Details

sample109.0ms

Algorithm

intervals

Results

29.0ms	60×	body	10240	exit
24.0ms	48×	body	1280	valid
13.0ms	49×	body	640	valid
6.0ms	114×	body	80	valid
5.0ms	26×	body	320	valid
4.0ms	4×	body	2560	valid
3.0ms	78×	body	80	nan
2.0ms	16×	body	160	valid
1.0ms	5×	body	1280	nan
1.0ms	6×	body	640	nan
1.0ms	7×	body	320	nan
0.0ms	1×	body	160	nan

simplify208.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	35	7
2	53	7
3	81	7
4	121	7
5	250	7
6	314	7
7	532	7
8	908	7
9	1397	7
10	1553	7
11	1892	7
12	4682	7
13	5001	7
done	5001	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.9b	(log (+ (- 1.0 y) (* y (exp z))))
2.9b	(+ (- 1.0 y) (* y (exp z)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

10.0ms	(* y (exp z))
51.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
18.0ms	(log (+ (- 1.0 y) (* y (exp z))))
33.0ms	(+ (- 1.0 y) (* y (exp z)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* y (exp z))
172.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
113.0ms	(log (+ (- 1.0 y) (* y (exp z))))
56.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify55.0ms

Counts

114 → 114

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	499	918
1	2002	785
2	5001	761
done	5001	761

prune365.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.4b

localize13.0ms

Local error

Found 3 expressions with local error:

4.8b	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
5.5b	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)
6.4b	(* (pow z 2) y)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log`
9×	`times-frac`
8×	`associate-l`
7×	`add-cbrt-cube`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-r` `prod-exp` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`unpow2` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `div-exp` `pow-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

3 → 68

Calls

3 calls:

0.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
5.0ms	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)
14.0ms	(* (pow z 2) y)

series172.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
94.0ms	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) t)
18.0ms	(* (pow z 2) y)

simplify154.0ms

Counts

77 → 77

Iterations

Useful iterations: 3 (142.0ms)

Iter	Nodes	Cost
0	227	586
1	791	528
2	4529	528
3	5001	524
done	5001	524

prune272.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.3b

localize13.0ms

Local error

Found 3 expressions with local error:

4.8b	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
5.6b	(* (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) (/ 1 t))
6.4b	(* (pow z 2) y)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
17×	`add-exp-log`
16×	`associate-r`
15×	`*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`times-frac` `associate-l`
10×	`add-cbrt-cube`
7×	`prod-exp` `unswap-sqr`
5×	`pow1`
4×	`unpow-prod-down`
3×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`div-exp` `*-commutative` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `1-exp` `associate-*r/` `pow-prod-down` `pow-exp` `un-div-inv` `fma-udef` `div-inv`

Counts

3 → 77

Calls

3 calls:

0.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
14.0ms	(* (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) (/ 1 t))
11.0ms	(* (pow z 2) y)

series175.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
93.0ms	(* (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) (/ 1 t))
18.0ms	(* (pow z 2) y)

simplify46.0ms

Counts

86 → 86

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	320	654
1	1463	566
2	5003	554
done	5003	554

prune296.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.3b

localize22.0ms

Local error

Found 4 expressions with local error:

1.8b	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) (cbrt t))
3.8b	(* (/ 1 (* (cbrt t) (cbrt t))) (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) (cbrt t)))
4.8b	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
6.4b	(* (pow z 2) y)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
56×	`add-exp-log`
51×	`times-frac`
40×	`*-un-lft-identity`
37×	`add-cube-cbrt`
25×	`associate-r`
24×	`cbrt-prod`
23×	`prod-exp`
21×	`add-cbrt-cube`
16×	`div-exp`
15×	`associate-l`
13×	`unswap-sqr`
9×	`cbrt-unprod`
8×	`cbrt-undiv`
6×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `unpow-prod-down` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`*-commutative` `unpow2` `sqr-pow`
1×	`frac-times` `pow-to-exp` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `clear-num` `fma-udef`

Counts

4 → 152

Calls

4 calls:

5.0ms	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) (cbrt t))
57.0ms	(* (/ 1 (* (cbrt t) (cbrt t))) (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) (cbrt t)))
0.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
11.0ms	(* (pow z 2) y)

series447.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) (cbrt t))
192.0ms	(* (/ 1 (* (cbrt t) (cbrt t))) (/ (fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0))) (cbrt t)))
64.0ms	(fma 0.5 (* (pow z 2) y) (fma 1.0 (* z y) (log 1.0)))
19.0ms	(* (pow z 2) y)

simplify94.0ms

Counts

164 → 164

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	655	2140
1	3251	1881
2	5001	1800
done	5001	1800

prune574.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.3b

regimes626.0ms

Accuracy

74.8% (4.0b remaining)

Error of 8.3b against oracle of 4.3b and baseline of 20.2b

bsearch156.0ms

Steps

Iters	Range		Point
7	1.2449861131513245e-115	3.07325320309632e-113	1.8264381599139905e-113
10	-0.7465447619262514	-3.2626108287873416e-11	-5.050049854843211e-06

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	32
1	47	32
done	47	32

end0.0ms

sample3.1s

Algorithm

intervals

Results

746.0ms	1554×	body	10240	exit
723.0ms	1396×	body	1280	valid
446.0ms	1574×	body	640	valid
214.0ms	3579×	body	80	valid
166.0ms	932×	body	320	valid
97.0ms	77×	body	2560	valid
86.0ms	2466×	body	80	nan
51.0ms	469×	body	160	valid
50.0ms	263×	body	640	nan
32.0ms	106×	body	1280	nan
22.0ms	159×	body	320	nan
8.0ms	100×	body	160	nan