Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	235×	body	80	valid
2.0ms	10×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	14×	body	160	valid

simplify8.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (31.0ms)

Iter	Nodes	Cost
0	11	13
1	22	13
2	51	13
3	103	13
4	205	12
5	408	12
6	672	12
7	935	12
8	1113	12
9	1379	12
10	1828	12
11	2805	12
12	3999	12
done	5000	12

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t z) (- a t))
3.0b	(fma (/ (- t z) (- a t)) y (+ x y))

rewrite16.0ms

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:

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

series227.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- t z) (- a t))
184.0ms	(fma (/ (- t z) (- a t)) y (+ x y))

simplify2.0s

Counts

70 → 70

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	113	906
1	258	878
2	589	826
3	1517	824
4	4609	822
done	5000	822

prune234.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
0.6b	(* (/ (- t z) (- a t)) y)
2.9b	(+ (* (/ (- t z) (- a t)) y) (+ x y))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 124

Calls

3 calls:

12.0ms	(/ (- t z) (- a t))
29.0ms	(* (/ (- t z) (- a t)) y)
15.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

series340.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (- t z) (- a t))
97.0ms	(* (/ (- t z) (- a t)) y)
198.0ms	(+ (* (/ (- t z) (- a t)) y) (+ x y))

simplify1.1s

Counts

133 → 133

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	195	1736
1	543	1646
2	1595	1560
done	5000	1552

prune391.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- t z) (/ 1 (- a t)))
0.6b	(* (* (- t z) (/ 1 (- a t))) y)
4.9b	(+ (* (* (- t z) (/ 1 (- a t))) y) (+ x y))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
26×	`associate-*l/`
25×	`add-cube-cbrt`
24×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1` `frac-add`
10×	`flip3--` `flip--`
9×	`add-log-exp`
8×	`frac-times` `distribute-lft-out--` `difference-of-squares`
7×	`flip3-+` `cbrt-unprod` `flip-+`
6×	`div-exp` `associate-l`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-*r/` `pow-prod-down` `associate-/r/` `un-div-inv` `log1p-expm1-u`
3×	`cbrt-undiv` `rec-exp` `1-exp` `sum-log` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `associate-+r+` `pow-flip` `fma-def` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 153

Calls

4 calls:

6.0ms	(/ 1 (- a t))
28.0ms	(* (- t z) (/ 1 (- a t)))
33.0ms	(* (* (- t z) (/ 1 (- a t))) y)
41.0ms	(+ (* (* (- t z) (/ 1 (- a t))) y) (+ x y))

series384.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (- a t))
47.0ms	(* (- t z) (/ 1 (- a t)))
98.0ms	(* (* (- t z) (/ 1 (- a t))) y)
203.0ms	(+ (* (* (- t z) (/ 1 (- a t))) y) (+ x y))

simplify1.2s

Counts

165 → 165

Iterations

Useful iterations: 2 (515.0ms)

Iter	Nodes	Cost
0	251	2482
1	754	2016
2	2780	1854
done	5000	1854

prune451.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.3b

localize14.0ms

Local error

Found 4 expressions with local error:

7.8b	(+ (* (* (cbrt (* y (/ (- t z) (- a t)))) (cbrt (* y (/ (- t z) (- a t))))) (cbrt (* y (/ (- t z) (- a t))))) (+ x y))
7.9b	(cbrt (* y (/ (- t z) (- a t))))
7.9b	(cbrt (* y (/ (- t z) (- a t))))
7.9b	(cbrt (* y (/ (- t z) (- a t))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

33×	`associate-*r/`
27×	`cbrt-div`
14×	`frac-add`
10×	`frac-times` `associate-*l/`
9×	`add-log-exp`
8×	`flip3-+` `flip-+`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `pow1/3` `sum-log`
1×	`+-commutative` `associate-+r+` `fma-def`

Counts

4 → 66

Calls

4 calls:

22.0ms	(+ (* (* (cbrt (* y (/ (- t z) (- a t)))) (cbrt (* y (/ (- t z) (- a t))))) (cbrt (* y (/ (- t z) (- a t))))) (+ x y))
7.0ms	(cbrt (* y (/ (- t z) (- a t))))
7.0ms	(cbrt (* y (/ (- t z) (- a t))))
7.0ms	(cbrt (* y (/ (- t z) (- a t))))

series753.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(+ (* (* (cbrt (* y (/ (- t z) (- a t)))) (cbrt (* y (/ (- t z) (- a t))))) (cbrt (* y (/ (- t z) (- a t))))) (+ x y))
185.0ms	(cbrt (* y (/ (- t z) (- a t))))
184.0ms	(cbrt (* y (/ (- t z) (- a t))))
185.0ms	(cbrt (* y (/ (- t z) (- a t))))

simplify1.4s

Counts

78 → 78

Iterations

Useful iterations: 3 (561.0ms)

Iter	Nodes	Cost
0	143	2312
1	411	2229
2	1250	1585
3	4276	1493
done	5000	1493

prune297.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.3b

regimes397.0ms

Accuracy

34% (5.7b remaining)

Error of 8.7b against oracle of 3.0b and baseline of 11.6b

bsearch94.0ms

Steps

Iters	Range		Point
8	1.4221983697485953e-93	4.860604208151661e-91	8.232213477554133e-92
8	-1.2174954204274436e-167	-9.750906339755104e-171	-8.94712349400521e-168

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	85
1	27	85
done	27	85

end0.0ms

sample693.0ms

Algorithm

intervals

Results

257.0ms	7365×	body	80	valid
57.0ms	460×	body	640	valid
45.0ms	287×	body	1280	valid
39.0ms	383×	body	320	valid
17.0ms	223×	body	160	valid
4.0ms	21×	body	2560	valid