Details

sample41.0ms

Algorithm

intervals

Results

20.0ms

272×

body

valid

simplify5.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	25	17
2	39	17
3	64	17
4	114	17
5	201	17
6	403	17
7	946	17
8	2515	17
done	5001	17

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* t z) x)
0.0b	(+ x (/ (- (* y z) x) (- (* t z) x)))
0.2b	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
9.6b	(/ (- (* y z) x) (- (* t z) x))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
25×	`times-frac`
24×	`add-sqr-sqrt` `add-cube-cbrt`
11×	`distribute-lft-out`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-/r` `associate-/l`
4×	`pow1` `expm1-log1p-u` `div-sub` `associate-/r/` `log1p-expm1-u` `associate-/l/`
3×	`flip3--` `fma-def` `flip3-+` `prod-diff` `flip--` `flip-+`
2×	`cbrt-undiv` `associate-+r-` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`+-commutative` `sub-neg` `fma-neg` `diff-log` `sum-log`

Counts

4 → 113

Calls

4 calls:

19.0ms	(- (* t z) x)
56.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
199.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
38.0ms	(/ (- (* y z) x) (- (* t z) x))

series444.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* t z) x)
149.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
167.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
84.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify3.4s

Counts

125 → 125

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	182	2295
1	454	2174
2	1308	2039
3	4498	2030
done	5000	2030

prune561.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))) (+ x 1.0))
3.4b	(fma (/ y (- (* t z) x)) z x)
3.4b	(/ x (- (* t z) x))
3.6b	(/ y (- (* t z) x))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
47×	`times-frac`
32×	`add-cube-cbrt`
12×	`associate-/l*`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `difference-of-squares`
7×	`distribute-lft-out`
6×	`associate-/r/`
5×	`distribute-lft-out--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`associate-/l/`
1×	`flip3-+` `div-sub` `flip-+` `fma-udef`

Counts

4 → 125

Calls

4 calls:

158.0ms	(/ (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))) (+ x 1.0))
1.0ms	(fma (/ y (- (* t z) x)) z x)
27.0ms	(/ x (- (* t z) x))
38.0ms	(/ y (- (* t z) x))

series433.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))) (+ x 1.0))
97.0ms	(fma (/ y (- (* t z) x)) z x)
88.0ms	(/ x (- (* t z) x))
49.0ms	(/ y (- (* t z) x))

simplify2.7s

Counts

137 → 137

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	215	2892
1	489	2833
2	1276	2663
3	3449	2657
done	5000	2651

prune509.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (- (* t z) x))
3.3b	(* x (/ 1 (- (* t z) x)))
3.4b	(fma (/ y (- (* t z) x)) z x)
3.6b	(/ y (- (* t z) x))

rewrite513.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `times-frac`
28×	`add-cube-cbrt`
19×	`add-exp-log`
15×	`associate-r`
13×	`add-cbrt-cube`
7×	`pow1`
6×	`associate-/r` `associate-/r/` `associate-/l`
5×	`div-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `associate-l` `flip--` `div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

4 → 116

Calls

4 calls:

27.0ms	(/ 1 (- (* t z) x))
463.0ms	(* x (/ 1 (- (* t z) x)))
1.0ms	(fma (/ y (- (* t z) x)) z x)
18.0ms	(/ y (- (* t z) x))

series227.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (- (* t z) x))
77.0ms	(* x (/ 1 (- (* t z) x)))
79.0ms	(fma (/ y (- (* t z) x)) z x)
40.0ms	(/ y (- (* t z) x))

simplify2.3s

Counts

128 → 128

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	160	1485
1	348	1328
2	779	1193
3	1788	1193
done	5000	1189

prune532.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ x 1.0))
0.0b	(+ x (/ (- (* y z) x) (- (* t z) x)))
0.3b	(* (+ x (/ (- (* y z) x) (- (* t z) x))) (/ 1 (+ x 1.0)))
9.6b	(/ (- (* y z) x) (- (* t z) x))

rewrite383.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
35×	`times-frac`
31×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube`
9×	`distribute-lft-out`
7×	`pow1` `associate-/r*`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`flip3-+` `div-exp` `flip-+`
4×	`expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-def` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `flip3--` `frac-2neg` `1-exp` `div-sub` `associate-*l/` `clear-num` `flip--` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `associate-+r-` `pow-flip` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 139

Calls

4 calls:

22.0ms	(/ 1 (+ x 1.0))
64.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
256.0ms	(* (+ x (/ (- (* y z) x) (- (* t z) x))) (/ 1 (+ x 1.0)))
33.0ms	(/ (- (* y z) x) (- (* t z) x))

series441.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (+ x 1.0))
111.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
207.0ms	(* (+ x (/ (- (* y z) x) (- (* t z) x))) (/ 1 (+ x 1.0)))
87.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify1.7s

Counts

151 → 151

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	206	2570
1	537	2318
2	1671	2123
done	5001	2118

prune524.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes225.0ms

Accuracy

29.5% (3.1b remaining)

Error of 3.5b against oracle of 0.4b and baseline of 4.8b

bsearch83.0ms

Steps

Iters	Range		Point
9	4.863564902743035e+100	5.86912954660432e+106	3.0678918401680893e+102
5	-5.278031834180875e+72	-2.1107077928971596e+72	-3.2224235875553088e+72

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	45
1	35	37
done	35	37

end0.0ms

sample1.2s

Algorithm

intervals

Results

736.0ms

8321×

body

valid