Details

sample56.0ms

Algorithm

intervals

Results

17.0ms	264×	body	80	valid
4.0ms	16×	body	640	valid
2.0ms	8×	body	1280	valid
1.0ms	7×	body	320	valid
1.0ms	10×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3616
5	935
4	334
3	122
2	44
1	23
0	11

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.7b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.2b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.7b	(* (- y z) (/ (- t x) (- a z)))

rewrite85.0ms

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/`
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` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-r/` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

19.0ms	(/ (- t x) (- a z))
6.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
54.0ms	(* (- y z) (/ (- t x) (- a z)))

series529.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(/ (- t x) (- a z))
268.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
172.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify1.5s

Counts

128 → 128

Iterations

Iter	Nodes
done	5002
2	2689
1	500
0	183

prune774.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
1.5b	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x)))))
7.8b	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cbrt-cube`
10×	`cbrt-prod`
9×	`cbrt-undiv` `div-exp`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`times-frac` `associate-/l*`
4×	`pow1` `cbrt-div` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `associate-/r/` `flip--`
2×	`pow1/3` `associate-/l/`
1×	`frac-times` `+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `flip3-+` `div-sub` `associate-l/` `associate-*r/` `flip-+` `div-inv`

Counts

4 → 78

Calls

4 calls:

3.0ms	(cbrt (- t x))
3.0ms	(cbrt (- t x))
45.0ms	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x)))))
5.0ms	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt (- t x))
212.0ms	(cbrt (- t x))
590.0ms	(/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x)))))
224.0ms	(+ x (* (/ (- y z) (* (/ (cbrt (- a z)) (cbrt (- t x))) (/ (cbrt (- a z)) (cbrt (- t x))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify823.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1759
1	552
0	208

prune584.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
2.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.3b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite148.0ms

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`
3×	`associate-l/` `associate-r/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
125.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
11.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

209.0ms	(cbrt (- a z))
163.0ms	(cbrt (- a z))
446.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
230.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify1.7s

Counts

146 → 146

Iterations

Iter	Nodes
done	5000
2	3437
1	755
0	255

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
3.9b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
5.7b	(* (- y z) (* (- t x) (/ 1 (- a z))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`times-frac` `add-exp-log`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`frac-times` `add-cbrt-cube`
17×	`flip3--` `flip--`
13×	`prod-exp`
12×	`pow1`
10×	`associate-l` `associate-l/` `associate-r/`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `add-log-exp`
5×	`associate-/r*`
4×	`pow-prod-down` `associate-/r/` `un-div-inv`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 146

Calls

4 calls:

9.0ms	(/ 1 (- a z))
54.0ms	(* (- t x) (/ 1 (- a z)))
15.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
73.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

series643.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ 1 (- a z))
97.0ms	(* (- t x) (/ 1 (- a z)))
280.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
203.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

simplify3.5s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	4376
1	620
0	221

prune704.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.2b

regimes518.0ms

Accuracy

17.5% (7.5b remaining)

Error of 11.0b against oracle of 3.5b and baseline of 12.6b

bsearch240.0ms

Steps

Iters	Range	Point
9	1.507532718961738e+201	3.8461080361265226e+208	2.62858846270372e+201
8	-6.521223775255793e-52	-1.3820274861952056e-55	-2.411587565692805e-52
9	-9.191769695611713e+243	-5.914462922423594e+238	-5.8034266786300305e+240

Iters

Range

Point

1.507532718961738e+201

3.8461080361265226e+208

2.62858846270372e+201

-6.521223775255793e-52

-1.3820274861952056e-55

-2.411587565692805e-52

-9.191769695611713e+243

-5.914462922423594e+238

-5.8034266786300305e+240

simplify5.0ms

Iterations

Iter	Nodes
done	52
1	52
0	40

end0.0ms

sample1.9s

Algorithm

intervals

Results

685.0ms	7739×	body	80	valid
474.0ms	473×	body	640	valid
75.0ms	283×	body	1280	valid
71.0ms	412×	body	320	valid
30.0ms	270×	body	160	valid
5.0ms	17×	body	2560	valid