Details

sample61.0ms

Algorithm

intervals

Results

18.0ms	238×	body	80	valid
5.0ms	18×	body	640	valid
3.0ms	10×	body	1280	valid
3.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	46	12
3	128	12
4	368	12
5	1103	12
6	4364	12
done	5000	12

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
14.0b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite53.0ms

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:

48.0ms	(/ (- t x) (- a z))
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series227.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(/ (- t x) (- a z))
143.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify2.4s

Counts

70 → 70

Iterations

Useful iterations: 3 (825.0ms)

Iter	Nodes	Cost
0	118	918
1	274	890
2	848	838
3	4610	834
done	5000	834

prune294.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.3b	(+ x (* (- y z) (/ (- t x) (- a z))))
4.3b	(* (- y z) (/ (- t x) (- a z)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`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` `fma-def` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 128

Calls

3 calls:

28.0ms	(/ (- t x) (- a z))
9.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
94.0ms	(* (- y z) (/ (- t x) (- a z)))

series446.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (- t x) (- a z))
215.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
159.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify2.1s

Counts

137 → 137

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	189	1881
1	515	1781
2	2711	1665
done	5000	1657

prune462.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (- a z))
0.3b	(- (/ t (- a z)) (/ x (- a z)))
3.1b	(+ x (* (- y z) (- (/ t (- a z)) (/ x (- a z)))))
4.3b	(* (- y z) (- (/ t (- a z)) (/ x (- a z))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

3248×	`*-un-lft-identity`
3230×	`add-sqr-sqrt`
3216×	`times-frac`
2205×	`prod-diff`
1920×	`add-cube-cbrt`
886×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
662×	`distribute-lft-out--`
650×	`difference-of-squares`
432×	`associate-/r/`
225×	`flip3--` `flip--`
216×	`div-inv`
21×	`fma-neg`
18×	`associate-r`
8×	`add-exp-log` `frac-times` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `distribute-rgt-out--`
5×	`sub-neg` `associate-l` `associate-/r*`
4×	`expm1-log1p-u` `associate-*r/` `frac-sub` `log1p-expm1-u` `sub-div`
3×	`fma-def` `associate-/l*`
2×	`associate-*l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `flip3-+` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 2371

Calls

4 calls:

18.0ms	(/ x (- a z))
170.0ms	(- (/ t (- a z)) (/ x (- a z)))
266.0ms	(+ x (* (- y z) (- (/ t (- a z)) (/ x (- a z)))))
469.0ms	(* (- y z) (- (/ t (- a z)) (/ x (- a z))))

series760.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ x (- a z))
187.0ms	(- (/ t (- a z)) (/ x (- a z)))
232.0ms	(+ x (* (- y z) (- (/ t (- a z)) (/ x (- a z)))))
281.0ms	(* (- y z) (- (/ t (- a z)) (/ x (- a z))))

simplify5.6s

Counts

2383 → 2383

Iterations

Useful iterations: done (5.3s)

Iter	Nodes	Cost
0	1972	121975
1	4200	111130
done	5000	110576

prune12.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
2.5b	(* (* (- y z) (/ 1 (- a z))) (- t x))
3.1b	(+ x (* (* (- y z) (/ 1 (- a z))) (- t x)))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
69×	`*-un-lft-identity`
50×	`add-cube-cbrt`
36×	`prod-diff`
32×	`add-exp-log` `times-frac`
26×	`associate-r`
22×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
20×	`frac-times` `add-cbrt-cube`
17×	`flip3--` `flip--`
14×	`associate-*l/`
13×	`prod-exp`
12×	`pow1`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`associate-r/` `div-exp` `associate-l*` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `sub-neg` `pow-prod-down` `associate-/r/` `un-div-inv` `log1p-expm1-u`
3×	`cbrt-undiv` `rec-exp` `fma-def` `1-exp` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 201

Calls

4 calls:

13.0ms	(/ 1 (- a z))
65.0ms	(* (- y z) (/ 1 (- a z)))
134.0ms	(* (* (- y z) (/ 1 (- a z))) (- t x))
19.0ms	(+ x (* (* (- y z) (/ 1 (- a z))) (- t x)))

series724.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1 (- a z))
65.0ms	(* (- y z) (/ 1 (- a z)))
392.0ms	(* (* (- y z) (/ 1 (- a z))) (- t x))
215.0ms	(+ x (* (* (- y z) (/ 1 (- a z))) (- t x)))

simplify629.0ms

Counts

213 → 213

Iterations

Useful iterations: done (621.0ms)

Iter	Nodes	Cost
0	305	3731
1	897	3252
done	5000	2640

prune536.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.1b

regimes387.0ms

Accuracy

20.5% (6.6b remaining)

Error of 9.9b against oracle of 3.3b and baseline of 11.6b

bsearch169.0ms

Steps

Iters	Range		Point
9	1.6041266388632134e-135	3.9263427962785025e-128	3.4234349167713246e-135
8	-1.743473553062761e-97	-2.4373357034560896e-100	-2.479409256430603e-100

simplify10.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	32	102
1	43	62
done	43	62

end0.0ms

sample1.2s

Algorithm

intervals

Results

546.0ms	7738×	body	80	valid
102.0ms	465×	body	640	valid
54.0ms	268×	body	1280	valid
53.0ms	428×	body	320	valid
24.0ms	269×	body	160	valid
3.0ms	12×	body	2560	valid