Details

sample36.0ms

Algorithm

intervals

Results

10.0ms	247×	body	80	valid
2.0ms	16×	body	320	valid
2.0ms	9×	body	1280	valid
1.0ms	9×	body	640	valid
1.0ms	9×	body	160	valid
0.0ms	1×	body	2560	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4619
5	1129
4	367
3	128
2	46
1	23
0	11

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.6b

localize32.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
13.6b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite38.0ms

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-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

35.0ms	(/ (- t x) (- a z))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series206.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(/ (- t x) (- a z))
127.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify2.4s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	4626
2	848
1	274
0	118

prune454.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.9b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.8b	(+ (* (/ (- t x) (- a z)) (- y z)) x)
5.1b	(* (/ (- t x) (- a z)) (- y z))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 170

Calls

3 calls:

26.0ms	(/ (- t x) (- a z))
30.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
65.0ms	(* (/ (- t x) (- a z)) (- y z))

series532.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(/ (- t x) (- a z))
185.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
258.0ms	(* (/ (- t x) (- a z)) (- y z))

simplify1.9s

Counts

179 → 179

Iterations

Iter	Nodes
done	5001
2	3330
1	717
0	256

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.6b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.1b	(* (- t x) (/ (- y z) (- a z)))
3.1b	(+ (* (- t x) (/ (- y z) (- a z))) x)

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 126

Calls

3 calls:

38.0ms	(/ (- y z) (- a z))
76.0ms	(* (- t x) (/ (- y z) (- a z)))
23.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

series471.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- y z) (- a z))
177.0ms	(* (- t x) (/ (- y z) (- a z)))
218.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

simplify1.9s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
2	2672
1	518
0	189

prune641.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ (- t x) (- a z)) y) (- x (* z (/ (- t x) (- a z)))))
3.5b	(* (/ (- t x) (- a z)) y)
3.6b	(- x (* z (/ (- t x) (- a z))))
4.7b	(* z (/ (- t x) (- a z)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
52×	`times-frac`
34×	`associate-r` `associate-l`
31×	`add-cube-cbrt`
20×	`distribute-lft-out--` `difference-of-squares`
14×	`add-cbrt-cube` `add-exp-log`
11×	`add-log-exp`
8×	`pow1`
6×	`prod-diff`
5×	`associate-+r+`
4×	`expm1-log1p-u` `flip3--` `prod-exp` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `flip--` `unswap-sqr`
3×	`fma-neg` `associate-*l/`
2×	`cbrt-undiv` `sum-log` `sub-neg` `diff-log` `div-exp` `pow-prod-down` `frac-add` `*-commutative` `div-inv`
1×	`+-commutative` `associate-+r-` `fma-def` `flip3-+` `associate-*r/` `flip-+`

Counts

4 → 147

Calls

4 calls:

36.0ms	(+ (* (/ (- t x) (- a z)) y) (- x (* z (/ (- t x) (- a z)))))
64.0ms	(* (/ (- t x) (- a z)) y)
8.0ms	(- x (* z (/ (- t x) (- a z))))
61.0ms	(* z (/ (- t x) (- a z)))

series573.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(+ (* (/ (- t x) (- a z)) y) (- x (* z (/ (- t x) (- a z)))))
150.0ms	(* (/ (- t x) (- a z)) y)
127.0ms	(- x (* z (/ (- t x) (- a z))))
110.0ms	(* z (/ (- t x) (- a z)))

simplify2.2s

Counts

159 → 159

Iterations

Iter	Nodes
done	5001
2	2973
1	680
0	240

prune825.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.4b

regimes876.0ms

Accuracy

30.8% (5.7b remaining)

Error of 9.4b against oracle of 3.7b and baseline of 11.9b

bsearch103.0ms

Steps

Iters	Range		Point
7	2.42011835416667e-163	8.820107011884713e-162	8.000849816726043e-162
8	-1.22663786197907e-171	-2.8633111244246464e-174	-1.1380041034613798e-171

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	22

end0.0ms

sample1.6s

Algorithm

intervals

Results

874.0ms	7728×	body	80	valid
123.0ms	505×	body	640	valid
98.0ms	269×	body	1280	valid
60.0ms	412×	body	320	valid
25.0ms	252×	body	160	valid
4.0ms	14×	body	2560	valid