Details

Time bar (total: 9.0s)

sample103.0ms

Algorithm
intervals
Results
39.0ms786×body80nan
10.0ms177×body80valid
8.0ms24×body640valid
6.0ms29×body320valid
4.0ms5×body1280valid
3.0ms22×body160valid

simplify68.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0279
1578
21368
33128
47098
516298
635648
750018

prune10.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 7.5b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- z 1.0) (log (- 1.0 y)))
0.0b
(- (* (- z 1.0) (log (- 1.0 y))) t)
0.1b
(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
6.7b
(log (- 1.0 y))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×log-prod
24×*-un-lft-identity
12×add-cube-cbrt
10×distribute-rgt-in distribute-lft-in associate--l+
8×pow1
7×add-exp-log
6×add-cbrt-cube distribute-lft-out-- add-log-exp difference-of-squares
5×associate-*l*
4×expm1-log1p-u associate-*r* log1p-expm1-u
3×flip3-- prod-diff flip--
2×log-div associate-*l/ log-pow
1×sub-neg fma-neg diff-log rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 91
Calls
4 calls:
12.0ms
(* (- z 1.0) (log (- 1.0 y)))
10.0ms
(- (* (- z 1.0) (log (- 1.0 y))) t)
1.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
4.0ms
(log (- 1.0 y))

series405.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (- z 1.0) (log (- 1.0 y)))
102.0ms
(- (* (- z 1.0) (log (- 1.0 y))) t)
198.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
59.0ms
(log (- 1.0 y))

simplify50.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0486752
11665669
25001653

prune329.0ms

Filtered
103 candidates to 80 candidates (77.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New976103
Fresh000
Picked101
Done000
Total986104

Merged error: 0.1b

Counts
104 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt
80×times-frac
78×*-un-lft-identity
74×associate-*r*
73×add-cube-cbrt
56×unpow-prod-down
51×prod-diff
46×associate--l+
34×distribute-rgt-in distribute-lft-in
29×add-exp-log
24×unpow2 sqr-pow
21×pow1
18×unswap-sqr
13×log-pow
12×log-prod
11×prod-exp add-cbrt-cube
9×div-exp
8×associate-*l*
7×flip3-- flip--
6×pow-to-exp pow-exp add-log-exp
5×sub-neg
4×expm1-log1p-u frac-times log1p-expm1-u
3×associate-*r/ cbrt-unprod distribute-lft-out--
2×pow-prod-down associate-*l/ *-commutative difference-of-squares
1×cbrt-undiv fma-neg diff-log fma-udef div-inv
Counts
4 → 241
Calls
4 calls:
22.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
16.0ms
(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
14.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
1.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series483.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
144.0ms
(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
69.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
217.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify133.0ms

Algorithm
egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010533734
146722536
250012536

prune876.0ms

Filtered
253 candidates to 157 candidates (62.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2512253
Fresh145
Picked011
Done000
Total2527259

Merged error: 0.1b

Counts
259 → 7

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
71×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
37×add-cube-cbrt *-un-lft-identity
26×add-exp-log
24×unpow2 sqr-pow
17×unswap-sqr
10×prod-exp
9×div-exp
8×add-cbrt-cube
6×pow-to-exp pow-exp
5×pow1
3×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×cbrt-unprod fma-udef
1×cbrt-undiv associate-*r/ pow-prod-down *-commutative div-inv
Counts
3 → 132
Calls
3 calls:
21.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
1.0ms
(fma (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
1.0ms
(fma (log y) (- x 1.0) (fma (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

series338.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
109.0ms
(fma (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))
175.0ms
(fma (log y) (- x 1.0) (fma (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

simplify64.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
06341102
13061865
25002862

prune514.0ms

Filtered
141 candidates to 94 candidates (66.7%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1410141
Fresh055
Picked011
Done011
Total1417148

Merged error: 0.1b

Counts
148 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (log y) (- x 1.0) (- (* (- z 1.0) (+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))) t))
11.8b
(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
13.8b
(log (+ (sqrt 1.0) (sqrt y)))
13.9b
(log (- (sqrt 1.0) (sqrt y)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
28×log-prod
25×add-sqr-sqrt
16×sqrt-prod
11×pow1
9×add-cube-cbrt associate-+r+
8×log-div distribute-lft-out difference-of-squares
7×log-pow
6×add-exp-log
5×associate-+l+
4×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u distribute-lft-out-- add-log-exp
3×flip3-+ flip-+
2×associate-+l- associate-+r- flip3-- rem-log-exp flip--
1×+-commutative sum-log fma-udef
Counts
4 → 89
Calls
4 calls:
1.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))) t))
15.0ms
(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
6.0ms
(log (+ (sqrt 1.0) (sqrt y)))
8.0ms
(log (- (sqrt 1.0) (sqrt y)))

series1.6s

Counts
4 → 12
Calls
4 calls:
1.0s
(fma (log y) (- x 1.0) (- (* (- z 1.0) (+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))) t))
301.0ms
(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
142.0ms
(log (+ (sqrt 1.0) (sqrt y)))
149.0ms
(log (- (sqrt 1.0) (sqrt y)))

simplify105.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
03971132
111011025
24427988
35001985

prune377.0ms

Filtered
101 candidates to 76 candidates (75.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1001101
Fresh134
Picked101
Done022
Total1026108

Merged error: 0.1b

Counts
108 → 6

regimes245.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02414
12414

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s24631×body80nan
337.0ms5978×body80valid
240.0ms762×body640valid
142.0ms230×body1280valid
123.0ms647×body320valid
50.0ms421×body160valid