Details

sample57.0ms

Algorithm

intervals

Results

15.0ms	250×	body	80	valid
4.0ms	17×	body	640	valid
3.0ms	10×	body	1280	valid
2.0ms	13×	body	320	valid
1.0ms	9×	body	160	valid

simplify6.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	46	12
3	128	12
4	360	12
5	877	12
6	2016	12
7	3586	12
done	5000	12

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.1b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
16.1b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

47.0ms	(/ (- t x) (- a z))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series222.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ (- t x) (- a z))
148.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.8s

Counts

70 → 70

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	118	918
1	269	890
2	658	838
3	1743	834
done	5000	830

prune276.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
4.2b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.2b	(* (- y z) (/ (- t x) (- a z)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `fma-def` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 128

Calls

3 calls:

34.0ms	(/ (- t x) (- a z))
8.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
70.0ms	(* (- y z) (/ (- t x) (- a z)))

series549.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- t x) (- a z))
253.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
221.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify1.4s

Counts

137 → 137

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	189	1881
1	484	1769
2	1787	1659
done	5002	1657

prune432.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
16.1b	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

13.0ms	(/ 1 (- a z))
78.0ms	(* (- t x) (/ 1 (- a z)))
1.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

series247.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ 1 (- a z))
75.0ms	(* (- t x) (/ 1 (- a z)))
126.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

simplify2.3s

Counts

114 → 114

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	155	1285
1	344	1052
2	954	948
3	3231	944
done	5000	942

prune360.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 3.1b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
16.1b	(fma (pow (/ (- t x) (- a z)) 1) (- y z) x)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

52.0ms	(/ (- t x) (- a z))
1.0ms	(fma (pow (/ (- t x) (- a z)) 1) (- y z) x)

series260.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(/ (- t x) (- a z))
163.0ms	(fma (pow (/ (- t x) (- a z)) 1) (- y z) x)

simplify1.5s

Counts

70 → 70

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	119	944
1	272	890
2	687	838
3	1963	834
done	5000	832

prune242.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 3.1b

regimes545.0ms

Accuracy

15.5% (9.5b remaining)

Error of 13.3b against oracle of 3.8b and baseline of 15.1b

bsearch100.0ms

Steps

Iters	Range		Point
9	1.2893535391803096e+185	1.3650528676108602e+190	1.8999923878100788e+186
4	-9.8607559020918e+108	-5.928196142097795e+108	-9.629551716185816e+108

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	23	46
1	29	33
done	29	33

end0.0ms

sample1.3s

Algorithm

intervals

Results

385.0ms	7766×	body	80	valid
89.0ms	491×	body	640	valid
61.0ms	283×	body	1280	valid
60.0ms	427×	body	320	valid
25.0ms	280×	body	160	valid
5.0ms	16×	body	2560	valid