Details

sample78.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
16.0ms	244×	body	80	nan

simplify940.0ms

Counts

1 → 1

Iterations

Useful iterations: 4 (239.0ms)

Iter	Nodes	Cost
0	28	33
1	50	33
2	108	32
3	387	32
4	1604	31
done	5001	31

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.3b	(/ (/ 2.0 t) 3.0)
1.9b	(fma (- (/ (/ 2.0 t) 3.0) (+ a (/ 5.0 6.0))) (- b c) (/ (* z (sqrt (+ t a))) t))
5.2b	(/ (* z (sqrt (+ t a))) t)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
55×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
51×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/l*`
7×	`associate-r`
6×	`pow1` `associate-/r*` `div-inv`
5×	`cbrt-undiv` `div-exp` `sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/l/`
2×	`frac-2neg` `flip3-+` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`pow-prod-down` `*-commutative` `fma-udef` `distribute-lft-out`

Counts

4 → 134

Calls

4 calls:

24.0ms	(* z (sqrt (+ t a)))
11.0ms	(/ (/ 2.0 t) 3.0)
0.0ms	(fma (- (/ (/ 2.0 t) 3.0) (+ a (/ 5.0 6.0))) (- b c) (/ (* z (sqrt (+ t a))) t))
14.0ms	(/ (* z (sqrt (+ t a))) t)

series348.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* z (sqrt (+ t a)))
20.0ms	(/ (/ 2.0 t) 3.0)
185.0ms	(fma (- (/ (/ 2.0 t) 3.0) (+ a (/ 5.0 6.0))) (- b c) (/ (* z (sqrt (+ t a))) t))
81.0ms	(/ (* z (sqrt (+ t a))) t)

simplify1.1s

Counts

146 → 146

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	319	1876
1	740	1756
2	1982	1622
done	5001	1602

prune763.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
1.3b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
1.9b	(fma (- (/ (/ 2.0 t) 3.0) (+ a (/ 5.0 6.0))) (- b c) (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
58×	`times-frac`
47×	`*-un-lft-identity`
46×	`associate-r`
35×	`add-cube-cbrt`
31×	`cbrt-prod`
28×	`sqrt-prod`
25×	`add-exp-log`
18×	`add-cbrt-cube`
10×	`unswap-sqr`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `associate-l`
6×	`pow1` `distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef`

Counts

4 → 125

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
66.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
0.0ms	(fma (- (/ (/ 2.0 t) 3.0) (+ a (/ 5.0 6.0))) (- b c) (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))))

series682.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt t)
179.0ms	(cbrt t)
108.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
223.0ms	(fma (- (/ (/ 2.0 t) 3.0) (+ a (/ 5.0 6.0))) (- b c) (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))))

simplify1.2s

Counts

137 → 137

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	245	2460
1	668	2293
2	2441	1806
done	5001	1678

prune665.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 2.0 t) 3.0)
1.4b	(log (exp (fma (- (/ (/ 2.0 t) 3.0) (+ a (/ 5.0 6.0))) (- b c) (/ (* z (sqrt (+ t a))) t))))
1.9b	(fma (- (/ (/ 2.0 t) 3.0) (+ a (/ 5.0 6.0))) (- b c) (/ (* z (sqrt (+ t a))) t))
5.2b	(/ (* z (sqrt (+ t a))) t)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
50×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
6×	`associate-/r*` `div-inv`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log-prod` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`exp-prod` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `associate-*r/` `clear-num` `fma-udef`
1×	`flip3-+` `rem-log-exp` `exp-sum` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 125

Calls

4 calls:

11.0ms	(/ (/ 2.0 t) 3.0)
3.0ms	(log (exp (fma (- (/ (/ 2.0 t) 3.0) (+ a (/ 5.0 6.0))) (- b c) (/ (* z (sqrt (+ t a))) t))))
0.0ms	(fma (- (/ (/ 2.0 t) 3.0) (+ a (/ 5.0 6.0))) (- b c) (/ (* z (sqrt (+ t a))) t))
14.0ms	(/ (* z (sqrt (+ t a))) t)

series488.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (/ 2.0 t) 3.0)
194.0ms	(log (exp (fma (- (/ (/ 2.0 t) 3.0) (+ a (/ 5.0 6.0))) (- b c) (/ (* z (sqrt (+ t a))) t))))
194.0ms	(fma (- (/ (/ 2.0 t) 3.0) (+ a (/ 5.0 6.0))) (- b c) (/ (* z (sqrt (+ t a))) t))
83.0ms	(/ (* z (sqrt (+ t a))) t)

simplify1.0s

Counts

137 → 137

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	298	2208
1	660	2076
2	1771	1890
done	5000	1878

prune853.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* z (sqrt (+ t a)))
0.2b	(/ 2.0 (* t 3.0))
2.3b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.2b	(/ (* z (sqrt (+ t a))) t)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
63×	`prod-diff`
62×	`associate--r+`
49×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
36×	`times-frac`
31×	`distribute-rgt-in` `distribute-lft-in`
20×	`frac-sub`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-lft-out`
12×	`div-inv`
9×	`flip3--` `flip--`
8×	`frac-times` `associate-*r/`
7×	`fma-neg` `associate-r`
6×	`pow1` `add-log-exp`
5×	`flip3-+` `sqrt-prod` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `sqrt-div` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`sub-neg` `associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `associate-*l/` `associate--l+` `clear-num` `associate-/l/` `unswap-sqr`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 179

Calls

4 calls:

22.0ms	(* z (sqrt (+ t a)))
7.0ms	(/ 2.0 (* t 3.0))
64.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
14.0ms	(/ (* z (sqrt (+ t a))) t)

series357.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* z (sqrt (+ t a)))
23.0ms	(/ 2.0 (* t 3.0))
196.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
76.0ms	(/ (* z (sqrt (+ t a))) t)

simplify585.0ms

Counts

191 → 191

Iterations

Useful iterations: done (578.0ms)

Iter	Nodes	Cost
0	485	5298
1	1361	4885
done	5000	4460

prune897.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes284.0ms

Accuracy

11.7% (1.8b remaining)

Error of 2.0b against oracle of 0.2b and baseline of 2.2b

bsearch501.0ms

Steps

Iters	Range		Point
7	-4.076907512221872e+21	-4.986141658482979e+19	-4.0181072141773345e+21
10	-2.531577485321311e+176	-2.8655997710594172e+163	-4.6777221766144635e+174

simplify11.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	48	115
1	63	79
2	67	79
3	68	79
done	68	79

end0.0ms

sample2.0s

Algorithm

intervals

Results

572.0ms	8000×	body	80	valid
527.0ms	7867×	body	80	nan