Details

Time bar (total: 15.1s)

sample203.0ms

Algorithm
intervals
Results
83.0ms1402×body80nan
27.0ms436×body80valid
4.0ms12×body640valid
4.0ms5×body1280valid
4.0ms16×body320valid
2.0ms14×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03110
16210
213710
334410
4115510
5500110

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (- (log (- 1.0 z)) b))
0.2b
(* y (- (log z) t))
1.5b
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.1b
(log (- 1.0 z))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
96×prod-diff
91×add-sqr-sqrt
89×*-un-lft-identity
73×add-cube-cbrt
72×distribute-rgt-in distribute-lft-in
38×associate-+r+
37×log-prod
35×pow1
34×associate-+l+
32×associate--l+
27×log-pow
12×associate-*r/ associate-*r*
9×add-exp-log distribute-lft-out--
8×sub-neg add-cbrt-cube
7×flip3-- flip-- difference-of-squares
6×associate-*l* add-log-exp
4×expm1-log1p-u frac-add log1p-expm1-u
2×log-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative fma-def flip3-+ rem-log-exp sum-log flip-+
Counts
4 → 230
Calls
4 calls:
21.0ms
(* a (- (log (- 1.0 z)) b))
15.0ms
(* y (- (log z) t))
20.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms
(log (- 1.0 z))

series386.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* a (- (log (- 1.0 z)) b))
73.0ms
(* y (- (log z) t))
192.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
44.0ms
(log (- 1.0 z))

simplify109.0ms

Algorithm
egg-herbie
Counts
242 → 242
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
09592405
139101813
250011810

prune736.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.0b
(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.2b
(* y (- (log z) t))
1.5b
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite770.0ms

Algorithm
rewrite-expression-head
Rules
168×prod-diff
155×*-un-lft-identity
141×add-sqr-sqrt
109×add-cube-cbrt
108×distribute-rgt-in distribute-lft-in
92×associate--l+
74×associate-+r+
46×pow1
38×log-pow
34×associate-+l+
31×distribute-lft-out--
24×log-prod
14×difference-of-squares
13×associate-*r*
12×sub-neg associate-*r/
9×add-log-exp
8×add-exp-log add-cbrt-cube
6×flip3-- associate-*l* flip--
4×expm1-log1p-u frac-add log1p-expm1-u
3×exp-prod
2×pow-prod-down prod-exp sum-log *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×+-commutative fma-def flip3-+ exp-sum flip-+
Counts
4 → 300
Calls
4 calls:
463.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
103.0ms
(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
16.0ms
(* y (- (log z) t))
166.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series592.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
170.0ms
(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
74.0ms
(* y (- (log z) t))
241.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify152.0ms

Algorithm
egg-herbie
Counts
312 → 312
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
010915982
144694426
250014420

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a)
0.0b
(exp (+ (fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a)) (* (fma (- b) 1 (* b 1)) a)))
0.1b
(fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1)))
0.3b
(fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity add-log-exp
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×exp-prod associate-*r* associate-*l*
2×fma-udef rem-exp-log
1×exp-sum pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
4 → 55
Calls
4 calls:
3.0ms
(* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a)
5.0ms
(exp (+ (fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a)) (* (fma (- b) 1 (* b 1)) a)))
0.0ms
(fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1)))
0.0ms
(fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a))

series3.3s

Counts
4 → 12
Calls
4 calls:
424.0ms
(* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a)
2.0s
(exp (+ (fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a)) (* (fma (- b) 1 (* b 1)) a)))
287.0ms
(fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1)))
527.0ms
(fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a))

simplify125.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 3 (101.0ms)

IterNodesCost
03111950
19711656
243991645
350011644

prune515.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (+ (* (log z) y) (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- t)))))
0.0b
(+ (* (log z) y) (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- t))))
0.3b
(* (log z) y)
1.3b
(fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- t)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u associate-*l* log1p-expm1-u
3×exp-prod associate-*r*
2×sum-log fma-udef rem-exp-log
1×+-commutative associate-+r+ fma-def flip3-+ exp-sum pow-prod-down prod-exp log-pow *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 61
Calls
4 calls:
8.0ms
(exp (+ (* (log z) y) (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- t)))))
3.0ms
(+ (* (log z) y) (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- t))))
3.0ms
(* (log z) y)
0.0ms
(fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- t)))

series635.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(exp (+ (* (log z) y) (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- t)))))
226.0ms
(+ (* (log z) y) (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- t))))
59.0ms
(* (log z) y)
184.0ms
(fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- t)))

simplify121.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0280824
1905755
24013749
35001749

prune557.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes160.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04834
15534
25534

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.3s40775×body80nan
795.0ms12543×body80valid
124.0ms356×body640valid
82.0ms374×body320valid
41.0ms55×body1280valid
37.0ms272×body160valid