Details

sample610.0ms

Algorithm

intervals

Results

222.0ms	97×	body	2560	valid
176.0ms	89×	body	1280	valid
125.0ms	63×	body	10240	exit
36.0ms	43×	body	640	valid
16.0ms	319×	pre	80	true
4.0ms	8×	body	320	valid
3.0ms	16×	body	80	valid
1.0ms	3×	body	160	valid

simplify411.0ms

Calls

1 calls:

Slowest

411.0ms

(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize46.0ms

Local error

Found 4 expressions with local error:

39.0b	(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
0.5b	(* (expm1 (* eps b)) (expm1 (* eps a)))
0.1b	(* (expm1 (* (+ a b) eps)) eps)
0.0b	(expm1 (* (+ a b) eps))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `associate-l`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`associate-r`
2×	`cbrt-undiv` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`expm1-log1p` `clear-num` `associate-/r` `frac-2neg` `times-frac` `pow-prod-down` `div-inv` `associate-/l` `expm1-udef`

Calls

4 calls:

Slowest

9.0ms	(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
5.0ms	(* (expm1 (* eps b)) (expm1 (* eps a)))
3.0ms	(* (expm1 (* (+ a b) eps)) eps)
0.0ms	(expm1 (* (+ a b) eps))

series654.0ms

Calls

4 calls:

Slowest

478.0ms	(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
95.0ms	(* (expm1 (* (+ a b) eps)) eps)
45.0ms	(* (expm1 (* eps b)) (expm1 (* eps a)))
36.0ms	(expm1 (* (+ a b) eps))

simplify3.8s

Calls

31 calls:

Slowest

762.0ms	(/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (* (expm1 (* eps b)) (expm1 (* eps a))) (* (expm1 (* eps b)) (expm1 (* eps a)))) (* (expm1 (* eps b)) (expm1 (* eps a)))))
650.0ms	(/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))))
407.0ms	(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
332.0ms	(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
312.0ms	(+ (* 1/2 (* (pow a 2) (pow eps 2))) (+ (* eps b) (* a eps)))

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity`
5×	`div-inv`
4×	`fma-def` `distribute-lft-out`
3×	`add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt`
1×	`expm1-log1p-u` `pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `insert-posit16` `log1p-expm1-u`

Calls

1 calls:

Slowest

9.0ms

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

series12.0ms

Calls

1 calls:

Slowest

12.0ms

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

simplify124.0ms

Calls

12 calls:

Slowest

15.0ms	(+ (/ 1 a) (/ 1 b))
14.0ms	(+ (/ 1 b) (/ 1 a))
13.0ms	(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
12.0ms	(* (exp (/ 1 a)) (exp (/ 1 b)))
11.0ms	(+ (/ 1 a) (/ 1 b))

prune154.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

29.6b	(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b)))
17.2b	(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b))) (expm1 (* eps a)))
0.1b	(* (expm1 (* (+ a b) eps)) eps)
0.0b	(expm1 (* (+ a b) eps))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
23×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/l*`
6×	`associate-/r*` `div-inv`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`associate-l`
2×	`clear-num` `frac-2neg`
1×	`expm1-log1p` `*-commutative` `expm1-udef` `associate-/l/`

Calls

4 calls:

Slowest

19.0ms	(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b))) (expm1 (* eps a)))
8.0ms	(* (expm1 (* (+ a b) eps)) eps)
8.0ms	(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b)))
0.0ms	(expm1 (* (+ a b) eps))

series657.0ms

Calls

4 calls:

Slowest

434.0ms	(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b))) (expm1 (* eps a)))
94.0ms	(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b)))
91.0ms	(* (expm1 (* (+ a b) eps)) eps)
39.0ms	(expm1 (* (+ a b) eps))

simplify5.7s

Calls

83 calls:

Slowest

413.0ms	(/ (/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b)))) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a))))
322.0ms	(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
303.0ms	(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
293.0ms	(- (log (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps b)))) (log (expm1 (* eps a))))
241.0ms	(+ (* 1/2 (/ (* (pow a 2) (pow eps 2)) b)) (+ (/ (* a eps) b) eps))

prune1.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes133.0ms

Accuracy

-4.5% (3.6b remaining)

Error of 3.6b against oracle of 0.0b and baseline of 3.4b

bsearch189.0ms

end0.0ms

sample19.9s

Algorithm

intervals

Results

7.0s	2616×	body	2560	valid
6.0s	3370×	body	1280	valid
4.5s	1967×	body	10240	exit
1.0s	1086×	body	640	valid
702.0ms	9969×	pre	80	true
271.0ms	351×	body	320	valid
81.0ms	460×	body	80	valid
44.0ms	119×	body	160	valid