Details

Time bar (total: 14.9s)

sample186.0ms

Algorithm
intervals
Results
62.0ms1208×body80nan
26.0ms394×body80valid
3.0ms6×body640valid
3.0ms15×body320valid
1.0ms7×body160valid
1.0ms1×body1280valid

simplify38.0ms

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: 2.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b
(* y (- (log z) t))
0.8b
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.2b
(log (- 1.0 z))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
72×prod-diff
66×add-sqr-sqrt
65×*-un-lft-identity
56×add-cube-cbrt
53×distribute-rgt-in distribute-lft-in
38×associate-+r+
34×associate-+l+
27×log-prod
26×pow1
22×associate--l+
20×log-pow
10×associate-*r/
9×add-log-exp
7×add-exp-log
6×sub-neg flip3-- associate-*r* add-cbrt-cube flip--
5×distribute-lft-out--
4×expm1-log1p-u frac-add log1p-expm1-u difference-of-squares
3×exp-prod associate-*l*
2×log-div sum-log rem-exp-log
1×+-commutative fma-def flip3-+ rem-log-exp exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 182
Calls
4 calls:
42.0ms
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
29.0ms
(* y (- (log z) t))
39.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.0ms
(log (- 1.0 z))

series460.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
69.0ms
(* y (- (log z) t))
191.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
46.0ms
(log (- 1.0 z))

simplify94.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
09041913
135011501
250011500

prune674.0ms

Pruning

5 alts after pruning (5 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))))
0.1b
(* y (- (log z) t))
0.8b
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite1.2s

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:
743.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
180.0ms
(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
31.0ms
(* y (- (log z) t))
274.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series617.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
186.0ms
(exp (+ (* y (- (log z) t)) (* 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)))

simplify140.0ms

Algorithm
egg-herbie
Counts
312 → 312
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
010915982
144694426
250014420

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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))
0.0b
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.3b
(fma 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
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:
12.0ms
(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
748.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
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))))
0.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series778.0ms

Counts
4 → 12
Calls
4 calls:
237.0ms
(* x (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
107.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
184.0ms
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
250.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify80.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05703486
120922505
250032306

prune509.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log add-cbrt-cube
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r*
5×add-log-exp
4×expm1-log1p-u sqrt-prod fma-udef log1p-expm1-u
3×exp-prod pow-prod-down prod-exp cbrt-unprod
2×exp-sum
1×associate-*l* *-commutative rem-exp-log
Counts
4 → 58
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))))
48.0ms
(* (* x (sqrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))) (sqrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
0.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series937.0ms

Counts
4 → 12
Calls
4 calls:
185.0ms
(exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
245.0ms
(* (* x (sqrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))) (sqrt (exp (fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))))
257.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
250.0ms
(fma y (- (log z) t) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify106.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
03051479
110501186
242051178
350011178

prune414.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes366.0ms

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
03765
13765

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.2s41860×body80nan
743.0ms12573×body80valid
123.0ms369×body640valid
86.0ms424×body320valid
57.0ms81×body1280valid
39.0ms285×body160valid