Details

Time bar (total: 24.9s)

sample179.0ms

Algorithm
intervals
Results
65.0ms1208×body80nan
23.0ms394×body80valid
3.0ms15×body320valid
2.0ms6×body640valid
1.0ms1×body1280valid
1.0ms7×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03010
15810
212910
331810
4107310
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))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
27×log-prod
24×add-sqr-sqrt
23×*-un-lft-identity
22×associate--l+
17×distribute-rgt-in distribute-lft-in
14×add-cube-cbrt associate-+r+
10×associate-+l+ associate-*r/
9×add-log-exp
8×pow1
7×add-exp-log
6×sub-neg flip3-- associate-*r* add-cbrt-cube flip--
5×distribute-lft-out--
4×frac-add difference-of-squares
3×exp-prod associate-*l*
2×log-div sum-log log-pow rem-exp-log
1×+-commutative flip3-+ rem-log-exp exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 101
Calls
4 calls:
40.0ms
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
24.0ms
(* y (- (log z) t))
28.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.0ms
(log (- 1.0 z))

series450.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
72.0ms
(* y (- (log z) t))
190.0ms
(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
42.0ms
(log (- 1.0 z))

simplify72.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0630971
12443914
25001902

prune415.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

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)))

rewrite945.0ms

Algorithm
rewrite-expression-head
Rules
44×associate--l+
27×*-un-lft-identity
25×add-sqr-sqrt
24×distribute-rgt-in log-prod distribute-lft-in
17×add-cube-cbrt
14×associate-+r+
13×associate-*r*
12×sub-neg associate-*r/
10×pow1 associate-+l+
9×add-log-exp
8×add-exp-log add-cbrt-cube
7×distribute-lft-out--
6×flip3-- associate-*l* flip--
4×frac-add
3×exp-prod
2×pow-prod-down prod-exp sum-log log-pow *-commutative cbrt-unprod rem-exp-log difference-of-squares unswap-sqr
1×+-commutative flip3-+ exp-sum flip-+
Counts
4 → 123
Calls
4 calls:
597.0ms
(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
165.0ms
(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
25.0ms
(* y (- (log z) t))
153.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series606.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* 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))))
76.0ms
(* y (- (log z) t))
247.0ms
(+ (* 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
135 → 135
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06451743
128101639
250021630

prune552.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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)))
0.8b
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
0.8b
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite482.0ms

Algorithm
rewrite-expression-head
Rules
72×associate--l+
42×associate-+r+ log-prod
41×distribute-rgt-in distribute-lft-in
30×associate-+l+
26×associate-*r/
24×add-sqr-sqrt
23×*-un-lft-identity
20×add-cube-cbrt sub-neg
13×flip3-- flip--
12×frac-add
10×add-log-exp
7×pow1
6×add-exp-log associate-*r* add-cbrt-cube
3×+-commutative flip3-+ associate-*l* sum-log flip-+
2×distribute-lft-out--
1×pow-prod-down prod-exp log-pow *-commutative cbrt-unprod difference-of-squares unswap-sqr
Counts
4 → 150
Calls
4 calls:
25.0ms
(* y (- (log z) t))
148.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
150.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
153.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series834.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* y (- (log z) t))
254.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
253.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
250.0ms
(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify72.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04942671
120472556
250032551

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

4.6b
(* (+ (log z) t) (* a (- (* (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (* b b))))
5.4b
(* a (- (* (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (* b b)))
6.3b
(* y (- (* (log z) (log z)) (* t t)))
18.3b
(/ (+ (* (* y (- (* (log z) (log z)) (* t t))) (+ (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)) (* (+ (log z) t) (* a (- (* (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (* b b))))) (* (+ (log z) t) (+ (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
142×associate-*r/
108×associate--l+
104×distribute-rgt-in distribute-lft-in
72×frac-times
66×associate-/l/
64×frac-add
58×flip3-+ flip-+
53×flip3-- flip--
48×log-prod
36×associate-*l/
31×add-sqr-sqrt
30×*-un-lft-identity
27×add-cube-cbrt
20×sub-neg
18×add-exp-log add-cbrt-cube
14×pow1
11×associate-*l*
9×associate-*r*
8×associate-/r/
6×prod-exp cbrt-unprod
5×pow-prod-down
4×add-log-exp
3×times-frac *-commutative associate-/l*
2×cbrt-undiv div-exp distribute-lft-out difference-of-squares unswap-sqr
1×frac-2neg clear-num associate-/r* log-pow div-inv
Counts
4 → 253
Calls
4 calls:
356.0ms
(* (+ (log z) t) (* a (- (* (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (* b b))))
315.0ms
(* a (- (* (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (* b b)))
31.0ms
(* y (- (* (log z) (log z)) (* t t)))
861.0ms
(/ (+ (* (* y (- (* (log z) (log z)) (* t t))) (+ (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)) (* (+ (log z) t) (* a (- (* (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (* b b))))) (* (+ (log z) t) (+ (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series8.3s

Counts
4 → 12
Calls
4 calls:
487.0ms
(* (+ (log z) t) (* a (- (* (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (* b b))))
556.0ms
(* a (- (* (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (* b b)))
148.0ms
(* y (- (* (log z) (log z)) (* t t)))
7.1s
(/ (+ (* (* y (- (* (log z) (log z)) (* t t))) (+ (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)) (* (+ (log z) t) (* a (- (* (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (* b b))))) (* (+ (log z) t) (+ (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify143.0ms

Algorithm
egg-herbie
Counts
265 → 265
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0215710482
1500210091

prune2.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes267.0ms

Accuracy

41.6% (7.9b remaining)

Error of 8.0b against oracle of 0.1b and baseline of 13.6b

bsearch333.0ms

Steps
ItersRangePoint
7
2.7730850617529893e-08
3.935477650172371e-06
5.487655812586682e-08
9
-1.6326032099926483e-150
-3.588803724731159e-156
-5.1996384838491834e-152

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0101110
1112110
2124110
3134110
4134110

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.2s41860×body80nan
741.0ms12573×body80valid
124.0ms369×body640valid
85.0ms424×body320valid
56.0ms81×body1280valid
35.0ms285×body160valid