Details

Time bar (total: 10.7s)

sample187.0ms

Algorithm
intervals
Results
79.0ms1378×body80nan
26.0ms421×body80valid
4.0ms11×body640valid
3.0ms14×body320valid
2.0ms3×body1280valid
2.0ms12×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03110
16210
213710
334410
4115510
5500110

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.0b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (- (log (- 1.0 z)) b))
0.2b
(* y (- (log z) t))
0.3b
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.3b
(log (- 1.0 z))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
103×*-un-lft-identity
98×add-sqr-sqrt
96×prod-diff
76×add-cube-cbrt
72×distribute-rgt-in distribute-lft-in
38×associate-+r+
37×log-prod
36×pow1
34×associate-+l+
32×associate--l+
28×log-pow
18×associate-*r*
15×fma-def
13×associate-*l*
12×associate-*r/
11×distribute-lft-out--
9×add-exp-log
8×sub-neg add-cbrt-cube difference-of-squares
7×flip3-- flip--
6×add-log-exp
4×expm1-log1p-u frac-add log1p-expm1-u distribute-lft-out
3×*-commutative unswap-sqr
2×log-div pow-prod-down prod-exp cbrt-unprod
1×+-commutative flip3-+ rem-log-exp sum-log flip-+
Counts
4 → 248
Calls
4 calls:
10.0ms
(* a (- (log (- 1.0 z)) b))
9.0ms
(* y (- (log z) t))
35.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms
(log (- 1.0 z))

series392.0ms

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)))
49.0ms
(log (- 1.0 z))

simplify110.0ms

Algorithm
egg-herbie
Counts
260 → 260
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
09482433
138541841
250011838

prune573.0ms

Filtered
260 candidates to 151 candidates (41.9%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New2582260
Fresh000
Picked101
Done000
Total2592261

Merged error: 0.0b

Counts
261 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log z) t)
0.0b
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.2b
(* y (- (log z) t))
0.3b
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
624×*-un-lft-identity
340×prod-diff
206×add-sqr-sqrt
188×distribute-rgt-in distribute-lft-in
181×associate-*l*
172×distribute-lft-out
168×add-cube-cbrt
159×associate--l+
154×associate-+r+
147×distribute-lft-out--
120×pow1
112×log-pow
34×associate-+l+
27×log-prod associate-*r*
16×difference-of-squares
15×fma-def
13×sub-neg
12×associate-*r/
9×add-log-exp
8×add-exp-log add-cbrt-cube
7×flip3-- flip--
4×expm1-log1p-u fma-neg frac-add log1p-expm1-u
3×*-commutative unswap-sqr
2×diff-log pow-prod-down prod-exp cbrt-unprod
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 508
Calls
4 calls:
5.0ms
(- (log z) t)
93.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
8.0ms
(* y (- (log z) t))
131.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (log z) t)
106.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
75.0ms
(* y (- (log z) t))
251.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify184.0ms

Algorithm
egg-herbie
Counts
520 → 520
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
010269233
141476802
250016794

prune1.2s

Filtered
520 candidates to 175 candidates (66.3%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New5191520
Fresh101
Picked101
Done000
Total5211522

Merged error: 0.0b

Counts
522 → 1

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log z) t)
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)
0.1b
(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))
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)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×*-un-lft-identity
15×add-cube-cbrt
12×prod-diff
11×pow1
7×add-log-exp
6×add-exp-log add-cbrt-cube
5×log-pow
4×expm1-log1p-u fma-neg log1p-expm1-u
3×log-prod associate-*r* associate-*l* associate--l+
2×diff-log fma-udef distribute-lft-out--
1×sub-neg flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod difference-of-squares unswap-sqr
Counts
4 → 77
Calls
4 calls:
5.0ms
(- (log z) t)
4.0ms
(* (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)
1.0ms
(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))
1.0ms
(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)))

series1.3s

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (log z) t)
425.0ms
(* (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)
536.0ms
(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))
294.0ms
(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)))

simplify47.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03671604
111611291
250021281

prune476.0ms

Filtered
89 candidates to 66 candidates (25.8%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New89089
Fresh000
Picked011
Done000
Total89190

Merged error: 0.0b

Counts
90 → 1

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04834
15534
25534

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.2s40684×body80nan
771.0ms12571×body80valid
125.0ms364×body640valid
85.0ms399×body320valid
41.0ms57×body1280valid
41.0ms316×body160valid