240.0ms

Steps

Iters	Range		Point
8	1.480310051413233e-94	6.047393629826733e-92	5.576242448142597e-92
1	1.280112060657045e-207	1.3592056375039546e-207	1.2998854548687724e-207
6	1.1427293617286463e-216	6.822520607954579e-216	6.704663585819556e-216

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	121
1	59	121
done	59	121

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.2s	45593×	body	80	nan
919.0ms	15210×	body	80	valid