Details

Time bar (total: 17.3s)

sample169.0ms

Algorithm
intervals
Results
69.0ms1245×body80nan
24.0ms395×body80valid
7.0ms20×body640valid
2.0ms9×body320valid
2.0ms2×body1280valid
0.0ms3×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03110
16210
213710
334410
4115510
5500110

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (- (log (- 1.0 z)) b))
0.1b
(* y (- (log z) t))
1.0b
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.9b
(log (- 1.0 z))

rewrite56.0ms

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:
10.0ms
(* a (- (log (- 1.0 z)) b))
8.0ms
(* y (- (log z) t))
20.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms
(log (- 1.0 z))

series370.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* a (- (log (- 1.0 z)) b))
69.0ms
(* y (- (log z) t))
180.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
47.0ms
(log (- 1.0 z))

simplify109.0ms

Algorithm
egg-herbie
Counts
242 → 242
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
09592405
139101813
250011810

prune697.0ms

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

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
168×prod-diff
156×*-un-lft-identity
144×add-sqr-sqrt
110×add-cube-cbrt
108×distribute-rgt-in distribute-lft-in
92×associate--l+
74×associate-+r+
48×pow1
38×log-pow
34×associate-+l+
31×distribute-lft-out--
24×log-prod
17×associate-*r*
14×difference-of-squares
12×sub-neg associate-*r/
10×add-cbrt-cube
9×add-exp-log associate-*l*
6×flip3-- flip-- add-log-exp
4×expm1-log1p-u frac-add log1p-expm1-u
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative fma-def flip3-+ exp-sum sum-log flip-+
Counts
4 → 306
Calls
4 calls:
22.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
27.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
8.0ms
(* y (- (log z) t))
31.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series631.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
101.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
70.0ms
(* y (- (log z) t))
238.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify162.0ms

Algorithm
egg-herbie
Counts
318 → 318
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
011196148
146764554
250014552

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* y (- (log z) t))
0.2b
(pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3)
0.5b
(fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))
31.3b
(cbrt (pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
31×*-un-lft-identity
28×add-cube-cbrt
24×prod-diff
17×distribute-rgt-in distribute-lft-in
14×pow1
12×cbrt-prod
7×add-exp-log log-pow add-cbrt-cube
6×unpow-prod-down log-prod cube-prod associate-*r* associate--l+
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*l*
2×cube-mult sub-neg unpow3 associate-*r/ distribute-lft-out-- sqr-pow
1×pow-to-exp flip3-- pow-pow pow1/3 pow-prod-down pow-exp prod-exp *-commutative flip-- rem-cbrt-cube cbrt-unprod fma-udef rem-cube-cbrt difference-of-squares unswap-sqr
Counts
4 → 117
Calls
4 calls:
9.0ms
(* y (- (log z) t))
2.0ms
(pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3)
1.0ms
(fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))
2.0ms
(cbrt (pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3))

series6.6s

Counts
4 → 12
Calls
4 calls:
71.0ms
(* y (- (log z) t))
6.1s
(pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3)
215.0ms
(fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))
220.0ms
(cbrt (pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3))

simplify66.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04651703
119521427
250031414

prune472.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.0b
(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
0.0b
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.6b
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
61×add-sqr-sqrt
60×prod-diff
43×add-cube-cbrt
40×associate--l+
37×distribute-rgt-in distribute-lft-in
21×pow1
17×distribute-lft-out--
13×log-pow
11×associate-*r*
8×add-cbrt-cube
7×add-exp-log difference-of-squares
6×log-prod associate-*l*
5×add-log-exp
4×expm1-log1p-u sub-neg log1p-expm1-u
3×exp-prod fma-udef
2×associate-*r/ exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- rem-exp-log
Counts
4 → 145
Calls
4 calls:
2.0ms
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
5.0ms
(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
24.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
1.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series717.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
212.0ms
(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
98.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
240.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify78.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05703486
120922505
250032306

prune466.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes153.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03016
13016

end0.0ms

sample5.1s

Algorithm
intervals
Results
2.2s40219×body80nan
764.0ms12447×body80valid
140.0ms403×body640valid
77.0ms364×body320valid
60.0ms82×body1280valid
35.0ms268×body160valid