Details

sample34.0ms

Algorithm

intervals

Results

12.0ms	253×	body	80	valid
2.0ms	14×	body	640	valid
2.0ms	9×	body	1280	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	2560	valid
0.0ms	5×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 3 (16.0ms)

Iter	Nodes	Cost
0	11	245
1	20	245
2	45	245
3	116	220
4	326	220
5	979	220
6	3874	220
done	5000	220

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.3b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
13.5b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite22.0ms

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:

19.0ms	(/ (- y x) (- a t))
0.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series233.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(/ (- y x) (- a t))
144.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify2.7s

Counts

70 → 70

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	118	18729
1	275	17805
2	851	17725
3	4618	17675
done	5000	17675

prune614.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.5b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
1.5b	(+ (* (/ (- y x) (- a t)) (- z t)) x)
6.6b	(* (/ (- y x) (- a t)) (- z t))

rewrite150.0ms

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:

35.0ms	(/ (- y x) (- a t))
33.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
69.0ms	(* (/ (- y x) (- a t)) (- z t))

series696.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- y x) (- a t))
289.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
328.0ms	(* (/ (- y x) (- a t)) (- z t))

simplify2.3s

Counts

179 → 179

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	256	61728
1	719	56140
2	3319	50842
done	5002	50712

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.7b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite131.0ms

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:

23.0ms	(/ (- z t) (- a t))
42.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)
61.0ms	(* (- y x) (/ (- z t) (- a t)))

series568.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(/ (- z t) (- a t))
265.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)
207.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify2.4s

Counts

135 → 135

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	189	37921
1	518	34642
2	2648	34051
done	5000	34001

prune757.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
1.9b	(* (- y x) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t)))))
7.1b	(+ (* (- y x) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t))))) x)

rewrite794.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-exp-log`
35×	`prod-exp`
26×	`add-cbrt-cube`
15×	`div-exp` `cbrt-unprod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`cbrt-prod`
9×	`frac-times` `pow1`
7×	`cbrt-undiv` `add-cube-cbrt`
6×	`flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`associate-l` `associate-*l/`
4×	`expm1-log1p-u` `rec-exp` `cbrt-div` `1-exp` `log1p-expm1-u`
3×	`pow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `associate-r` `*-commutative` `flip-+`

Counts

4 → 99

Calls

4 calls:

4.0ms	(cbrt (- a t))
7.0ms	(cbrt (- a t))
409.0ms	(* (- y x) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t)))))
371.0ms	(+ (* (- y x) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t))))) x)

series897.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(cbrt (- a t))
168.0ms	(cbrt (- a t))
288.0ms	(* (- y x) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t)))))
244.0ms	(+ (* (- y x) (* (/ 1 (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t))))) x)

simplify2.7s

Counts

111 → 111

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	231	50260
1	666	41893
2	3007	41058
done	5000	31008

prune687.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.4b

regimes805.0ms

Accuracy

15.1% (6.6b remaining)

Error of 10.3b against oracle of 3.6b and baseline of 11.4b

bsearch131.0ms

Steps

Iters	Range		Point
6	1.0082166471488646e-224	1.4491102947312779e-223	3.763484657368967e-224
10	-1.4224725025320182e-228	-1.6312618396316042e-239	-6.2380006859628235e-230

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	722
1	28	722
done	28	722

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	7915×	body	80	valid
101.0ms	433×	body	320	valid
92.0ms	450×	body	640	valid
71.0ms	274×	body	1280	valid
27.0ms	222×	body	160	valid
4.0ms	15×	body	2560	valid