Details

sample47.0ms

Algorithm

intervals

Results

12.0ms	251×	body	80	valid
6.0ms	7×	body	1280	valid
2.0ms	13×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	2560	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1910
5	805
4	299
3	108
2	43
1	20
0	11

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.8b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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:

22.0ms	(/ (- t x) (- a z))
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series185.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(/ (- t x) (- a z))
117.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.7s

Counts

70 → 70

Iterations

Iter	Nodes
done	5045
3	2171
2	671
1	274
0	118

prune556.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.6b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite118.0ms

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:

18.0ms	(/ (- t x) (- a z))
24.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
68.0ms	(* (/ (- t x) (- a z)) (- y z))

series664.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(/ (- t x) (- a z))
238.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
327.0ms	(* (/ (- t x) (- a z)) (- y z))

simplify1.8s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
2	1995
1	712
0	256

prune1.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.6b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.8b	(* (- t x) (/ (- y z) (- a z)))
1.9b	(+ (* (- t x) (/ (- y z) (- a z))) x)

rewrite173.0ms

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:

36.0ms	(/ (- y z) (- a z))
100.0ms	(* (- t x) (/ (- y z) (- a z)))
25.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

series520.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ (- y z) (- a z))
202.0ms	(* (- t x) (/ (- y z) (- a z)))
254.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

simplify2.0s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1770
1	518
0	189

prune919.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.3b

localize59.0ms

Local error

Found 4 expressions with local error:

1.9b	(+ (* (* (- t x) (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z))))) (cbrt (/ (- y z) (- a z)))) x)
3.3b	(cbrt (/ (- y z) (- a z)))
3.3b	(cbrt (/ (- y z) (- a z)))
3.3b	(cbrt (/ (- y z) (- a z)))

rewrite407.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
37×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`cbrt-div` `flip3--` `pow1/3` `div-inv` `flip--`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 140

Calls

4 calls:

350.0ms	(+ (* (* (- t x) (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z))))) (cbrt (/ (- y z) (- a z)))) x)
12.0ms	(cbrt (/ (- y z) (- a z)))
13.0ms	(cbrt (/ (- y z) (- a z)))
21.0ms	(cbrt (/ (- y z) (- a z)))

series1.8s

Counts

4 → 12

Calls

4 calls:

315.0ms	(+ (* (* (- t x) (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z))))) (cbrt (/ (- y z) (- a z)))) x)
445.0ms	(cbrt (/ (- y z) (- a z)))
504.0ms	(cbrt (/ (- y z) (- a z)))
548.0ms	(cbrt (/ (- y z) (- a z)))

simplify3.1s

Counts

152 → 152

Iterations

Iter	Nodes
done	5001
3	3016
2	949
1	412
0	192

prune1.1s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.3b

regimes917.0ms

Accuracy

12.8% (7.3b remaining)

Error of 10.5b against oracle of 3.3b and baseline of 11.6b

bsearch51.0ms

Steps

Iters	Range		Point
7	6.036969748268729e+177	7.011571433264632e+179	2.692918381213643e+179

simplify6.0ms

Iterations

Iter	Nodes
done	20
1	20
0	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

727.0ms	7813×	body	80	valid
172.0ms	484×	body	640	valid
107.0ms	413×	body	320	valid
75.0ms	252×	body	1280	valid
30.0ms	253×	body	160	valid
7.0ms	20×	body	2560	valid