Details

sample419.0ms

Algorithm

intervals

Results

125.0ms	91×	body	2560	valid
114.0ms	69×	body	10240	exit
78.0ms	102×	body	1280	valid
12.0ms	25×	body	640	valid
8.0ms	325×	pre	80	true
6.0ms	18×	body	320	valid
2.0ms	16×	body	80	valid
1.0ms	4×	body	160	valid

simplify1.6s

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
1.9b	(- (exp (* b eps)) 1.0)
3.1b	(- (exp (* a eps)) 1.0)
4.0b	(- (exp (* (+ a b) eps)) 1.0)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `flip3--` `*-un-lft-identity` `flip--` `add-log-exp`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `frac-times` `add-cube-cbrt` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/` `associate-/l/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 73

Calls

4 calls:

55.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
22.0ms	(- (exp (* b eps)) 1.0)
13.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

series346.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
38.0ms	(- (exp (* b eps)) 1.0)
37.0ms	(- (exp (* a eps)) 1.0)
54.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify857.0ms

Counts: 85 → 85

prune454.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

24.0ms

(+ (/ 1 b) (/ 1 a))

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

(+ (/ 1 b) (/ 1 a))

simplify1.0s

Counts: 22 → 22

prune80.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))
0.1b	(sqrt (+ (/ 1 b) (/ 1 a)))
0.1b	(sqrt (+ (/ 1 b) (/ 1 a)))
0.2b	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))

rewrite344.0ms

Algorithm

rewrite-expression-head

Rules

138×	`*-un-lft-identity`
106×	`sqrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`add-sqr-sqrt` `times-frac`
35×	`swap-sqr`
30×	`sqrt-div`
28×	`add-cube-cbrt`
21×	`pow1`
13×	`associate-r` `associate-l`
11×	`flip3-+` `frac-add` `flip-+`
10×	`sqrt-pow1` `pow1/2`
9×	`frac-times`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr`
2×	`rem-sqrt-square`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 170

Calls

4 calls:

24.0ms	(+ (/ 1 b) (/ 1 a))
43.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
39.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
228.0ms	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+ (/ 1 b) (/ 1 a))
73.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
74.0ms	(sqrt (+ (/ 1 b) (/ 1 a)))
24.0ms	(* (sqrt (+ (/ 1 b) (/ 1 a))) (sqrt (+ (/ 1 b) (/ 1 a))))

simplify1.1s

Counts: 182 → 182

prune412.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (sqrt (+ (/ 1 b) (/ 1 a))))
0.2b	(cbrt (sqrt (+ (/ 1 b) (/ 1 a))))
0.2b	(* (* (* (cbrt (sqrt (+ (/ 1 b) (/ 1 a)))) (cbrt (sqrt (+ (/ 1 b) (/ 1 a))))) (cbrt (sqrt (+ (/ 1 b) (/ 1 a))))) (sqrt (+ (/ 1 b) (/ 1 a))))
0.3b	(* (cbrt (sqrt (+ (/ 1 b) (/ 1 a)))) (cbrt (sqrt (+ (/ 1 b) (/ 1 a)))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

798×	`sqrt-div`
606×	`cbrt-div`
522×	`frac-times`
266×	`flip3-+` `frac-add` `flip-+`
174×	`associate-*l/`
146×	`*-un-lft-identity`
134×	`cbrt-prod`
118×	`sqrt-prod`
81×	`distribute-lft-out`
66×	`associate-*r/`
60×	`div-inv`
58×	`add-sqr-sqrt`
42×	`times-frac`
39×	`swap-sqr`
37×	`add-cube-cbrt`
29×	`associate-r`
22×	`pow1`
20×	`pow1/3`
17×	`associate-l`
15×	`add-exp-log`
10×	`pow-prod-up`
9×	`add-cbrt-cube` `unswap-sqr`
8×	`pow-prod-down`
7×	`prod-exp` `cbrt-unprod`
4×	`pow-sqr` `add-log-exp`
3×	`pow-plus`
2×	`*-commutative`
1×	`pow2`

Counts

4 → 451

Calls

4 calls:

20.0ms	(cbrt (sqrt (+ (/ 1 b) (/ 1 a))))
33.0ms	(cbrt (sqrt (+ (/ 1 b) (/ 1 a))))
1.2s	(* (* (* (cbrt (sqrt (+ (/ 1 b) (/ 1 a)))) (cbrt (sqrt (+ (/ 1 b) (/ 1 a))))) (cbrt (sqrt (+ (/ 1 b) (/ 1 a))))) (sqrt (+ (/ 1 b) (/ 1 a))))
227.0ms	(* (cbrt (sqrt (+ (/ 1 b) (/ 1 a)))) (cbrt (sqrt (+ (/ 1 b) (/ 1 a)))))

series443.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (sqrt (+ (/ 1 b) (/ 1 a))))
143.0ms	(cbrt (sqrt (+ (/ 1 b) (/ 1 a))))
22.0ms	(* (* (* (cbrt (sqrt (+ (/ 1 b) (/ 1 a)))) (cbrt (sqrt (+ (/ 1 b) (/ 1 a))))) (cbrt (sqrt (+ (/ 1 b) (/ 1 a))))) (sqrt (+ (/ 1 b) (/ 1 a))))
154.0ms	(* (cbrt (sqrt (+ (/ 1 b) (/ 1 a)))) (cbrt (sqrt (+ (/ 1 b) (/ 1 a)))))

simplify2.5s

Counts: 463 → 463

prune1.7s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes164.0ms

Accuracy

0% (3.1b remaining)

Error of 3.2b against oracle of 0.1b and baseline of 3.2b

bsearch0.0ms

simplify13.0ms

end0.0ms

sample15.4s

Algorithm

intervals

Results

5.1s	2038×	body	10240	exit
4.4s	2599×	body	2560	valid
3.9s	3347×	body	1280	valid
772.0ms	1108×	body	640	valid
467.0ms	10039×	pre	80	true
151.0ms	407×	body	320	valid
44.0ms	422×	body	80	valid
26.0ms	118×	body	160	valid