Details

sample61.0ms

Algorithm

intervals

Results

18.0ms	234×	body	80	valid
5.0ms	16×	body	640	valid
4.0ms	11×	body	1280	valid
3.0ms	14×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	1×	body	2560	valid

simplify12.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
6	1919
5	803
4	299
3	108
2	43
1	20
0	11

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.3b

localize32.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
16.5b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite74.0ms

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:

68.0ms	(/ (- y x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series556.0ms

Counts

2 → 6

Calls

2 calls:

220.0ms	(/ (- y x) (- a t))
336.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify4.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	2150
2	672
1	275
0	118

prune838.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.3b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
2.9b	(+ (* (/ (- y x) (- a t)) (- z t)) x)
6.4b	(* (/ (- y x) (- a t)) (- z t))

rewrite722.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 170

Calls

3 calls:

129.0ms	(/ (- y x) (- a t))
89.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
370.0ms	(* (/ (- y x) (- a t)) (- z t))

series1.4s

Counts

3 → 9

Calls

3 calls:

167.0ms	(/ (- y x) (- a t))
379.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
870.0ms	(* (/ (- y x) (- a t)) (- z t))

simplify5.4s

Counts

179 → 179

Iterations

Iter	Nodes
done	5004
2	1992
1	714
0	256

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.3b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.6b	(* (- y x) (/ (- z t) (- a t)))
1.9b	(+ (* (- y x) (/ (- z t) (- a t))) x)

rewrite267.0ms

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-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 126

Calls

3 calls:

49.0ms	(/ (- z t) (- a t))
144.0ms	(* (- y x) (/ (- z t) (- a t)))
64.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

series752.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(/ (- z t) (- a t))
274.0ms	(* (- y x) (/ (- z t) (- a t)))
376.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

simplify3.4s

Counts

135 → 135

Iterations

Iter	Nodes
done	5002
2	1756
1	519
0	189

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ t (- a t))
0.0b	(/ z (- a t))
1.6b	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))
1.9b	(+ (* (- y x) (- (/ z (- a t)) (/ t (- a t)))) x)

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

2592×	`*-un-lft-identity`
2584×	`add-sqr-sqrt`
2568×	`times-frac`
1764×	`prod-diff`
1540×	`add-cube-cbrt`
886×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
525×	`distribute-lft-out--`
519×	`difference-of-squares`
344×	`associate-/r/`
180×	`flip3--` `flip--`
172×	`div-inv`
18×	`associate-r`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
8×	`frac-times`
6×	`pow1` `associate-/l*` `add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `log1p-expm1-u`
3×	`distribute-rgt-out--` `frac-sub` `sub-div`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-*l/` `clear-num`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 1915

Calls

4 calls:

25.0ms	(/ t (- a t))
23.0ms	(/ z (- a t))
719.0ms	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))
472.0ms	(+ (* (- y x) (- (/ z (- a t)) (/ t (- a t)))) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

196.0ms	(/ t (- a t))
102.0ms	(/ z (- a t))
432.0ms	(* (- y x) (- (/ z (- a t)) (/ t (- a t))))
572.0ms	(+ (* (- y x) (- (/ z (- a t)) (/ t (- a t)))) x)

simplify8.3s

Counts

1927 → 1927

Iterations

Iter	Nodes
done	5002
1	3037
0	1364

prune24.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.1b

regimes1.1s

Accuracy

2% (5.3b remaining)

Error of 8.7b against oracle of 3.4b and baseline of 8.8b

bsearch247.0ms

Steps

Iters	Range		Point
9	1.4872881677548498e-274	2.2755194218609991e-268	1.5123583715198347e-269
8	2.0406820065813185e-300	1.4755203203888105e-296	4.4650642175356816e-300

simplify11.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	7812×	body	80	valid
183.0ms	403×	body	320	valid
142.0ms	474×	body	640	valid
110.0ms	291×	body	1280	valid
81.0ms	272×	body	160	valid
7.0ms	15×	body	2560	valid