Details

Time bar (total: 32.3s)

sample101.0ms

Algorithm
intervals
Results
72.0ms98×body10240exit
17.0ms256×body80valid

simplify4.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
4.0ms
(/ (exp a) (+ (exp a) (exp b)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize37.0ms

Local error

Found 2 expressions with local error:

1.0b
(/ (exp a) (+ (exp a) (exp b)))
0.0b
(+ (exp a) (exp b))

rewrite32.0ms

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
23.0ms
(/ (exp a) (+ (exp a) (exp b)))
8.0ms
(+ (exp a) (exp b))

series413.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
361.0ms
(+ (exp a) (exp b))
52.0ms
(/ (exp a) (+ (exp a) (exp b)))

simplify1.2s

Counts
44 → 60
Calls
44 calls:
Slowest
406.0ms
(/ (* (* (exp a) (exp a)) (exp a)) (* (* (+ (exp a) (exp b)) (+ (exp a) (exp b))) (+ (exp a) (exp b))))
134.0ms
(+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))
94.0ms
(- (+ (* 1/4 a) 1/2) (* 1/4 b))
64.0ms
(/ (* (cbrt (exp a)) (cbrt (exp a))) (* (cbrt (+ (exp a) (exp b))) (cbrt (+ (exp a) (exp b)))))
32.0ms
(/ (* (cbrt (exp a)) (cbrt (exp a))) (sqrt (+ (exp a) (exp b))))

prune573.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize37.0ms

Local error

Found 4 expressions with local error:

3.9b
(log (+ (exp a) (exp b)))
0.8b
(- a (log (+ (exp a) (exp b))))
0.0b
(exp (- a (log (+ (exp a) (exp b)))))
0.0b
(+ (exp a) (exp b))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
27×add-sqr-sqrt
24×prod-diff
23×add-cube-cbrt
16×exp-sum
13×pow1
9×log-pow add-log-exp
8×log-prod
6×log-div exp-prod
5×add-exp-log
4×expm1-log1p-u flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u associate--r+ distribute-lft-out-- associate--r-
3×fma-def fma-neg distribute-lft-out
2×sub-neg diff-log difference-of-squares rem-exp-log
1×+-commutative sum-log flip3-- exp-diff rem-log-exp flip--
Counts
4 → 110
Calls
4 calls:
Slowest
16.0ms
(+ (exp a) (exp b))
15.0ms
(log (+ (exp a) (exp b)))
14.0ms
(exp (- a (log (+ (exp a) (exp b)))))
13.0ms
(- a (log (+ (exp a) (exp b))))

series166.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
55.0ms
(- a (log (+ (exp a) (exp b))))
54.0ms
(exp (- a (log (+ (exp a) (exp b)))))
36.0ms
(log (+ (exp a) (exp b)))
21.0ms
(+ (exp a) (exp b))

simplify7.0s

Counts
85 → 122
Calls
85 calls:
Slowest
596.0ms
(exp (fma (* (cbrt a) (cbrt a)) (cbrt a) (- (* (cbrt (log (+ (exp a) (exp b)))) (* (cbrt (log (+ (exp a) (exp b)))) (cbrt (log (+ (exp a) (exp b)))))))))
411.0ms
(exp (- a (log (+ (pow (exp a) 3) (pow (exp b) 3)))))
380.0ms
(exp (fma (sqrt a) (sqrt a) (- (* (cbrt (log (+ (exp a) (exp b)))) (* (cbrt (log (+ (exp a) (exp b)))) (cbrt (log (+ (exp a) (exp b)))))))))
354.0ms
(exp (fma 1 a (- (* (cbrt (log (+ (exp a) (exp b)))) (* (cbrt (log (+ (exp a) (exp b)))) (cbrt (log (+ (exp a) (exp b)))))))))
301.0ms
(- (+ (exp (- (log 2))) (* 1/2 (* a (exp (- (log 2)))))) (* 1/2 (* (exp (- (log 2))) b)))

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (sqrt (exp a)) (+ (exp a) (exp b)))
0.7b
(* (sqrt (exp a)) (/ (sqrt (exp a)) (+ (exp a) (exp b))))
0.0b
(sqrt (exp a))
0.0b
(sqrt (exp a))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
60×add-sqr-sqrt
52×times-frac
42×add-cube-cbrt
41×sqrt-prod
30×associate-*r*
13×distribute-lft-out
11×add-cbrt-cube add-exp-log
8×pow1 sqrt-pow1
6×exp-prod associate-*l* associate-/l* unswap-sqr
4×expm1-log1p-u associate-/r* associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv rem-sqrt-square flip3-+ pow1/2 div-exp prod-exp cbrt-unprod flip-+ div-inv
1×clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
4 → 148
Calls
4 calls:
Slowest
67.0ms
(* (sqrt (exp a)) (/ (sqrt (exp a)) (+ (exp a) (exp b))))
37.0ms
(/ (sqrt (exp a)) (+ (exp a) (exp b)))
4.0ms
(sqrt (exp a))
4.0ms
(sqrt (exp a))

series164.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
88.0ms
(/ (sqrt (exp a)) (+ (exp a) (exp b)))
41.0ms
(* (sqrt (exp a)) (/ (sqrt (exp a)) (+ (exp a) (exp b))))
22.0ms
(sqrt (exp a))
13.0ms
(sqrt (exp a))

simplify2.9s

Counts
142 → 160
Calls
142 calls:
Slowest
191.0ms
(* (* (* (sqrt (exp a)) (sqrt (exp a))) (sqrt (exp a))) (/ (* (* (sqrt (exp a)) (sqrt (exp a))) (sqrt (exp a))) (* (* (+ (exp a) (exp b)) (+ (exp a) (exp b))) (+ (exp a) (exp b)))))
185.0ms
(* (* (* (sqrt (exp a)) (sqrt (exp a))) (sqrt (exp a))) (* (* (/ (sqrt (exp a)) (+ (exp a) (exp b))) (/ (sqrt (exp a)) (+ (exp a) (exp b)))) (/ (sqrt (exp a)) (+ (exp a) (exp b)))))
161.0ms
(- 1/2 (+ (* 1/16 (pow a 2)) (* 1/4 b)))
149.0ms
(+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))
140.0ms
(/ (* (* (sqrt (exp a)) (sqrt (exp a))) (sqrt (exp a))) (* (* (+ (exp a) (exp b)) (+ (exp a) (exp b))) (+ (exp a) (exp b))))

prune1.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
44×prod-diff associate--l+
30×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
28×exp-sum
22×distribute-rgt-in distribute-lft-in
6×sub-neg
5×add-log-exp
4×pow1
3×log-prod exp-prod associate--r+
2×expm1-log1p-u add-cbrt-cube diff-log add-exp-log log-pow insert-posit16 log1p-expm1-u rem-exp-log
1×flip3-- exp-diff fma-neg flip--
Counts
2 → 89
Calls
2 calls:
Slowest
39.0ms
(exp (- (* 1/2 (- a b)) (log 2)))
15.0ms
(- (* 1/2 (- a b)) (log 2))

series115.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
63.0ms
(exp (- (* 1/2 (- a b)) (log 2)))
52.0ms
(- (* 1/2 (- a b)) (log 2))

simplify10.3s

Counts
74 → 95
Calls
74 calls:
Slowest
414.0ms
(exp (* 1/2 (fma 1 a (- (* (cbrt b) (* (cbrt b) (cbrt b)))))))
394.0ms
(- (+ (exp (- (log 2))) (* 1/2 (* a (exp (- (log 2)))))) (* 1/2 (* (exp (- (log 2))) b)))
390.0ms
(exp (* 1/2 (fma (sqrt a) (sqrt a) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))))
331.0ms
(exp (* (fma (* (cbrt a) (cbrt a)) (cbrt a) (- (* (sqrt b) (sqrt b)))) 1/2))
318.0ms
(exp (* 1/2 (fma (* (cbrt a) (cbrt a)) (cbrt a) (- (* b 1)))))

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

regimes190.0ms

Accuracy

0% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 0.6b

bsearch2.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
3.1s3460×body10240exit
986.0ms8000×body80valid