Details

sample84.0ms

Algorithm

intervals

Results

34.0ms	87×	body	1280	valid
15.0ms	29×	body	320	valid
11.0ms	190×	body	80	valid
10.0ms	37×	body	640	valid
1.0ms	11×	body	160	valid

simplify6.6s

Counts: 1 → 1

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize18.0ms

Local error

Found 2 expressions with local error:

3.1b	(- (exp (* a x)) 1)
0.0b	(exp (* a x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-log-exp`
5×	`*-un-lft-identity`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `difference-of-squares`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `difference-of-sqr-1` `flip--` `distribute-lft-out--` `rem-exp-log`

Counts

2 → 28

Calls

2 calls:

Slowest

12.0ms	(- (exp (* a x)) 1)
4.0ms	(exp (* a x))

series80.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

52.0ms	(- (exp (* a x)) 1)
27.0ms	(exp (* a x))

simplify1.2s

Counts: 34 → 34

prune420.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

11.8b	(+ (+ (* (* 1/2 (* a x)) (* a x)) (* a x)) (* (* (* (* a x) (* a x)) (* a x)) 1/6))
3.2b	(+ (* (* 1/2 (* a x)) (* a x)) (* a x))
0.2b	(* (* 1/2 (* a x)) (* a x))
0.2b	(* (* a x) (* a x))

rewrite505.0ms

Algorithm

rewrite-expression-head

Rules

64×	`pow1`
37×	`add-cbrt-cube` `add-exp-log`
32×	`pow-prod-down`
23×	`prod-exp` `cbrt-unprod`
11×	`add-log-exp`
4×	`add-sqr-sqrt` `sum-log` `*-un-lft-identity` `pow-sqr` `pow-prod-up` `add-cube-cbrt` `insert-posit16`
2×	`+-commutative` `flip3-+` `pow-plus` `associate-r` `associate-l` `*-commutative` `flip-+`
1×	`pow2` `associate-+l+` `distribute-lft1-in` `swap-sqr`

Counts

4 → 91

Calls

4 calls:

Slowest

373.0ms	(+ (+ (* (* 1/2 (* a x)) (* a x)) (* a x)) (* (* (* (* a x) (* a x)) (* a x)) 1/6))
59.0ms	(* (* 1/2 (* a x)) (* a x))
49.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (* a x))
24.0ms	(* (* a x) (* a x))

series326.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

141.0ms	(+ (+ (* (* 1/2 (* a x)) (* a x)) (* a x)) (* (* (* (* a x) (* a x)) (* a x)) 1/6))
95.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (* a x))
45.0ms	(* (* a x) (* a x))
44.0ms	(* (* 1/2 (* a x)) (* a x))

simplify497.0ms

Counts: 103 → 103

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

11.8b	(+ (* (+ (* 1/2 (* a x)) 1) (* a x)) (* (* (* (* a x) (* a x)) (* a x)) 1/6))
0.2b	(* (* a x) (* a x))
0.1b	(* (* (* (* a x) (* a x)) (* a x)) 1/6)
0.1b	(* (* (* a x) (* a x)) (* a x))

rewrite670.0ms

Algorithm

rewrite-expression-head

Rules

251×	`pow1`
128×	`pow-prod-down`
110×	`add-cbrt-cube` `add-exp-log`
81×	`prod-exp` `cbrt-unprod`
38×	`pow-prod-up`
19×	`pow-plus`
16×	`pow-sqr`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`pow2` `insert-posit16`
3×	`associate-l` `*-commutative`
1×	`+-commutative` `sum-log` `flip3-+` `swap-sqr` `pow3` `flip-+`

Counts

4 → 168

Calls

4 calls:

Slowest

415.0ms	(* (* (* (* a x) (* a x)) (* a x)) 1/6)
120.0ms	(* (* (* a x) (* a x)) (* a x))
97.0ms	(+ (* (+ (* 1/2 (* a x)) 1) (* a x)) (* (* (* (* a x) (* a x)) (* a x)) 1/6))
31.0ms	(* (* a x) (* a x))

series382.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

128.0ms	(+ (* (+ (* 1/2 (* a x)) 1) (* a x)) (* (* (* (* a x) (* a x)) (* a x)) 1/6))
107.0ms	(* (* (* (* a x) (* a x)) (* a x)) 1/6)
89.0ms	(* (* (* a x) (* a x)) (* a x))
58.0ms	(* (* a x) (* a x))

simplify5.9s

Counts: 180 → 180

prune2.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (* (exp (* a x)) (exp (* a x))) 1)
0.0b	(/ (- (* (exp (* a x)) (exp (* a x))) 1) (+ (exp (* a x)) 1))
0.0b	(* (exp (* a x)) (exp (* a x)))
0.0b	(+ (exp (* a x)) 1)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
24×	`times-frac`
20×	`add-cube-cbrt` `add-log-exp`
12×	`exp-prod` `exp-to-pow` `difference-of-squares`
11×	`pow1`
8×	`add-cbrt-cube` `distribute-lft-out`
6×	`difference-of-sqr-1` `add-exp-log` `associate-/l*`
5×	`pow-prod-down` `pow-sqr` `pow-prod-up`
4×	`associate-/r*` `insert-posit16`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`pow2` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

Slowest

44.0ms	(/ (- (* (exp (* a x)) (exp (* a x))) 1) (+ (exp (* a x)) 1))
29.0ms	(- (* (exp (* a x)) (exp (* a x))) 1)
21.0ms	(* (exp (* a x)) (exp (* a x)))
18.0ms	(+ (exp (* a x)) 1)

series193.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

84.0ms	(/ (- (* (exp (* a x)) (exp (* a x))) 1) (+ (exp (* a x)) 1))
65.0ms	(- (* (exp (* a x)) (exp (* a x))) 1)
24.0ms	(+ (exp (* a x)) 1)
20.0ms	(* (exp (* a x)) (exp (* a x)))

simplify2.0s

Counts: 131 → 131

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes358.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 20.9b

bsearch42.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.2s	2696×	body	1280	valid
775.0ms	5376×	body	80	valid
390.0ms	1350×	body	640	valid
138.0ms	744×	body	320	valid
83.0ms	426×	body	160	valid