Details

sample57.0ms

Algorithm

intervals

Results

13.0ms	251×	body	80	valid
11.0ms	13×	body	640	valid
2.0ms	13×	body	320	valid
2.0ms	7×	body	1280	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	2560	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
6	2502
5	895
4	343
3	126
2	46
1	23
0	11

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
13.0b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite41.0ms

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:

36.0ms	(/ (- t x) (- a z))
1.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series233.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(/ (- t x) (- a z))
154.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify1.6s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
3	2173
2	663
1	274
0	118

prune490.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.2b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.1b	(+ (* (- y z) (/ (- t x) (- a z))) x)
5.1b	(* (- y z) (/ (- t x) (- a z)))

rewrite150.0ms

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:

37.0ms	(/ (- t x) (- a z))
37.0ms	(+ (* (- y z) (/ (- t x) (- a z))) x)
67.0ms	(* (- y z) (/ (- t x) (- a z)))

series462.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(/ (- t x) (- a z))
219.0ms	(+ (* (- y z) (/ (- t x) (- a z))) x)
174.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify1.5s

Counts

135 → 135

Iterations

Iter	Nodes
done	5003
2	1799
1	516
0	189

prune815.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.5b	(+ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-l/` `associate-r/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 143

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
189.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
71.0ms	(+ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

205.0ms	(cbrt (- a z))
218.0ms	(cbrt (- a z))
445.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
293.0ms	(+ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

simplify2.5s

Counts

155 → 155

Iterations

Iter	Nodes
done	5000
2	2925
1	762
0	261

prune1.3s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 3.3b

localize58.0ms

Local error

Found 4 expressions with local error:

1.1b	(cbrt (/ (- t x) (cbrt (- a z))))
1.1b	(cbrt (/ (- t x) (cbrt (- a z))))
3.1b	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (/ (- t x) (cbrt (- a z))))) (/ (cbrt (- a z)) (cbrt (/ (- t x) (cbrt (- a z)))))))
7.3b	(+ (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (/ (- t x) (cbrt (- a z))))) (/ (cbrt (- a z)) (cbrt (/ (- t x) (cbrt (- a z))))))) (cbrt (/ (- t x) (cbrt (- a z))))) x)

rewrite592.0ms

Algorithm

rewrite-expression-head

Rules

142×	`cbrt-prod`
100×	`add-sqr-sqrt` `*-un-lft-identity`
85×	`times-frac`
44×	`add-cube-cbrt`
28×	`distribute-lft-out--` `difference-of-squares`
22×	`add-exp-log`
14×	`add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
7×	`associate-/r/`
6×	`cbrt-div` `add-log-exp`
5×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3--` `div-inv` `flip--`
2×	`pow1/3` `associate-/l/`
1×	`frac-times` `+-commutative` `clear-num` `associate-/r` `sum-log` `fma-def` `frac-2neg` `flip3-+` `div-sub` `associate-l/` `associate-*r/` `flip-+`

Counts

4 → 167

Calls

4 calls:

20.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
14.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
116.0ms	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (/ (- t x) (cbrt (- a z))))) (/ (cbrt (- a z)) (cbrt (/ (- t x) (cbrt (- a z)))))))
428.0ms	(+ (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (/ (- t x) (cbrt (- a z))))) (/ (cbrt (- a z)) (cbrt (/ (- t x) (cbrt (- a z))))))) (cbrt (/ (- t x) (cbrt (- a z))))) x)

series1.5s

Counts

4 → 12

Calls

4 calls:

367.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
346.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
436.0ms	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (/ (- t x) (cbrt (- a z))))) (/ (cbrt (- a z)) (cbrt (/ (- t x) (cbrt (- a z)))))))
305.0ms	(+ (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (/ (- t x) (cbrt (- a z))))) (/ (cbrt (- a z)) (cbrt (/ (- t x) (cbrt (- a z))))))) (cbrt (/ (- t x) (cbrt (- a z))))) x)

simplify2.4s

Counts

179 → 179

Iterations

Iter	Nodes
done	5002
2	2224
1	799
0	340

prune1.5s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 3.3b

regimes945.0ms

Accuracy

13.7% (7.9b remaining)

Error of 11.2b against oracle of 3.3b and baseline of 12.4b

bsearch57.0ms

Steps

Iters	Range		Point
7	6.036969748268729e+177	7.011571433264632e+179	2.504149558291548e+179

simplify10.0ms

Iterations

Iter	Nodes
done	27
1	27
0	24

end0.0ms

sample2.2s

Algorithm

intervals

Results

655.0ms	7814×	body	80	valid
461.0ms	251×	body	160	valid
115.0ms	484×	body	640	valid
107.0ms	252×	body	1280	valid
77.0ms	414×	body	320	valid
8.0ms	20×	body	2560	valid