Details

Time bar (total: 19.7s)

sample244.0ms

Algorithm
intervals
Results
116.0ms1336×body80nan
41.0ms402×body80valid
6.0ms10×body640valid
4.0ms13×body320valid
2.0ms2×body1280valid
2.0ms9×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03110
16210
213710
334410
4115510
5500110

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.2b
(* y (- (log z) t))
0.3b
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
8.6b
(log (- 1.0 z))

rewrite68.0ms

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:
17.0ms
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
15.0ms
(* y (- (log z) t))
21.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.0ms
(log (- 1.0 z))

series444.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
71.0ms
(* y (- (log z) t))
185.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
48.0ms
(log (- 1.0 z))

simplify295.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
09041913
135011501
250011500

prune665.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite348.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
128×*-un-lft-identity
108×prod-diff
107×add-cube-cbrt
80×times-frac
74×associate-+r+ associate-*r*
71×distribute-rgt-in distribute-lft-in
56×unpow-prod-down
52×associate--l+
34×associate-+l+
33×pow1
29×add-exp-log
25×log-pow
24×unpow2 sqr-pow
18×log-prod unswap-sqr
14×distribute-lft-out--
11×associate-*r/ prod-exp add-cbrt-cube
9×div-exp add-log-exp
8×sub-neg
7×difference-of-squares
6×pow-to-exp associate-*l* pow-exp
5×flip3-- flip--
4×expm1-log1p-u frac-add log1p-expm1-u
3×exp-prod cbrt-unprod
2×pow-prod-down sum-log *-commutative rem-exp-log
1×cbrt-undiv +-commutative fma-def flip3-+ exp-sum flip-+ div-inv
Counts
4 → 312
Calls
4 calls:
28.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
108.0ms
(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
18.0ms
(* y (- (log z) t))
175.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series524.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
166.0ms
(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
67.0ms
(* y (- (log z) t))
239.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify70.0ms

Algorithm
egg-herbie
Counts
324 → 324
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
014814058
150013215

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
0.1b
(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)) (* a (fma (- b) 1 (* b 1)))))
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)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
73×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
39×add-cube-cbrt *-un-lft-identity
27×add-exp-log
24×unpow2 sqr-pow
17×unswap-sqr
10×prod-exp
9×div-exp add-cbrt-cube
7×add-log-exp
6×pow1 pow-to-exp pow-exp
4×expm1-log1p-u log1p-expm1-u
3×exp-prod associate-*l*
2×cbrt-unprod fma-udef rem-exp-log
1×cbrt-undiv associate-*r/ exp-sum pow-prod-down sum-log *-commutative div-inv
Counts
4 → 147
Calls
4 calls:
26.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
8.0ms
(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)) (* a (fma (- b) 1 (* 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))
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)))

series2.8s

Counts
4 → 12
Calls
4 calls:
49.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
1.9s
(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)) (* a (fma (- b) 1 (* b 1)))))
522.0ms
(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))
283.0ms
(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)))

simplify81.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
07402014
133761649
250011646

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
0.0b
(pow E (+ (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)) (* a (fma (- b) 1 (* b 1)))))
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)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
74×add-sqr-sqrt
68×associate-*r*
59×unpow-prod-down
40×add-cube-cbrt *-un-lft-identity
28×add-exp-log
25×sqr-pow
24×unpow2
17×unswap-sqr
10×prod-exp
9×div-exp add-cbrt-cube
8×pow-exp
7×pow1 pow-to-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*l*
2×cbrt-unprod fma-udef
1×cbrt-undiv unpow-prod-up e-exp-1 pow-pow associate-*r/ pow-prod-down *-commutative div-inv
Counts
4 → 153
Calls
4 calls:
26.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
6.0ms
(pow E (+ (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)) (* a (fma (- b) 1 (* 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))
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)))

series2.8s

Counts
4 → 12
Calls
4 calls:
55.0ms
(* 1/2 (/ (pow z 2) (pow 1.0 2)))
1.9s
(pow E (+ (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)) (* a (fma (- b) 1 (* b 1)))))
514.0ms
(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))
288.0ms
(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)))

simplify84.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
07902274
132932000
250011991

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes284.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04664
14664

end0.0ms

sample7.2s

Algorithm
intervals
Results
3.4s40735×body80nan
1.3s12496×body80valid
197.0ms381×body640valid
129.0ms378×body320valid
72.0ms78×body1280valid
51.0ms240×body160valid