Details

sample112.0ms

Algorithm

intervals

Results

80.0ms	115×	body	10240	exit
17.0ms	256×	body	80	valid

simplify10.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

10.0ms

(/ (exp a) (+ (exp a) (exp b)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize21.0ms

Local error

Found 2 expressions with local error:

0.8b	(/ (exp a) (+ (exp a) (exp b)))
0.0b	(+ (exp a) (exp b))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `times-frac` `add-cube-cbrt`
5×	`distribute-lft-out`
4×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`fma-def` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `pow1` `flip3-+` `associate-/r/` `flip-+` `insert-posit16` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 54

Calls

2 calls:

Slowest

48.0ms	(/ (exp a) (+ (exp a) (exp b)))
11.0ms	(+ (exp a) (exp b))

series59.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

37.0ms	(/ (exp a) (+ (exp a) (exp b)))
21.0ms	(+ (exp a) (exp b))

simplify1.1s

Counts

44 → 60

Calls

44 calls:

Slowest

357.0ms	(/ (* (* (exp a) (exp a)) (exp a)) (* (* (+ (exp a) (exp b)) (+ (exp a) (exp b))) (+ (exp a) (exp b))))
132.0ms	(+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))
84.0ms	(- (+ (* 1/4 a) 1/2) (* 1/4 b))
55.0ms	(/ (* (cbrt (exp a)) (cbrt (exp a))) (* (cbrt (+ (exp a) (exp b))) (cbrt (+ (exp a) (exp b)))))
28.0ms	(/ (* (cbrt (exp a)) (cbrt (exp a))) (sqrt (+ (exp a) (exp b))))

prune604.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (exp a) (+ (exp a) (exp b)))
0.0b	(+ (exp a) (exp b))
0.0b	(log (exp (/ (exp a) (+ (exp a) (exp b)))))
0.0b	(exp (/ (exp a) (+ (exp a) (exp b))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
36×	`exp-prod` `times-frac`
31×	`add-sqr-sqrt` `add-cube-cbrt`
19×	`log-pow`
11×	`distribute-lft-out`
7×	`add-log-exp`
6×	`add-cbrt-cube` `associate-/r/`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `associate-/r*` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `fma-def` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `rem-log-exp` `rem-exp-log`

Counts

4 → 116

Calls

4 calls:

Slowest

37.0ms	(exp (/ (exp a) (+ (exp a) (exp b))))
30.0ms	(/ (exp a) (+ (exp a) (exp b)))
30.0ms	(log (exp (/ (exp a) (+ (exp a) (exp b)))))
16.0ms	(+ (exp a) (exp b))

series210.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

61.0ms	(/ (exp a) (+ (exp a) (exp b)))
59.0ms	(exp (/ (exp a) (+ (exp a) (exp b))))
53.0ms	(log (exp (/ (exp a) (+ (exp a) (exp b)))))
36.0ms	(+ (exp a) (exp b))

simplify2.8s

Counts

91 → 128

Calls

91 calls:

Slowest

343.0ms	(/ (* (* (exp a) (exp a)) (exp a)) (* (* (+ (exp a) (exp b)) (+ (exp a) (exp b))) (+ (exp a) (exp b))))
340.0ms	(- (+ (* 1/4 (* a (exp 1/2))) (exp 1/2)) (* 1/4 (* b (exp 1/2))))
283.0ms	(exp (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))))
192.0ms	(exp (/ (exp a) (- (* (exp a) (exp a)) (* (exp b) (exp b)))))
152.0ms	(+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (exp a) (+ (exp a) (exp b)))
0.0b	(+ (exp a) (exp b))
0.0b	(expm1 (log1p (log (exp (/ (exp a) (+ (exp a) (exp b)))))))
0.0b	(log1p (log (exp (/ (exp a) (+ (exp a) (exp b))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
6×	`add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u` `add-exp-log` `distribute-lft-out`
4×	`pow1` `associate-/r*` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `log1p-udef` `expm1-log1p` `clear-num` `sum-log` `frac-2neg` `div-exp` `log1p-expm1` `div-inv` `expm1-udef`

Counts

4 → 78

Calls

4 calls:

Slowest

15.0ms	(/ (exp a) (+ (exp a) (exp b)))
10.0ms	(+ (exp a) (exp b))
1.0ms	(expm1 (log1p (log (exp (/ (exp a) (+ (exp a) (exp b)))))))
1.0ms	(log1p (log (exp (/ (exp a) (+ (exp a) (exp b))))))

series259.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

88.0ms	(expm1 (log1p (log (exp (/ (exp a) (+ (exp a) (exp b)))))))
70.0ms	(log1p (log (exp (/ (exp a) (+ (exp a) (exp b))))))
66.0ms	(/ (exp a) (+ (exp a) (exp b)))
34.0ms	(+ (exp a) (exp b))

simplify1.2s

Counts

52 → 90

Calls

52 calls:

Slowest

391.0ms	(/ (* (* (exp a) (exp a)) (exp a)) (* (* (+ (exp a) (exp b)) (+ (exp a) (exp b))) (+ (exp a) (exp b))))
149.0ms	(+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))
101.0ms	(- (+ (* 1/6 a) (log 3/2)) (* 1/6 b))
84.0ms	(- (+ (* 1/4 a) 1/2) (* 1/4 b))
61.0ms	(- (+ (* 1/4 a) 1/2) (* 1/4 b))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (- a b) (exp 1/2))
0.0b	(log (fma 1/4 (* (- a b) (exp 1/2)) (exp 1/2)))
0.0b	(fma 1/4 (* (- a b) (exp 1/2)) (exp 1/2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`pow1` `add-cube-cbrt`
5×	`add-cbrt-cube` `associate-l` `add-exp-log`
3×	`expm1-log1p-u` `log-prod` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-*l/`
1×	`flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

Slowest

42.0ms	(* (- a b) (exp 1/2))
2.0ms	(log (fma 1/4 (* (- a b) (exp 1/2)) (exp 1/2)))
0.0ms	(fma 1/4 (* (- a b) (exp 1/2)) (exp 1/2))

series402.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

187.0ms	(log (fma 1/4 (* (- a b) (exp 1/2)) (exp 1/2)))
111.0ms	(* (- a b) (exp 1/2))
104.0ms	(fma 1/4 (* (- a b) (exp 1/2)) (exp 1/2))

simplify3.4s

Counts

26 → 60

Calls

26 calls:

Slowest

376.0ms	(log (* (cbrt (fma 1/4 (* (- a b) (exp 1/2)) (exp 1/2))) (cbrt (fma 1/4 (* (- a b) (exp 1/2)) (exp 1/2)))))
367.0ms	(- (+ (* 1/4 (* a (exp 1/2))) (exp 1/2)) (* 1/4 (* b (exp 1/2))))
334.0ms	(- (+ (* 1/4 (* a (exp 1/2))) (exp 1/2)) (* 1/4 (* b (exp 1/2))))
314.0ms	(- (+ (* 1/4 (* a (exp 1/2))) (exp 1/2)) (* 1/4 (* b (exp 1/2))))
308.0ms	(log (sqrt (fma 1/4 (* (- a b) (exp 1/2)) (exp 1/2))))

prune564.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

regimes257.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.6b and baseline of 0.6b

bsearch1.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

3.2s	3541×	body	10240	exit
674.0ms	8000×	body	80	valid